libMesh::ContinuationSystem Class Reference

This class inherits from the FEMSystem. More...

#include <continuation_system.h>

Inheritance diagram for libMesh::ContinuationSystem:

Public Types
enum	Predictor { Euler, AB2, Invalid_Predictor }
	The code provides the ability to select from different predictor schemes for getting the initial guess for the solution at the next point on the solution arc. More...
typedef ContinuationSystem	sys_type
	The type of system. More...
typedef FEMSystem	Parent
	The type of the parent. More...
typedef bool(TimeSolver::*	TimeSolverResPtr) (bool, DiffContext &)
	Syntax sugar to make numerical_jacobian() declaration easier. More...
typedef Number(*	ValueFunctionPointer) (const Point &p, const Parameters &Parameters, const std::string &sys_name, const std::string &unknown_name)
	Projects arbitrary functions onto the current solution. More...
typedef Gradient(*	GradientFunctionPointer) (const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name)
typedef std::map< std::string, std::unique_ptr< NumericVector< Number > >, std::less<> >::iterator	vectors_iterator
	Vector iterator typedefs. More...
typedef std::map< std::string, std::unique_ptr< NumericVector< Number > >, std::less<> >::const_iterator	const_vectors_iterator
typedef std::map< std::string, std::unique_ptr< SparseMatrix< Number > >, std::less<> >::iterator	matrices_iterator
	Matrix iterator typedefs. More...
typedef std::map< std::string, std::unique_ptr< SparseMatrix< Number > >, std::less<> >::const_iterator	const_matrices_iterator

Public Member Functions
	ContinuationSystem (EquationSystems &es, const std::string &name, const unsigned int number)
	Constructor. More...
	ContinuationSystem (const ContinuationSystem &)=delete
	Special functions. More...
ContinuationSystem &	operator= (const ContinuationSystem &)=delete
	ContinuationSystem (ContinuationSystem &&)=delete
ContinuationSystem &	operator= (ContinuationSystem &&)=delete
virtual	~ContinuationSystem ()
virtual void	clear () override
	Clear all the data structures associated with the system. More...
virtual void	solve () override
	Perform a standard "solve" of the system, without doing continuation. More...
void	continuation_solve ()
	Perform a continuation solve of the system. More...
void	advance_arcstep ()
	Call this function after a continuation solve to compute the tangent and get the next initial guess. More...
void	set_max_arclength_stepsize (Real maxds)
	Sets (initializes) the max-allowable ds value and the current ds value. More...
void	save_current_solution ()
	Stores the current solution and continuation parameter (as "previous_u" and "old_continuation_parameter") for later referral. More...
virtual void	assembly (bool get_residual, bool get_jacobian, bool apply_heterogeneous_constraints=false, bool apply_no_constraints=false) override
	Prepares matrix or rhs for matrix assembly. More...
void	mesh_position_get ()
	Tells the FEMSystem to set the degree of freedom coefficients which should correspond to mesh nodal coordinates. More...
void	mesh_position_set ()
	Tells the FEMSystem to set the mesh nodal coordinates which should correspond to degree of freedom coefficients. More...
virtual std::unique_ptr< DiffContext >	build_context () override
	Builds a FEMContext object with enough information to do evaluations on each element. More...
virtual void	init_context (DiffContext &) override
virtual void	postprocess () override
	Runs a postprocessing loop over all elements, and if postprocess_sides is true over all sides. More...
virtual void	assemble_qoi (const QoISet &indices=QoISet()) override
	Runs a qoi assembly loop over all elements, and if assemble_qoi_sides is true over all sides. More...
virtual void	assemble_qoi_derivative (const QoISet &qoi_indices=QoISet(), bool include_liftfunc=true, bool apply_constraints=true) override
	Runs a qoi derivative assembly loop over all elements, and if assemble_qoi_sides is true over all sides. More...
Real	numerical_jacobian_h_for_var (unsigned int var_num) const
	If numerical_jacobian_h_for_var(var_num) is changed from its default value (numerical_jacobian_h), the FEMSystem will perturb solution vector entries for variable var_num by that amount when calculating finite differences with respect to that variable. More...
void	set_numerical_jacobian_h_for_var (unsigned int var_num, Real new_h)
void	numerical_jacobian (TimeSolverResPtr res, FEMContext &context) const
	Uses the results of multiple res calls to numerically differentiate the corresponding jacobian. More...
void	numerical_elem_jacobian (FEMContext &context) const
	Uses the results of multiple element_residual() calls to numerically differentiate the corresponding jacobian on an element. More...
void	numerical_side_jacobian (FEMContext &context) const
	Uses the results of multiple side_residual() calls to numerically differentiate the corresponding jacobian on an element's side. More...
void	numerical_nonlocal_jacobian (FEMContext &context) const
	Uses the results of multiple side_residual() calls to numerically differentiate the corresponding jacobian on nonlocal DoFs. More...
virtual void	reinit () override
	Reinitializes the member data fields associated with the system, so that, e.g., assemble() may be used. More...
virtual void	assemble () override
	Prepares matrix and rhs for matrix assembly. More...
virtual LinearSolver< Number > *	get_linear_solver () const override
virtual std::pair< unsigned int, Real >	get_linear_solve_parameters () const override
virtual std::pair< unsigned int, Real >	adjoint_solve (const QoISet &qoi_indices=QoISet()) override
	This function sets the _is_adjoint boolean member of TimeSolver to true and then calls the adjoint_solve in implicit system. More...
virtual std::unique_ptr< DifferentiablePhysics >	clone_physics () override
	We don't allow systems to be attached to each other. More...
virtual std::unique_ptr< DifferentiableQoI >	clone () override
	We don't allow systems to be attached to each other. More...
const DifferentiablePhysics *	get_physics () const
DifferentiablePhysics *	get_physics ()
void	attach_physics (DifferentiablePhysics *physics_in)
	Attach external Physics object. More...
void	swap_physics (DifferentiablePhysics *&swap_physics)
	Swap current physics object with external object. More...
void	push_physics (DifferentiablePhysics &new_physics)
	Push a clone of a new physics object onto our stack, overriding the current physics until the new physics is popped off again (or until something else is pushed on top of it). More...
void	pop_physics ()
	Pop a physics object off of our stack. More...
const DifferentiableQoI *	get_qoi () const
DifferentiableQoI *	get_qoi ()
void	attach_qoi (DifferentiableQoI *qoi_in)
	Attach external QoI object. More...
void	set_time_solver (std::unique_ptr< TimeSolver > _time_solver)
	Sets the time_solver FIXME: This code is a little dangerous as it transfers ownership from the TimeSolver creator to this class. More...
TimeSolver &	get_time_solver ()
const TimeSolver &	get_time_solver () const
	Non-const version of the above. More...
virtual void	element_postprocess (DiffContext &)
	Does any work that needs to be done on elem in a postprocessing loop. More...
virtual void	side_postprocess (DiffContext &)
	Does any work that needs to be done on side of elem in a postprocessing loop. More...
unsigned int	get_second_order_dot_var (unsigned int var) const
	For a given second order (in time) variable var, this method will return the index to the corresponding "dot" variable. More...
bool	have_first_order_scalar_vars () const
	Check for any first order vars that are also belong to FEFamily::SCALAR. More...
bool	have_second_order_scalar_vars () const
	Check for any second order vars that are also belong to FEFamily::SCALAR. More...
virtual void	set_constrain_in_solver (bool enable)
	set_constrain_in_solver to false to apply constraints only via residual terms in the systems to be solved. More...
virtual bool	get_constrain_in_solver ()
sys_type &	system ()
virtual void	disable_cache () override
	Avoids use of any cached data that might affect any solve result. More...
virtual std::string	system_type () const override
virtual void	release_linear_solver (LinearSolver< Number > *) const
	Currently a no-op. More...
virtual void	assemble_residual_derivatives (const ParameterVector &parameters) override
	Residual parameter derivative function. More...
virtual std::pair< unsigned int, Real >	sensitivity_solve (const ParameterVector &parameters) override
	Assembles & solves the linear system(s) (dR/du)*u_p = -dR/dp, for those parameters contained within parameters. More...
virtual std::pair< unsigned int, Real >	weighted_sensitivity_solve (const ParameterVector &parameters, const ParameterVector &weights) override
	Assembles & solves the linear system(s) (dR/du)*u_w = sum(w_p*-dR/dp), for those parameters p contained within parameters weighted by the values w_p found within weights. More...
virtual std::pair< unsigned int, Real >	weighted_sensitivity_adjoint_solve (const ParameterVector &parameters, const ParameterVector &weights, const QoISet &qoi_indices=QoISet()) override
	Assembles & solves the linear system(s) (dR/du)^T*z_w = sum(w_p*(d^2q/dudp - d^2R/dudp*z)), for those parameters p contained within parameters, weighted by the values w_p found within weights. More...
virtual void	adjoint_qoi_parameter_sensitivity (const QoISet &qoi_indices, const ParameterVector &parameters, SensitivityData &sensitivities) override
	Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j]. More...
virtual void	forward_qoi_parameter_sensitivity (const QoISet &qoi_indices, const ParameterVector &parameters, SensitivityData &sensitivities) override
	Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j]. More...
virtual void	qoi_parameter_hessian (const QoISet &qoi_indices, const ParameterVector &parameters, SensitivityData &hessian) override
	For each of the system's quantities of interest q in qoi[qoi_indices], and for a vector of parameters p, the parameter sensitivity Hessian H_ij is defined as H_ij = (d^2 q)/(d p_i d p_j) This Hessian is the output of this method, where for each q_i, H_jk is stored in hessian.second_derivative(i,j,k). More...
virtual void	qoi_parameter_hessian_vector_product (const QoISet &qoi_indices, const ParameterVector &parameters, const ParameterVector &vector, SensitivityData &product) override
	For each of the system's quantities of interest q in qoi[qoi_indices], and for a vector of parameters p, the parameter sensitivity Hessian H_ij is defined as H_ij = (d^2 q)/(d p_i d p_j) The Hessian-vector product, for a vector v_k in parameter space, is S_j = H_jk v_k This product is the output of this method, where for each q_i, S_j is stored in sensitivities[i][j]. More...
const SparseMatrix< Number > &	get_system_matrix () const
SparseMatrix< Number > &	get_system_matrix ()
virtual void	create_static_condensation () override
	Request that static condensation be performed for this system. More...
StaticCondensation &	get_static_condensation ()
void	init ()
	Initializes degrees of freedom on the current mesh. More...
virtual void	reinit_constraints ()
	Reinitializes the constraints for this system. More...
virtual void	reinit_mesh ()
	Reinitializes the system with a new mesh. More...
bool	is_initialized () const
virtual void	update ()
	Update the local values to reflect the solution on neighboring processors. More...
virtual void	restrict_solve_to (const SystemSubset *subset, const SubsetSolveMode subset_solve_mode=SUBSET_ZERO)
	After calling this method, any solve will be restricted to the given subdomain. More...
bool	is_adjoint_already_solved () const
	Accessor for the adjoint_already_solved boolean. More...
void	set_adjoint_already_solved (bool setting)
	Setter for the adjoint_already_solved boolean. More...
virtual void	qoi_parameter_sensitivity (const QoISet &qoi_indices, const ParameterVector &parameters, SensitivityData &sensitivities)
	Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j]. More...
virtual bool	compare (const System &other_system, const Real threshold, const bool verbose) const
const std::string &	name () const
void	project_solution (FunctionBase< Number > *f, FunctionBase< Gradient > *g=nullptr) const
	Projects arbitrary functions onto the current solution. More...
void	project_solution (FEMFunctionBase< Number > *f, FEMFunctionBase< Gradient > *g=nullptr) const
	Projects arbitrary functions onto the current solution. More...
void	project_solution (ValueFunctionPointer fptr, GradientFunctionPointer gptr, const Parameters &parameters) const
	This method projects an arbitrary function onto the solution via L2 projections and nodal interpolations on each element. More...
void	project_vector (NumericVector< Number > &new_vector, FunctionBase< Number > *f, FunctionBase< Gradient > *g=nullptr, int is_adjoint=-1) const
	Projects arbitrary functions onto a vector of degree of freedom values for the current system. More...
void	project_vector (NumericVector< Number > &new_vector, FEMFunctionBase< Number > *f, FEMFunctionBase< Gradient > *g=nullptr, int is_adjoint=-1) const
	Projects arbitrary functions onto a vector of degree of freedom values for the current system. More...
void	project_vector (ValueFunctionPointer fptr, GradientFunctionPointer gptr, const Parameters &parameters, NumericVector< Number > &new_vector, int is_adjoint=-1) const
	Projects arbitrary functions onto a vector of degree of freedom values for the current system. More...
void	boundary_project_solution (const std::set< boundary_id_type > &b, const std::vector< unsigned int > &variables, FunctionBase< Number > *f, FunctionBase< Gradient > *g=nullptr)
	Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system. More...
void	boundary_project_solution (const std::set< boundary_id_type > &b, const std::vector< unsigned int > &variables, ValueFunctionPointer fptr, GradientFunctionPointer gptr, const Parameters &parameters)
	Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system. More...
void	boundary_project_vector (const std::set< boundary_id_type > &b, const std::vector< unsigned int > &variables, NumericVector< Number > &new_vector, FunctionBase< Number > *f, FunctionBase< Gradient > *g=nullptr, int is_adjoint=-1) const
	Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system. More...
void	boundary_project_vector (const std::set< boundary_id_type > &b, const std::vector< unsigned int > &variables, ValueFunctionPointer fptr, GradientFunctionPointer gptr, const Parameters &parameters, NumericVector< Number > &new_vector, int is_adjoint=-1) const
	Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system. More...
unsigned int	number () const
void	update_global_solution (std::vector< Number > &global_soln) const
	Fill the input vector global_soln so that it contains the global solution on all processors. More...
void	update_global_solution (std::vector< Number > &global_soln, const processor_id_type dest_proc) const
	Fill the input vector global_soln so that it contains the global solution on processor dest_proc. More...
const MeshBase &	get_mesh () const
MeshBase &	get_mesh ()
const DofMap &	get_dof_map () const
DofMap &	get_dof_map ()
const EquationSystems &	get_equation_systems () const
EquationSystems &	get_equation_systems ()
bool	active () const
void	activate ()
	Activates the system. More...
void	deactivate ()
	Deactivates the system. More...
void	set_basic_system_only ()
	Sets the system to be "basic only": i.e. More...
vectors_iterator	vectors_begin ()
	Beginning of vectors container. More...
const_vectors_iterator	vectors_begin () const
	Beginning of vectors container. More...
vectors_iterator	vectors_end ()
	End of vectors container. More...
const_vectors_iterator	vectors_end () const
	End of vectors container. More...
matrices_iterator	matrices_begin ()
	Beginning of matrices container. More...
const_matrices_iterator	matrices_begin () const
	Beginning of matrices container. More...
matrices_iterator	matrices_end ()
	End of matrices container. More...
const_matrices_iterator	matrices_end () const
	End of matrices container. More...
NumericVector< Number > &	add_vector (std::string_view vec_name, const bool projections=true, const ParallelType type=PARALLEL)
	Adds the additional vector vec_name to this system. More...
void	remove_vector (std::string_view vec_name)
	Removes the additional vector vec_name from this system. More...
bool &	project_solution_on_reinit (void)
	Tells the System whether or not to project the solution vector onto new grids when the system is reinitialized. More...
bool	have_vector (std::string_view vec_name) const
const NumericVector< Number > *	request_vector (std::string_view vec_name) const
NumericVector< Number > *	request_vector (std::string_view vec_name)
const NumericVector< Number > *	request_vector (const unsigned int vec_num) const
NumericVector< Number > *	request_vector (const unsigned int vec_num)
const NumericVector< Number > &	get_vector (std::string_view vec_name) const
NumericVector< Number > &	get_vector (std::string_view vec_name)
const NumericVector< Number > &	get_vector (const unsigned int vec_num) const
NumericVector< Number > &	get_vector (const unsigned int vec_num)
const std::string &	vector_name (const unsigned int vec_num) const
const std::string &	vector_name (const NumericVector< Number > &vec_reference) const
void	set_vector_as_adjoint (const std::string &vec_name, int qoi_num)
	Allows one to set the QoI index controlling whether the vector identified by vec_name represents a solution from the adjoint (qoi_num >= 0) or primal (qoi_num == -1) space. More...
int	vector_is_adjoint (std::string_view vec_name) const
void	set_vector_preservation (const std::string &vec_name, bool preserve)
	Allows one to set the boolean controlling whether the vector identified by vec_name should be "preserved": projected to new meshes, saved, etc. More...
bool	vector_preservation (std::string_view vec_name) const
NumericVector< Number > &	add_adjoint_solution (unsigned int i=0)
NumericVector< Number > &	get_adjoint_solution (unsigned int i=0)
const NumericVector< Number > &	get_adjoint_solution (unsigned int i=0) const
NumericVector< Number > &	add_sensitivity_solution (unsigned int i=0)
NumericVector< Number > &	get_sensitivity_solution (unsigned int i=0)
const NumericVector< Number > &	get_sensitivity_solution (unsigned int i=0) const
NumericVector< Number > &	add_weighted_sensitivity_adjoint_solution (unsigned int i=0)
NumericVector< Number > &	get_weighted_sensitivity_adjoint_solution (unsigned int i=0)
const NumericVector< Number > &	get_weighted_sensitivity_adjoint_solution (unsigned int i=0) const
NumericVector< Number > &	add_weighted_sensitivity_solution ()
NumericVector< Number > &	get_weighted_sensitivity_solution ()
const NumericVector< Number > &	get_weighted_sensitivity_solution () const
NumericVector< Number > &	add_adjoint_rhs (unsigned int i=0)
NumericVector< Number > &	get_adjoint_rhs (unsigned int i=0)
const NumericVector< Number > &	get_adjoint_rhs (unsigned int i=0) const
NumericVector< Number > &	add_sensitivity_rhs (unsigned int i=0)
NumericVector< Number > &	get_sensitivity_rhs (unsigned int i=0)
const NumericVector< Number > &	get_sensitivity_rhs (unsigned int i=0) const
unsigned int	n_vectors () const
unsigned int	n_matrices () const
unsigned int	n_vars () const
unsigned int	n_variable_groups () const
unsigned int	n_components () const
dof_id_type	n_dofs () const
dof_id_type	n_active_dofs () const
dof_id_type	n_constrained_dofs () const
dof_id_type	n_local_constrained_dofs () const
dof_id_type	n_local_dofs () const
unsigned int	add_variable (std::string_view var, const FEType &type, const std::set< subdomain_id_type > *const active_subdomains=nullptr)
	Adds the variable var to the list of variables for this system. More...
unsigned int	add_variable (std::string_view var, const Order order=FIRST, const FEFamily=LAGRANGE, const std::set< subdomain_id_type > *const active_subdomains=nullptr)
	Adds the variable var to the list of variables for this system. More...
unsigned int	add_variables (const std::vector< std::string > &vars, const FEType &type, const std::set< subdomain_id_type > *const active_subdomains=nullptr)
	Adds the variable var to the list of variables for this system. More...
unsigned int	add_variables (const std::vector< std::string > &vars, const Order order=FIRST, const FEFamily=LAGRANGE, const std::set< subdomain_id_type > *const active_subdomains=nullptr)
	Adds the variable var to the list of variables for this system. More...
const Variable &	variable (unsigned int var) const
	Return a constant reference to Variable var. More...
const VariableGroup &	variable_group (unsigned int vg) const
	Return a constant reference to VariableGroup vg. More...
bool	has_variable (std::string_view var) const
const std::string &	variable_name (const unsigned int i) const
unsigned int	variable_number (std::string_view var) const
void	get_all_variable_numbers (std::vector< unsigned int > &all_variable_numbers) const
	Fills all_variable_numbers with all the variable numbers for the variables that have been added to this system. More...
unsigned int	variable_scalar_number (std::string_view var, unsigned int component) const
unsigned int	variable_scalar_number (unsigned int var_num, unsigned int component) const
const FEType &	variable_type (const unsigned int i) const
const FEType &	variable_type (std::string_view var) const
bool	identify_variable_groups () const
void	identify_variable_groups (const bool)
	Toggle automatic VariableGroup identification. More...
Real	calculate_norm (const NumericVector< Number > &v, unsigned int var, FEMNormType norm_type, std::set< unsigned int > *skip_dimensions=nullptr) const
Real	calculate_norm (const NumericVector< Number > &v, const SystemNorm &norm, std::set< unsigned int > *skip_dimensions=nullptr) const
void	read_header (Xdr &io, std::string_view version, const bool read_header=true, const bool read_additional_data=true, const bool read_legacy_format=false)
	Reads the basic data header for this System. More...
void	read_legacy_data (Xdr &io, const bool read_additional_data=true)
	Reads additional data, namely vectors, for this System. More...
template<typename ValType >
void	read_serialized_data (Xdr &io, const bool read_additional_data=true)
	Reads additional data, namely vectors, for this System. More...
void	read_serialized_data (Xdr &io, const bool read_additional_data=true)
	Non-templated version for backward compatibility. More...
template<typename InValType >
std::size_t	read_serialized_vectors (Xdr &io, const std::vector< NumericVector< Number > *> &vectors) const
	Read a number of identically distributed vectors. More...
std::size_t	read_serialized_vectors (Xdr &io, const std::vector< NumericVector< Number > *> &vectors) const
	Non-templated version for backward compatibility. More...
template<typename InValType >
void	read_parallel_data (Xdr &io, const bool read_additional_data)
	Reads additional data, namely vectors, for this System. More...
void	read_parallel_data (Xdr &io, const bool read_additional_data)
	Non-templated version for backward compatibility. More...
void	write_header (Xdr &io, std::string_view version, const bool write_additional_data) const
	Writes the basic data header for this System. More...
void	write_serialized_data (Xdr &io, const bool write_additional_data=true) const
	Writes additional data, namely vectors, for this System. More...
std::size_t	write_serialized_vectors (Xdr &io, const std::vector< const NumericVector< Number > *> &vectors) const
	Serialize & write a number of identically distributed vectors. More...
void	write_parallel_data (Xdr &io, const bool write_additional_data) const
	Writes additional data, namely vectors, for this System. More...
std::string	get_info () const
void	attach_init_function (void fptr(EquationSystems &es, const std::string &name))
	Register a user function to use in initializing the system. More...
void	attach_init_object (Initialization &init)
	Register a user class to use to initialize the system. More...
void	attach_assemble_function (void fptr(EquationSystems &es, const std::string &name))
	Register a user function to use in assembling the system matrix and RHS. More...
void	attach_assemble_object (Assembly &assemble)
	Register a user object to use in assembling the system matrix and RHS. More...
void	attach_constraint_function (void fptr(EquationSystems &es, const std::string &name))
	Register a user function for imposing constraints. More...
void	attach_constraint_object (Constraint &constrain)
	Register a user object for imposing constraints. More...
bool	has_constraint_object () const
Constraint &	get_constraint_object ()
	Return the user object for imposing constraints. More...
void	attach_QOI_function (void fptr(EquationSystems &es, const std::string &name, const QoISet &qoi_indices))
	Register a user function for evaluating the quantities of interest, whose values should be placed in System::qoi. More...
void	attach_QOI_object (QOI &qoi)
	Register a user object for evaluating the quantities of interest, whose values should be placed in System::qoi. More...
void	attach_QOI_derivative (void fptr(EquationSystems &es, const std::string &name, const QoISet &qoi_indices, bool include_liftfunc, bool apply_constraints))
	Register a user function for evaluating derivatives of a quantity of interest with respect to test functions, whose values should be placed in System::rhs. More...
void	attach_QOI_derivative_object (QOIDerivative &qoi_derivative)
	Register a user object for evaluating derivatives of a quantity of interest with respect to test functions, whose values should be placed in System::rhs. More...
virtual void	user_initialization ()
	Calls user's attached initialization function, or is overridden by the user in derived classes. More...
virtual void	user_assembly ()
	Calls user's attached assembly function, or is overridden by the user in derived classes. More...
virtual void	user_constrain ()
	Calls user's attached constraint function, or is overridden by the user in derived classes. More...
virtual void	user_QOI (const QoISet &qoi_indices)
	Calls user's attached quantity of interest function, or is overridden by the user in derived classes. More...
virtual void	user_QOI_derivative (const QoISet &qoi_indices=QoISet(), bool include_liftfunc=true, bool apply_constraints=true)
	Calls user's attached quantity of interest derivative function, or is overridden by the user in derived classes. More...
virtual void	re_update ()
	Re-update the local values when the mesh has changed. More...
virtual void	restrict_vectors ()
	Restrict vectors after the mesh has coarsened. More...
virtual void	prolong_vectors ()
	Prolong vectors after the mesh has refined. More...
Number	current_solution (const dof_id_type global_dof_number) const
unsigned int	n_qois () const
	Number of currently active quantities of interest. More...
void	init_qois (unsigned int n_qois)
	Accessors for qoi and qoi_error_estimates vectors. More...
void	set_qoi (unsigned int qoi_index, Number qoi_value)
void	set_qoi (std::vector< Number > new_qoi)
Number	get_qoi_value (unsigned int qoi_index) const
std::vector< Number >	get_qoi_values () const
	Returns a copy of qoi, not a reference. More...
void	set_qoi_error_estimate (unsigned int qoi_index, Number qoi_error_estimate)
Number	get_qoi_error_estimate_value (unsigned int qoi_index) const
Number	point_value (unsigned int var, const Point &p, const bool insist_on_success=true, const NumericVector< Number > *sol=nullptr) const
Number	point_value (unsigned int var, const Point &p, const Elem &e, const NumericVector< Number > *sol=nullptr) const
Number	point_value (unsigned int var, const Point &p, const Elem *e) const
	Calls the version of point_value() which takes a reference. More...
Number	point_value (unsigned int var, const Point &p, const NumericVector< Number > *sol) const
	Calls the parallel version of point_value(). More...
Gradient	point_gradient (unsigned int var, const Point &p, const bool insist_on_success=true, const NumericVector< Number > *sol=nullptr) const
Gradient	point_gradient (unsigned int var, const Point &p, const Elem &e, const NumericVector< Number > *sol=nullptr) const
Gradient	point_gradient (unsigned int var, const Point &p, const Elem *e) const
	Calls the version of point_gradient() which takes a reference. More...
Gradient	point_gradient (unsigned int var, const Point &p, const NumericVector< Number > *sol) const
	Calls the parallel version of point_gradient(). More...
Tensor	point_hessian (unsigned int var, const Point &p, const bool insist_on_success=true, const NumericVector< Number > *sol=nullptr) const
Tensor	point_hessian (unsigned int var, const Point &p, const Elem &e, const NumericVector< Number > *sol=nullptr) const
Tensor	point_hessian (unsigned int var, const Point &p, const Elem *e) const
	Calls the version of point_hessian() which takes a reference. More...
Tensor	point_hessian (unsigned int var, const Point &p, const NumericVector< Number > *sol) const
	Calls the parallel version of point_hessian(). More...
void	local_dof_indices (const unsigned int var, std::set< dof_id_type > &var_indices) const
	Fills the std::set with the degrees of freedom on the local processor corresponding the the variable number passed in. More...
void	zero_variable (NumericVector< Number > &v, unsigned int var_num) const
	Zeroes all dofs in v that correspond to variable number var_num. More...
bool	get_project_with_constraints ()
	Setter and getter functions for project_with_constraints boolean. More...
void	set_project_with_constraints (bool _project_with_constraints)
bool &	hide_output ()
void	projection_matrix (SparseMatrix< Number > &proj_mat) const
	This method creates a projection matrix which corresponds to the operation of project_vector between old and new solution spaces. More...
SparseMatrix< Number > &	add_matrix (std::string_view mat_name, ParallelType type=PARALLEL, MatrixBuildType mat_build_type=MatrixBuildType::AUTOMATIC)
	Adds the additional matrix mat_name to this system. More...
template<template< typename > class>
SparseMatrix< Number > &	add_matrix (std::string_view mat_name, ParallelType=PARALLEL)
	Adds the additional matrix mat_name to this system. More...
SparseMatrix< Number > &	add_matrix (std::string_view mat_name, std::unique_ptr< SparseMatrix< Number >> matrix, ParallelType type=PARALLEL)
	Adds the additional matrix mat_name to this system. More...
void	remove_matrix (std::string_view mat_name)
	Removes the additional matrix mat_name from this system. More...
bool	have_matrix (std::string_view mat_name) const
const SparseMatrix< Number > *	request_matrix (std::string_view mat_name) const
SparseMatrix< Number > *	request_matrix (std::string_view mat_name)
const SparseMatrix< Number > &	get_matrix (std::string_view mat_name) const
SparseMatrix< Number > &	get_matrix (std::string_view mat_name)
void	prefer_hash_table_matrix_assembly (bool preference)
	Sets whether to use hash table matrix assembly if the matrix sub-classes support it. More...
void	prefix_with_name (bool value)
	Instructs this system to prefix solve options with its name for solvers that leverage prefixes. More...
bool	prefix_with_name () const
std::string	prefix () const
bool	has_static_condensation () const
const Parallel::Communicator &	comm () const
processor_id_type	n_processors () const
processor_id_type	processor_id () const
virtual void	clear_physics ()
	Clear any data structures associated with the physics. More...
virtual void	init_physics (const System &sys)
	Initialize any data structures associated with the physics. More...
virtual bool	element_time_derivative (bool request_jacobian, DiffContext &)
	Adds the time derivative contribution on elem to elem_residual. More...
virtual bool	element_constraint (bool request_jacobian, DiffContext &)
	Adds the constraint contribution on elem to elem_residual. More...
virtual bool	side_time_derivative (bool request_jacobian, DiffContext &)
	Adds the time derivative contribution on side of elem to elem_residual. More...
virtual bool	side_constraint (bool request_jacobian, DiffContext &)
	Adds the constraint contribution on side of elem to elem_residual. More...
virtual bool	nonlocal_time_derivative (bool request_jacobian, DiffContext &)
	Adds any nonlocal time derivative contributions (e.g. More...
virtual bool	nonlocal_constraint (bool request_jacobian, DiffContext &)
	Adds any nonlocal constraint contributions (e.g. More...
virtual void	time_evolving (unsigned int var, unsigned int order)
	Tells the DiffSystem that variable var is evolving with respect to time. More...
bool	is_time_evolving (unsigned int var) const
virtual bool	eulerian_residual (bool request_jacobian, DiffContext &)
	Adds a pseudo-convection contribution on elem to elem_residual, if the nodes of elem are being translated by a moving mesh. More...
virtual bool	eulerian_residual (bool request_jacobian, DiffContext &context) override
	Adds a pseudo-convection contribution on elem to elem_residual, if the nodes of elem are being translated by a moving mesh. More...
virtual bool	mass_residual (bool request_jacobian, DiffContext &)
	Subtracts a mass vector contribution on elem from elem_residual. More...
virtual bool	mass_residual (bool request_jacobian, DiffContext &) override
	Subtracts a mass vector contribution on elem from elem_residual. More...
virtual bool	side_mass_residual (bool request_jacobian, DiffContext &)
	Subtracts a mass vector contribution on side of elem from elem_residual. More...
virtual bool	nonlocal_mass_residual (bool request_jacobian, DiffContext &c)
	Subtracts any nonlocal mass vector contributions (e.g. More...
virtual bool	damping_residual (bool request_jacobian, DiffContext &)
	Subtracts a damping vector contribution on elem from elem_residual. More...
virtual bool	side_damping_residual (bool request_jacobian, DiffContext &)
	Subtracts a damping vector contribution on side of elem from elem_residual. More...
virtual bool	nonlocal_damping_residual (bool request_jacobian, DiffContext &)
	Subtracts any nonlocal damping vector contributions (e.g. More...
virtual void	set_mesh_system (System *sys)
	Tells the DifferentiablePhysics that system sys contains the isoparametric Lagrangian variables which correspond to the coordinates of mesh nodes, in problems where the mesh itself is expected to move in time. More...
const System *	get_mesh_system () const
System *	get_mesh_system ()
virtual void	set_mesh_x_var (unsigned int var)
	Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the x coordinate of mesh nodes, in problems where the mesh itself is expected to move in time. More...
unsigned int	get_mesh_x_var () const
virtual void	set_mesh_y_var (unsigned int var)
	Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the y coordinate of mesh nodes. More...
unsigned int	get_mesh_y_var () const
virtual void	set_mesh_z_var (unsigned int var)
	Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the z coordinate of mesh nodes. More...
unsigned int	get_mesh_z_var () const
bool	_eulerian_time_deriv (bool request_jacobian, DiffContext &)
	This method simply combines element_time_derivative() and eulerian_residual(), which makes its address useful as a pointer-to-member-function when refactoring. More...
bool	have_first_order_vars () const
const std::set< unsigned int > &	get_first_order_vars () const
bool	is_first_order_var (unsigned int var) const
bool	have_second_order_vars () const
const std::set< unsigned int > &	get_second_order_vars () const
bool	is_second_order_var (unsigned int var) const
virtual void	init_qoi (std::vector< Number > &)
	Initialize system qoi. More...
void	init_qoi (std::vector< Number > &)
	Non-virtual, to try to help deprecated user code catch this change at compile time (if they specified override) More...
virtual void	init_qoi_count (System &)
	Initialize system qoi. More...
virtual void	clear_qoi ()
	Clear all the data structures associated with the QoI. More...
virtual void	element_qoi (DiffContext &, const QoISet &)
	Does any work that needs to be done on elem in a quantity of interest assembly loop, outputting to elem_qoi. More...
virtual void	element_qoi_derivative (DiffContext &, const QoISet &)
	Does any work that needs to be done on elem in a quantity of interest derivative assembly loop, outputting to elem_qoi_derivative. More...
virtual void	side_qoi (DiffContext &, const QoISet &)
	Does any work that needs to be done on side of elem in a quantity of interest assembly loop, outputting to elem_qoi. More...
virtual void	side_qoi_derivative (DiffContext &, const QoISet &)
	Does any work that needs to be done on side of elem in a quantity of interest derivative assembly loop, outputting to elem_qoi_derivative. More...
virtual void	thread_join (std::vector< Number > &qoi, const std::vector< Number > &other_qoi, const QoISet &qoi_indices)
	Method to combine thread-local qois. More...
virtual void	parallel_op (const Parallel::Communicator &communicator, std::vector< Number > &sys_qoi, std::vector< Number > &local_qoi, const QoISet &qoi_indices)
	Method to populate system qoi data structure with process-local qoi. More...
virtual void	finalize_derivative (NumericVector< Number > &derivatives, std::size_t qoi_index)
	Method to finalize qoi derivatives which require more than just a simple sum of element contributions. More...

Static Public Member Functions
static std::string	get_info ()
	Gets a string containing the reference information. More...
static void	print_info (std::ostream &out_stream=libMesh::out)
	Prints the reference information, by default to libMesh::out. More...
static unsigned int	n_objects ()
	Prints the number of outstanding (created, but not yet destroyed) objects. More...
static void	enable_print_counter_info ()
	Methods to enable/disable the reference counter output from print_info() More...
static void	disable_print_counter_info ()

Public Attributes
Real *	continuation_parameter
	The continuation parameter must be a member variable of the derived class, and the "continuation_parameter" pointer defined here must be a pointer to that variable. More...
bool	quiet
	If quiet==false, the System prints extra information about what it is doing. More...
double	continuation_parameter_tolerance
	How tightly should the Newton iterations attempt to converge delta_lambda. More...
double	solution_tolerance
	How tightly should the Newton iterations attempt to converge ||delta_u|| Defaults to 1.e-6. More...
double	initial_newton_tolerance
	How much to try to reduce the residual by at the first (inexact) Newton step. More...
Real	old_continuation_parameter
	The system also keeps track of the old value of the continuation parameter. More...
Real	min_continuation_parameter
	The minimum-allowable value of the continuation parameter. More...
Real	max_continuation_parameter
	The maximum-allowable value of the continuation parameter. More...
Real	Theta
	Arclength normalization parameter. More...
Real	Theta_LOCA
	Another normalization parameter, which is described in the LOCA manual. More...
unsigned int	n_backtrack_steps
	Another scaling parameter suggested by the LOCA people. More...
unsigned int	n_arclength_reductions
	Number of arclength reductions to try when Newton fails to reduce the residual. More...
Real	ds_min
	The minimum-allowed steplength, defaults to 1.e-8. More...
Predictor	predictor
Real	newton_stepgrowth_aggressiveness
	A measure of how rapidly one should attempt to grow the arclength stepsize based on the number of Newton iterations required to solve the problem. More...
bool	newton_progress_check
	True by default, the Newton progress check allows the Newton loop to exit if half the allowed iterations have elapsed without a reduction in the initial residual. More...
bool	fe_reinit_during_postprocess
	If fe_reinit_during_postprocess is true (it is true by default), FE objects will be reinit()ed with their default quadrature rules. More...
Real	numerical_jacobian_h
	If calculating numeric jacobians is required, the FEMSystem will perturb each solution vector entry by numerical_jacobian_h when calculating finite differences. More...
Real	verify_analytic_jacobians
	If verify_analytic_jacobian is equal to zero (as it is by default), no numeric jacobians will be calculated unless an overridden element_time_derivative(), element_constraint(), side_time_derivative(), or side_constraint() function cannot provide an analytic jacobian upon request. More...
std::unique_ptr< TimeSolver >	time_solver
	A pointer to the solver object we're going to use. More...
Real	deltat
	For time-dependent problems, this is the amount delta t to advance the solution in time. More...
bool	postprocess_sides
	If postprocess_sides is true (it is false by default), the postprocessing loop will loop over all sides as well as all elements. More...
bool	print_solution_norms
	Set print_residual_norms to true to print |U| whenever it is used in an assembly() call. More...
bool	print_solutions
	Set print_solutions to true to print U whenever it is used in an assembly() call. More...
bool	print_residual_norms
	Set print_residual_norms to true to print |F| whenever it is assembled. More...
bool	print_residuals
	Set print_residuals to true to print F whenever it is assembled. More...
bool	print_jacobian_norms
	Set print_jacobian_norms to true to print |J| whenever it is assembled. More...
bool	print_jacobians
	Set print_jacobians to true to print J whenever it is assembled. More...
bool	print_element_solutions
	Set print_element_solutions to true to print each U_elem input. More...
bool	print_element_residuals
	Set print_element_residuals to true to print each R_elem contribution. More...
bool	print_element_jacobians
	Set print_element_jacobians to true to print each J_elem contribution. More...
SparseMatrix< Number > *	matrix
	The system matrix. More...
bool	zero_out_matrix_and_rhs
	By default, the system will zero out the matrix and the right hand side. More...
std::unique_ptr< LinearSolver< Number > >	linear_solver
	This class handles all the details of interfacing with various linear algebra packages like PETSc or LASPACK. More...
NumericVector< Number > *	rhs
	The system matrix. More...
Parameters	parameters
	Parameters for the system. If a parameter is not provided, it should be retrieved from the EquationSystems. More...
bool	assemble_before_solve
	Flag which tells the system to whether or not to call the user assembly function during each call to solve(). More...
bool	use_fixed_solution
	A boolean to be set to true by systems using elem_fixed_solution, for optional use by e.g. More...
int	extra_quadrature_order
	A member int that can be employed to indicate increased or reduced quadrature order. More...
std::unique_ptr< NumericVector< Number > >	solution
	Data structure to hold solution values. More...
std::unique_ptr< NumericVector< Number > >	current_local_solution
	All the values I need to compute my contribution to the simulation at hand. More...
Real	time
	For time-dependent problems, this is the time t at the beginning of the current timestep. More...
bool	compute_internal_sides
	compute_internal_sides is false by default, indicating that side_* computations will only be done on boundary sides. More...
bool	assemble_qoi_sides
	If assemble_qoi_sides is true (it is false by default), the assembly loop for a quantity of interest or its derivatives will loop over domain boundary sides. More...
bool	assemble_qoi_internal_sides
	If assemble_qoi_internal_sides is true (it is false by default), the assembly loop for a quantity of interest or its derivatives will loop over element sides which do not fall on domain boundaries. More...
bool	assemble_qoi_elements
	If assemble_qoi_elements is false (it is true by default), the assembly loop for a quantity of interest or its derivatives will skip computing on mesh elements, and will only compute on mesh sides. More...

Protected Types
enum	RHS_Mode { Residual, G_Lambda }
	There are (so far) two different vectors which may be assembled using the assembly routine: 1.) The Residual = the normal PDE weighted residual 2.) G_Lambda = the derivative wrt the parameter lambda of the PDE weighted residual. More...
typedef std::map< std::string, std::pair< unsigned int, unsigned int > >	Counts
	Data structure to log the information. More...

Protected Member Functions
virtual void	init_data () override
	Initializes the member data fields associated with the system, so that, e.g., assemble() may be used. More...
void	add_second_order_dot_vars ()
	Helper function to add "velocity" variables that are cousins to second order-in-time variables in the DifferentiableSystem. More...
void	add_dot_var_dirichlet_bcs (unsigned int var_idx, unsigned int dot_var_idx)
	Helper function to and Dirichlet boundary conditions to "dot" variable cousins of second order variables in the system. More...
virtual void	add_matrices () override
	Adds the system matrix. More...
template<typename T >
void	setup_static_condensation_preconditioner (T &solver)
	Sets up the static condensation preconditioner for the supplied solver. More...
void	project_vector (NumericVector< Number > &, int is_adjoint=-1) const
	Projects the vector defined on the old mesh onto the new mesh. More...
void	project_vector (const NumericVector< Number > &, NumericVector< Number > &, int is_adjoint=-1) const
	Projects the vector defined on the old mesh onto the new mesh. More...
virtual void	init_matrices ()
	Initializes the matrices associated with this system. More...
bool	can_add_matrices () const
void	solve_for_unconstrained_dofs (NumericVector< Number > &, int is_adjoint=-1) const
virtual bool	condense_constrained_dofs () const
	Whether this object should condense out constrained degrees of freedom. More...
void	increment_constructor_count (const std::string &name) noexcept
	Increments the construction counter. More...
void	increment_destructor_count (const std::string &name) noexcept
	Increments the destruction counter. More...

Protected Attributes
RHS_Mode	rhs_mode
bool	_constrain_in_solver
	_constrain_in_solver defaults to true; if false then we apply constraints only via residual terms in the systems to be solved. More...
const Parallel::Communicator &	_communicator
System *	_mesh_sys
	System from which to acquire moving mesh information. More...
unsigned int	_mesh_x_var
	Variables from which to acquire moving mesh information. More...
unsigned int	_mesh_y_var
unsigned int	_mesh_z_var
std::vector< unsigned int >	_time_evolving
	Stores unsigned int to tell us which variables are evolving as first order in time (1), second order in time (2), or are not time evolving (0). More...
std::set< unsigned int >	_first_order_vars
	Variable indices for those variables that are first order in time. More...
std::set< unsigned int >	_second_order_vars
	Variable indices for those variables that are second order in time. More...
std::map< unsigned int, unsigned int >	_second_order_dot_vars
	If the user adds any second order variables, then we need to also cache the map to their corresponding dot variable that will be added by this TimeSolver class. More...

Static Protected Attributes
static Counts	_counts
	Actually holds the data. More...
static Threads::atomic< unsigned int >	_n_objects
	The number of objects. More...
static Threads::spin_mutex	_mutex
	Mutual exclusion object to enable thread-safe reference counting. More...
static bool	_enable_print_counter = true
	Flag to control whether reference count information is printed when print_info is called. More...

Private Member Functions
void	initialize_tangent ()
	Before starting arclength continuation, we need at least 2 prior solutions (both solution and u_previous should be filled with meaningful values) And we need to initialize the tangent vector. More...
void	solve_tangent ()
	Special solve algorithm for solving the tangent system. More...
void	update_solution ()
	This function (which assumes the most recent tangent vector has been computed) updates the solution and the control parameter with the initial guess for the next point on the continuation path. More...
void	set_Theta ()
	A centralized function for setting the normalization parameter theta. More...
void	set_Theta_LOCA ()
	A centralized function for setting the other normalization parameter, i.e. More...
void	apply_predictor ()
	Applies the predictor to the current solution to get a guess for the next solution. More...

Private Attributes
NumericVector< Number > *	du_ds
	Extra work vectors used by the continuation algorithm. More...
NumericVector< Number > *	previous_du_ds
	The value of du_ds from the previous solution. More...
NumericVector< Number > *	previous_u
	The solution at the previous value of the continuation variable. More...
NumericVector< Number > *	y
	Temporary vector "y" ... More...
NumericVector< Number > *	y_old
	Temporary vector "y_old" ... More...
NumericVector< Number > *	z
	Temporary vector "z" ... More...
NumericVector< Number > *	delta_u
	Temporary vector "delta u" ... More...
bool	tangent_initialized
	False until initialize_tangent() is called. More...
NewtonSolver *	newton_solver
	A pointer to the underlying Newton solver used by the DiffSystem. More...
Real	dlambda_ds
	The most recent value of the derivative of the continuation parameter with respect to s. More...
Real	ds
	The initial arclength stepsize, selected by the user. More...
Real	ds_current
	Value of stepsize currently in use. More...
Real	previous_dlambda_ds
	The old parameter tangent value. More...
Real	previous_ds
	The previous arcstep length used. More...
unsigned int	newton_step
	Loop counter for nonlinear (Newton) iteration loop. More...

Detailed Description

This class inherits from the FEMSystem.

It can be used to do arclength continuation. Most of the ideas and the notation here come from HB Keller's 1977 paper:

* @InProceedings{Kell-1977,
*   author    = {H.~B.~Keller},
*   title     = {{Numerical solution of bifurcation and nonlinear eigenvalue problems}},
*   booktitle = {Applications of Bifurcation Theory, P.~H.~Rabinowitz (ed.)},
*   year      = 1977,
*   publisher = {Academic Press},
*   pages     = {359--389},
*   notes     = {QA 3 U45 No.\ 38 (PMA)}
* }
* 

Author

John W. Peterson

Date

2007

Definition at line 53 of file continuation_system.h.

Member Typedef Documentation

const_matrices_iterator

typedef std::map<std::string, std::unique_ptr<SparseMatrix<Number> >, std::less<> >::const_iterator libMesh::System::const_matrices_iterator

inherited

Definition at line 784 of file system.h.

const_vectors_iterator

typedef std::map<std::string, std::unique_ptr<NumericVector<Number> >, std::less<> >::const_iterator libMesh::System::const_vectors_iterator

inherited

Definition at line 758 of file system.h.

Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts

protectedinherited

Data structure to log the information.

The log is identified by the class name.

Definition at line 119 of file reference_counter.h.

GradientFunctionPointer

typedef Gradient(* libMesh::System::GradientFunctionPointer) (const Point &p, const Parameters &parameters, const std::string &sys_name, const std::string &unknown_name)

inherited

Definition at line 541 of file system.h.

matrices_iterator

typedef std::map<std::string, std::unique_ptr<SparseMatrix<Number> >, std::less<> >::iterator libMesh::System::matrices_iterator

inherited

Matrix iterator typedefs.

Definition at line 783 of file system.h.

Parent

typedef FEMSystem libMesh::ContinuationSystem::Parent

The type of the parent.

Definition at line 83 of file continuation_system.h.

sys_type

typedef ContinuationSystem libMesh::ContinuationSystem::sys_type

The type of system.

Definition at line 78 of file continuation_system.h.

TimeSolverResPtr

typedef bool(TimeSolver::* libMesh::FEMSystem::TimeSolverResPtr) (bool, DiffContext &)

inherited

Syntax sugar to make numerical_jacobian() declaration easier.

Definition at line 220 of file fem_system.h.

ValueFunctionPointer

typedef Number(* libMesh::System::ValueFunctionPointer) (const Point &p, const Parameters &Parameters, const std::string &sys_name, const std::string &unknown_name)

inherited

Projects arbitrary functions onto the current solution.

The function value fptr and its gradient gptr are represented by function pointers. A gradient gptr is only required/used for projecting onto finite element spaces with continuous derivatives.

Definition at line 537 of file system.h.

vectors_iterator

typedef std::map<std::string, std::unique_ptr<NumericVector<Number> >, std::less<> >::iterator libMesh::System::vectors_iterator

inherited

Vector iterator typedefs.

Definition at line 757 of file system.h.

Member Enumeration Documentation

Predictor

enum libMesh::ContinuationSystem::Predictor

The code provides the ability to select from different predictor schemes for getting the initial guess for the solution at the next point on the solution arc.

Enumerator
Euler	First-order Euler predictor.
AB2	Second-order explicit Adams-Bashforth predictor.
Invalid_Predictor	Invalid predictor.

Definition at line 225 of file continuation_system.h.

                 {
    Euler,

    AB2,

    Invalid_Predictor
  };

RHS_Mode

enum libMesh::ContinuationSystem::RHS_Mode

protected

There are (so far) two different vectors which may be assembled using the assembly routine: 1.) The Residual = the normal PDE weighted residual 2.) G_Lambda = the derivative wrt the parameter lambda of the PDE weighted residual.

It is up to the derived class to handle writing separate assembly code for the different cases. Usually something like: switch (rhs_mode) { case Residual: { Fu(i) += ... // normal PDE residual break; }

case G_Lambda: { Fu(i) += ... // derivative wrt control parameter break; }

Enumerator
Residual
G_Lambda

Definition at line 290 of file continuation_system.h.

                {Residual,
                 G_Lambda};

Constructor & Destructor Documentation

ContinuationSystem() [1/3]

libMesh::ContinuationSystem::ContinuationSystem	(	EquationSystems &	es,
		const std::string &	name,
		const unsigned int	number
	)

Constructor.

Optionally initializes required data structures.

Definition at line 30 of file continuation_system.C.

References libMesh::LinearSolver< T >::build(), libMesh::ParallelObject::comm(), libMesh::ImplicitSystem::linear_solver, and libMesh::System::prefix_with_name().

                                                                      :
  Parent(es, name_in, number_in),
  continuation_parameter(nullptr),
  quiet(true),
  continuation_parameter_tolerance(1.e-6),
  solution_tolerance(1.e-6),
  initial_newton_tolerance(0.01),
  old_continuation_parameter(0.),
  min_continuation_parameter(0.),
  max_continuation_parameter(0.),
  Theta(1.),
  Theta_LOCA(1.),
  n_backtrack_steps(5),
  n_arclength_reductions(5),
  ds_min(1.e-8),
  predictor(Euler),
  newton_stepgrowth_aggressiveness(1.),
  newton_progress_check(true),
  rhs_mode(Residual),
  tangent_initialized(false),
  newton_solver(nullptr),
  dlambda_ds(0.707),
  ds(0.1),
  ds_current(0.1),
  previous_dlambda_ds(0.),
  previous_ds(0.),
  newton_step(0)
{
  // Warn about using untested code
  libmesh_experimental();

  // linear_solver is now in the ImplicitSystem base class, but we are
  // going to keep using it basically the way we did before it was
  // moved.
  linear_solver = LinearSolver<Number>::build(es.comm());

  if (this->prefix_with_name())
    linear_solver->init(this->prefix().c_str());
  else
    linear_solver->init();

  linear_solver->init_names(*this);
}

ContinuationSystem() [2/3]

libMesh::ContinuationSystem::ContinuationSystem ( const ContinuationSystem &  )

delete

Special functions.

• This class has the same restrictions as its base class.
• The destructor is defaulted out-of-line.

ContinuationSystem() [3/3]

libMesh::ContinuationSystem::ContinuationSystem ( ContinuationSystem &&  )

delete

~ContinuationSystem()

libMesh::ContinuationSystem::~ContinuationSystem ( )

virtualdefault

Member Function Documentation

_eulerian_time_deriv()

bool libMesh::DifferentiablePhysics::_eulerian_time_deriv ( bool  request_jacobian, DiffContext &  context  )

inherited

This method simply combines element_time_derivative() and eulerian_residual(), which makes its address useful as a pointer-to-member-function when refactoring.

Definition at line 96 of file diff_physics.C.

References libMesh::DifferentiablePhysics::element_time_derivative(), and libMesh::DifferentiablePhysics::eulerian_residual().

Referenced by libMesh::EulerSolver::element_residual(), libMesh::Euler2Solver::element_residual(), and libMesh::NewmarkSolver::element_residual().

{
  // For any problem we need time derivative terms
  request_jacobian =
    this->element_time_derivative(request_jacobian, context);

  // For a moving mesh problem we may need the pseudoconvection term too
  return this->eulerian_residual(request_jacobian, context) &&
    request_jacobian;
}

activate()

void libMesh::System::activate ( )

inlineinherited

Activates the system.

Only active systems are solved.

Definition at line 2398 of file system.h.

References libMesh::System::_active.

{
  _active = true;
}

active()

bool libMesh::System::active ( ) const

inlineinherited

Returns

true if the system is active, false otherwise. An active system will be solved.

Definition at line 2390 of file system.h.

References libMesh::System::_active.

{
  return _active;
}

add_adjoint_rhs()

NumericVector< Number > & libMesh::System::add_adjoint_rhs ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's adjoint rhs vectors, by default the one corresponding to the first qoi. Creates the vector if it doesn't already exist.

Definition at line 1297 of file system.C.

References libMesh::System::add_vector().

Referenced by libMesh::ExplicitSystem::assemble_qoi_derivative(), and libMesh::FEMSystem::assemble_qoi_derivative().

{
  std::ostringstream adjoint_rhs_name;
  adjoint_rhs_name << "adjoint_rhs" << i;

  return this->add_vector(adjoint_rhs_name.str(), false);
}

add_adjoint_solution()

NumericVector< Number > & libMesh::System::add_adjoint_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's adjoint solution vectors, by default the one corresponding to the first qoi. Creates the vector if it doesn't already exist.

Definition at line 1233 of file system.C.

References libMesh::System::add_vector(), and libMesh::System::set_vector_as_adjoint().

Referenced by libMesh::ImplicitSystem::adjoint_solve().

{
  std::ostringstream adjoint_name;
  adjoint_name << "adjoint_solution" << i;

  NumericVector<Number> & returnval = this->add_vector(adjoint_name.str());
  this->set_vector_as_adjoint(adjoint_name.str(), i);
  return returnval;
}

add_dot_var_dirichlet_bcs()

void libMesh::DifferentiableSystem::add_dot_var_dirichlet_bcs ( unsigned int  var_idx, unsigned int  dot_var_idx  )

protectedinherited

Helper function to and Dirichlet boundary conditions to "dot" variable cousins of second order variables in the system.

The function takes the second order variable index, it's corresponding "dot" variable index and then searches for DirichletBoundary objects for var_idx and then adds a DirichletBoundary object for dot_var_idx using the same boundary ids and functors for the var_idx DirichletBoundary.

Definition at line 214 of file diff_system.C.

References libMesh::DofMap::add_dirichlet_boundary(), libMesh::DofMap::get_dirichlet_boundaries(), libMesh::System::get_dof_map(), and libMesh::libmesh_assert().

Referenced by libMesh::DifferentiableSystem::add_second_order_dot_vars().

{
  // We're assuming that there could be a lot more variables than
  // boundary conditions, so we search each of the boundary conditions
  // for this variable rather than looping over boundary conditions
  // in a separate loop and searching through all the variables.
  const DirichletBoundaries * all_dbcs =
    this->get_dof_map().get_dirichlet_boundaries();

  if (all_dbcs)
    {
      // We need to cache the DBCs to be added so that we add them
      // after looping over the existing DBCs. Otherwise, we're polluting
      // the thing we're looping over.
      std::vector<DirichletBoundary> new_dbcs;

      for (const auto & dbc : *all_dbcs)
        {
          libmesh_assert(dbc);

          // Look for second order variable in the current
          // DirichletBoundary object
          std::vector<unsigned int>::const_iterator dbc_var_it =
            std::find( dbc->variables.begin(), dbc->variables.end(), var_idx );

          // If we found it, then we also need to add it's corresponding
          // "dot" variable to a DirichletBoundary
          std::vector<unsigned int> vars_to_add;
          if (dbc_var_it != dbc->variables.end())
            vars_to_add.push_back(dot_var_idx);

          if (!vars_to_add.empty())
            {
              // We need to check if the boundary condition is time-dependent.
              // Currently, we cannot automatically differentiate w.r.t. time
              // so if the user supplies a time-dependent Dirichlet BC, then
              // we can't automatically support the Dirichlet BC for the
              // "velocity" boundary condition, so we error. Otherwise,
              // the "velocity boundary condition will just be zero.
              bool is_time_evolving_bc = false;
              if (dbc->f)
                is_time_evolving_bc = dbc->f->is_time_dependent();
              else if (dbc->f_fem)
                // We it's a FEMFunctionBase object, it will be implicitly
                // time-dependent since it is assumed to depend on the solution.
                is_time_evolving_bc = true;
              else
                libmesh_error_msg("Could not find valid boundary function!");

              libmesh_error_msg_if(is_time_evolving_bc, "Cannot currently support time-dependent Dirichlet BC for dot variables!");
              libmesh_error_msg_if(!dbc->f, "Expected valid DirichletBoundary function");

              new_dbcs.emplace_back(dbc->b, vars_to_add, ZeroFunction<Number>());
            }
        }

      // Let the DofMap make its own deep copy of the DirichletBC objects
      for (const auto & dbc : new_dbcs)
        this->get_dof_map().add_dirichlet_boundary(dbc);

    } // if (all_dbcs)
}

add_matrices()

void libMesh::ImplicitSystem::add_matrices ( )

overrideprotectedvirtualinherited

Adds the system matrix.

Reimplemented from libMesh::System.

Definition at line 109 of file implicit_system.C.

References libMesh::System::add_matrices(), libMesh::System::add_matrix(), libMesh::libmesh_assert(), libMesh::ImplicitSystem::matrix, and libMesh::System::n_matrices().

{
  Parent::add_matrices();

  // Possible that we cleared the _matrices but
  // forgot to update the matrix pointer?
  if (this->n_matrices() == 0)
    matrix = nullptr;

  // Only need to add the matrix if it isn't there
  // already!
  if (matrix == nullptr)
    matrix = &(this->add_matrix ("System Matrix"));

  libmesh_assert(matrix);
}

add_matrix() [1/3]

SparseMatrix< Number > & libMesh::System::add_matrix ( std::string_view  mat_name, ParallelType  type = PARALLEL, MatrixBuildType  mat_build_type = MatrixBuildType::AUTOMATIC  )

inherited

Adds the additional matrix mat_name to this system.

Only allowed prior to assemble(). All additional matrices have the same sparsity pattern as the matrix used during solution. When not System but the user wants to initialize the main/system matrix, then all the additional matrices, if existent, have to be initialized by the user, too.

This non-template method will add a derived matrix type corresponding to the solver package. If the user wishes to specify the matrix type to add, use the templated add_matrix method instead

Parameters

mat_name	A name for the matrix
type	The serial/parallel/ghosted type of the matrix
mat_build_type	The matrix type to build

Definition at line 1010 of file system.C.

References libMesh::System::_matrices, libMesh::System::_matrix_types, libMesh::SparseMatrix< T >::build(), libMesh::ParallelObject::comm(), libMesh::default_solver_package(), libMesh::DIAGONAL, libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::DofMap::get_static_condensation(), libMesh::System::has_static_condensation(), libMesh::if(), libMesh::System::late_matrix_init(), and libMesh::libmesh_assert().

Referenced by libMesh::ImplicitSystem::add_matrices(), libMesh::EigenSystem::add_matrices(), alternative_fe_assembly(), libMesh::ClawSystem::assemble_boundary_condition_matrices(), libMesh::ImplicitSystem::create_static_condensation_system_matrix(), form_matrixA(), libMesh::EigenTimeSolver::init(), main(), and libMesh::NewmarkSystem::NewmarkSystem().

{
  parallel_object_only();

  libmesh_assert(this->comm().verify(std::string(mat_name)));
  libmesh_assert(this->comm().verify(int(type)));
  libmesh_assert(this->comm().verify(int(mat_build_type)));

  // Return the matrix if it is already there.
  if (auto it = this->_matrices.find(mat_name);
      it != this->_matrices.end())
    return *it->second;

  // Otherwise build the matrix to return.
  std::unique_ptr<SparseMatrix<Number>> matrix;
  if (this->has_static_condensation())
    {
      if (mat_build_type == MatrixBuildType::DIAGONAL)
        libmesh_error_msg(
            "We do not currently support static condensation of the diagonal matrix type");
      matrix = std::make_unique<StaticCondensation>(this->get_mesh(),
                                                    *this,
                                                    this->get_dof_map(),
                                                    this->get_dof_map().get_static_condensation());
    }
  else
    matrix = SparseMatrix<Number>::build(this->comm(), libMesh::default_solver_package());
  auto & mat = *matrix;

  _matrices.emplace(mat_name, std::move(matrix));

  _matrix_types.emplace(mat_name, type);

  // Initialize it first if we've already initialized the others.
  this->late_matrix_init(mat, type);

  return mat;
}

add_matrix() [2/3]

template<template< typename > class MatrixType>

SparseMatrix< Number > & libMesh::System::add_matrix ( std::string_view  mat_name, ParallelType  type = PARALLEL  )

inlineinherited

Adds the additional matrix mat_name to this system.

Only allowed prior to assemble(). All additional matrices have the same sparsity pattern as the matrix used during solution. When not System but the user wants to initialize the main/system matrix, then all the additional matrices, if existent, have to be initialized by the user, too.

This method will create add a derived matrix of type MatrixType<Number>. One can use the non-templated add_matrix method to add a matrix corresponding to the default solver package

Parameters

mat_name	A name for the matrix
type	The serial/parallel/ghosted type of the matrix

Definition at line 2707 of file system.h.

References libMesh::System::_matrices, libMesh::System::_matrix_types, and libMesh::System::late_matrix_init().

{
  // Return the matrix if it is already there.
  auto it = this->_matrices.find(mat_name);
  if (it != this->_matrices.end())
    return *it->second;

  // Otherwise build the matrix to return.
  auto pr = _matrices.emplace(mat_name, std::make_unique<MatrixType<Number>>(this->comm()));
  _matrix_types.emplace(mat_name, type);

  SparseMatrix<Number> & mat = *(pr.first->second);

  // Initialize it first if we've already initialized the others.
  this->late_matrix_init(mat, type);

  return mat;
}

add_matrix() [3/3]

SparseMatrix< Number > & libMesh::System::add_matrix ( std::string_view  mat_name, std::unique_ptr< SparseMatrix< Number >>  matrix, ParallelType  type = PARALLEL  )

inherited

Adds the additional matrix mat_name to this system.

Only allowed prior to assemble(). All additional matrices have the same sparsity pattern as the matrix used during solution. When not System but the user wants to initialize the main/system matrix, then all the additional matrices, if existent, have to be initialized by the user, too.

Parameters

mat_name	A name for the matrix
matrix	The matrix we are handing over the System for ownership
type	The serial/parallel/ghosted type of the matrix

Definition at line 1053 of file system.C.

References libMesh::System::_matrices, libMesh::System::_matrix_types, libMesh::ParallelObject::comm(), libMesh::System::late_matrix_init(), and libMesh::libmesh_assert().

{
  parallel_object_only();

  libmesh_assert(this->comm().verify(std::string(mat_name)));
  libmesh_assert(this->comm().verify(int(type)));

  auto [it, inserted] = _matrices.emplace(mat_name, std::move(matrix));
  libmesh_error_msg_if(!inserted,
                       "Tried to add '" << mat_name << "' but the matrix already exists");

  _matrix_types.emplace(mat_name, type);

  SparseMatrix<Number> & mat = *(it->second);

  // Initialize it first if we've already initialized the others.
  this->late_matrix_init(mat, type);

  return mat;
}

add_second_order_dot_vars()

void libMesh::DifferentiableSystem::add_second_order_dot_vars ( )

protectedinherited

Helper function to add "velocity" variables that are cousins to second order-in-time variables in the DifferentiableSystem.

This function is only called if the TimeSolver is a FirstOrderUnsteadySolver.

Definition at line 182 of file diff_system.C.

References libMesh::DifferentiablePhysics::_second_order_dot_vars, libMesh::Variable::active_subdomains(), libMesh::DifferentiableSystem::add_dot_var_dirichlet_bcs(), libMesh::System::add_variable(), libMesh::DifferentiablePhysics::get_second_order_vars(), libMesh::Variable::name(), libMesh::DifferentiablePhysics::time_evolving(), libMesh::Variable::type(), and libMesh::System::variable().

Referenced by libMesh::DifferentiableSystem::init_data().

{
  const std::set<unsigned int> & second_order_vars = this->get_second_order_vars();
  if (!second_order_vars.empty())
    {
      for (const auto & var_id : second_order_vars)
        {
          const Variable & var = this->variable(var_id);
          std::string new_var_name = std::string("dot_")+var.name();

          unsigned int v_var_idx;

          if (var.active_subdomains().empty())
            v_var_idx = this->add_variable( new_var_name, var.type() );
          else
            v_var_idx = this->add_variable( new_var_name, var.type(), &var.active_subdomains() );

          _second_order_dot_vars.insert(std::pair<unsigned int, unsigned int>(var_id, v_var_idx));

          // The new velocities are time evolving variables of first order
          this->time_evolving( v_var_idx, 1 );

#ifdef LIBMESH_ENABLE_DIRICHLET
          // And if there are any boundary conditions set on the second order
          // variable, we also need to set it on its velocity variable.
          this->add_dot_var_dirichlet_bcs(var_id, v_var_idx);
#endif
        }
    }
}

add_sensitivity_rhs()

NumericVector< Number > & libMesh::System::add_sensitivity_rhs ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's sensitivity rhs vectors, by default the one corresponding to the first parameter. Creates the vector if it doesn't already exist.

Definition at line 1327 of file system.C.

References libMesh::System::add_vector().

Referenced by libMesh::ImplicitSystem::assemble_residual_derivatives().

{
  std::ostringstream sensitivity_rhs_name;
  sensitivity_rhs_name << "sensitivity_rhs" << i;

  return this->add_vector(sensitivity_rhs_name.str(), false);
}

add_sensitivity_solution()

NumericVector< Number > & libMesh::System::add_sensitivity_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's solution sensitivity vectors, by default the one corresponding to the first parameter. Creates the vector if it doesn't already exist.

Definition at line 1182 of file system.C.

References libMesh::System::add_vector().

Referenced by libMesh::ImplicitSystem::sensitivity_solve().

{
  std::ostringstream sensitivity_name;
  sensitivity_name << "sensitivity_solution" << i;

  return this->add_vector(sensitivity_name.str());
}

add_variable() [1/2]

unsigned int libMesh::System::add_variable ( std::string_view  var, const FEType &  type, const std::set< subdomain_id_type > *const  active_subdomains = nullptr  )

inherited

Adds the variable var to the list of variables for this system.

If active_subdomains is either nullptr (the default) or points to an empty set, then it will be assumed that var has no subdomain restrictions

Returns

The index number for the new variable.

Definition at line 1357 of file system.C.

References libMesh::System::_variable_groups, libMesh::System::_variable_numbers, libMesh::System::_variables, libMesh::Variable::active_subdomains(), libMesh::System::add_variables(), libMesh::ParallelObject::comm(), libMesh::System::identify_variable_groups(), libMesh::Variable::implicitly_active(), libMesh::System::is_initialized(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::System::n_variable_groups(), libMesh::System::n_vars(), libMesh::System::variable(), libMesh::System::variable_name(), and libMesh::System::variable_type().

Referenced by libMesh::DifferentiableSystem::add_second_order_dot_vars(), libMesh::System::add_variable(), assemble_and_solve(), OverlappingTestBase::init(), SolidSystem::init_data(), CurlCurlSystem::init_data(), SimpleEIMConstruction::init_data(), libMesh::VariationalSmootherSystem::init_data(), libMesh::AdvectionSystem::init_data(), HeatSystem::init_data(), SimpleRBConstruction::init_data(), NonManifoldCouplingTestBase::init_es(), main(), libMesh::ErrorVector::plot_error(), libMesh::System::read_header(), RationalMapTest< elem_type >::setUp(), SlitMeshRefinedSystemTest::setUp(), FETestBase< order, family, elem_type, 1 >::setUp(), WriteVecAndScalar::setupTests(), SystemsTest::simpleSetup(), MultiEvaluablePredTest::test(), ConstraintOperatorTest::test1DCoarseningNewNodes(), ConstraintOperatorTest::test1DCoarseningOperator(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), MeshFunctionTest::test_subdomain_id_sets(), SystemsTest::testAssemblyWithDgFemContext(), DofMapTest::testBadElemFECombo(), EquationSystemsTest::testBadVarNames(), SystemsTest::testBlockRestrictedVarNDofs(), SystemsTest::testBoundaryProjectCube(), DofMapTest::testConstraintLoopDetection(), MeshInputTest::testCopyElementSolutionImpl(), MeshInputTest::testCopyElementVectorImpl(), MeshInputTest::testCopyNodalSolutionImpl(), ConstraintOperatorTest::testCoreform(), DefaultCouplingTest::testCoupling(), PointNeighborCouplingTest::testCoupling(), SystemsTest::testDofCouplingWithVarGroups(), DofMapTest::testDofOwner(), MeshInputTest::testDynaReadPatch(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), MeshAssignTest::testMeshMoveAssign(), PeriodicBCTest::testPeriodicBC(), EquationSystemsTest::testPostInitAddElem(), EquationSystemsTest::testPostInitAddRealSystem(), SystemsTest::testProjectCubeWithMeshFunction(), MeshInputTest::testProjectionRegression(), SystemsTest::testProjectMatrix1D(), SystemsTest::testProjectMatrix2D(), SystemsTest::testProjectMatrix3D(), InfFERadialTest::testRefinement(), EquationSystemsTest::testRefineThenReinitPreserveFlags(), EquationSystemsTest::testReinitWithNodeElem(), EquationSystemsTest::testRepartitionThenReinit(), EquationSystemsTest::testSelectivePRefine(), SystemsTest::testSetSystemParameterOverEquationSystem(), BoundaryInfoTest::testShellFaceConstraints(), MeshInputTest::testSingleElementImpl(), WriteVecAndScalar::testWriteExodus(), and WriteVecAndScalar::testWriteNemesis().

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  libmesh_assert(this->comm().verify(std::string(var)));
  libmesh_assert(this->comm().verify(type));
  libmesh_assert(this->comm().verify((active_subdomains == nullptr)));

  if (active_subdomains)
    libmesh_assert(this->comm().verify(active_subdomains->size()));

  // Make sure the variable isn't there already
  // or if it is, that it's the type we want
  for (auto v : make_range(this->n_vars()))
    if (this->variable_name(v) == var)
      {
        if (this->variable_type(v) == type)
          {
            // Check whether the existing variable's active subdomains also matches
            // the incoming variable's active subdomains. If they don't match, then
            // either it is an error by the user or the user is trying to change the
            // subdomain restriction after the variable has already been added, which
            // is not supported.
            const Variable & existing_var = this->variable(v);

            // Check whether active_subdomains is not provided/empty and the existing_var is implicitly_active()
            bool check1 = (!active_subdomains || active_subdomains->empty()) && existing_var.implicitly_active();

            // Check if the provided active_subdomains is equal to the existing_var's active_subdomains
            bool check2 = (active_subdomains && (*active_subdomains == existing_var.active_subdomains()));

            // If either of these checks passed, then we already have this variable
            if (check1 || check2)
              return _variables[v].number();
          }

        libmesh_error_msg("ERROR: incompatible variable " << var << " has already been added for this system!");
      }

  libmesh_assert(!this->is_initialized());

  if (this->n_variable_groups())
    {
      // Optimize for VariableGroups here - if the user is adding multiple
      // variables of the same FEType and subdomain restriction, catch
      // that here and add them as members of the same VariableGroup.
      //
      // start by setting this flag to whatever the user has requested
      // and then consider the conditions which should negate it.
      bool should_be_in_vg = this->identify_variable_groups();

      VariableGroup & vg(_variable_groups.back());

      // get a pointer to their subdomain restriction, if any.
      const std::set<subdomain_id_type> * const
        their_active_subdomains (vg.implicitly_active() ?
                                 nullptr : &vg.active_subdomains());

      // Different types?
      if (vg.type() != type)
        should_be_in_vg = false;

      // they are restricted, we aren't?
      if (their_active_subdomains &&
          (!active_subdomains || (active_subdomains && active_subdomains->empty())))
        should_be_in_vg = false;

      // they aren't restricted, we are?
      if (!their_active_subdomains && (active_subdomains && !active_subdomains->empty()))
        should_be_in_vg = false;

      if (their_active_subdomains && active_subdomains)
        // restricted to different sets?
        if (*their_active_subdomains != *active_subdomains)
          should_be_in_vg = false;

      // OK, after all that, append the variable to the vg if none of the conditions
      // were violated
      if (should_be_in_vg)
        {
          const unsigned int curr_n_vars = this->n_vars();

          std::string varstr(var);

          _variable_numbers[varstr] = curr_n_vars;
          vg.append (std::move(varstr));
          _variables.push_back(vg(vg.n_variables()-1));

          return curr_n_vars;
        }
    }

  // otherwise, fall back to adding a single variable group
  return this->add_variables (std::vector<std::string>(1, std::string(var)),
                              type,
                              active_subdomains);
}

add_variable() [2/2]

unsigned int libMesh::System::add_variable ( std::string_view  var, const Order  order = FIRST, const FEFamily  family = LAGRANGE, const std::set< subdomain_id_type > *const  active_subdomains = nullptr  )

inherited

Adds the variable var to the list of variables for this system.

Same as before, but assumes LAGRANGE as default value for FEType.family. If active_subdomains is either nullptr (the default) or points to an empty set, then it will be assumed that var has no subdomain restrictions

Definition at line 1459 of file system.C.

References libMesh::System::add_variable().

{
  return this->add_variable(var,
                            FEType(order, family),
                            active_subdomains);
}

add_variables() [1/2]

unsigned int libMesh::System::add_variables ( const std::vector< std::string > &  vars, const FEType &  type, const std::set< subdomain_id_type > *const  active_subdomains = nullptr  )

inherited

Adds the variable var to the list of variables for this system.

If active_subdomains is either nullptr (the default) or points to an empty set, then it will be assumed that var has no subdomain restrictions

Returns

The index number for the new variable.

Definition at line 1471 of file system.C.

References libMesh::System::_variable_groups, libMesh::System::_variable_numbers, libMesh::System::_variables, libMesh::ParallelObject::comm(), libMesh::System::identify_variable_groups(), libMesh::System::is_initialized(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::System::n_components(), libMesh::System::n_variable_groups(), libMesh::System::n_vars(), libMesh::System::variable_name(), and libMesh::System::variable_type().

Referenced by libMesh::System::add_variable(), libMesh::System::add_variables(), and SystemsTest::test100KVariables().

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  libmesh_assert(!this->is_initialized());

  libmesh_assert(this->comm().verify(vars.size()));
  libmesh_assert(this->comm().verify(type));
  libmesh_assert(this->comm().verify((active_subdomains == nullptr)));

  if (active_subdomains)
    libmesh_assert(this->comm().verify(active_subdomains->size()));

  // Make sure the variable isn't there already
  // or if it is, that it's the type we want
  for (auto ovar : vars)
    {
      libmesh_assert(this->comm().verify(ovar));

      for (auto v : make_range(this->n_vars()))
        if (this->variable_name(v) == ovar)
          {
            if (this->variable_type(v) == type)
              return _variables[v].number();

            libmesh_error_msg("ERROR: incompatible variable " << ovar << " has already been added for this system!");
          }
    }

  if (this->n_variable_groups())
    {
      // Optimize for VariableGroups here - if the user is adding multiple
      // variables of the same FEType and subdomain restriction, catch
      // that here and add them as members of the same VariableGroup.
      //
      // start by setting this flag to whatever the user has requested
      // and then consider the conditions which should negate it.
      bool should_be_in_vg = this->identify_variable_groups();

      VariableGroup & vg(_variable_groups.back());

      // get a pointer to their subdomain restriction, if any.
      const std::set<subdomain_id_type> * const
        their_active_subdomains (vg.implicitly_active() ?
                                 nullptr : &vg.active_subdomains());

      // Different types?
      if (vg.type() != type)
        should_be_in_vg = false;

      // they are restricted, we aren't?
      if (their_active_subdomains &&
          (!active_subdomains || (active_subdomains && active_subdomains->empty())))
        should_be_in_vg = false;

      // they aren't restricted, we are?
      if (!their_active_subdomains && (active_subdomains && !active_subdomains->empty()))
        should_be_in_vg = false;

      if (their_active_subdomains && active_subdomains)
        // restricted to different sets?
        if (*their_active_subdomains != *active_subdomains)
          should_be_in_vg = false;

      // If after all that none of the conditions were violated,
      // append the variables to the vg and we're done
      if (should_be_in_vg)
        {
          unsigned int curr_n_vars = this->n_vars();

          for (auto ovar : vars)
            {
              curr_n_vars = this->n_vars();

              vg.append (ovar);

              _variables.push_back(vg(vg.n_variables()-1));
              _variable_numbers[ovar] = curr_n_vars;
            }
          return curr_n_vars;
        }
    }

  const unsigned int curr_n_vars = this->n_vars();

  const unsigned int next_first_component = this->n_components();

  // We weren't able to add to an existing variable group, so
  // add a new variable group to the list
  _variable_groups.push_back((active_subdomains == nullptr) ?
                             VariableGroup(this, vars, curr_n_vars,
                                           next_first_component, type) :
                             VariableGroup(this, vars, curr_n_vars,
                                           next_first_component, type, *active_subdomains));

  const VariableGroup & vg (_variable_groups.back());

  // Add each component of the group individually
  for (auto v : make_range(vars.size()))
    {
      _variables.push_back (vg(v));
      _variable_numbers[vars[v]] = curr_n_vars+v;
    }

  libmesh_assert_equal_to ((curr_n_vars+vars.size()), this->n_vars());

  // BSK - Defer this now to System::init_data() so we can detect
  // VariableGroups 12/28/2012
  // // Add the variable group to the _dof_map
  // _dof_map->add_variable_group (vg);

  // Return the number of the new variable
  return cast_int<unsigned int>(curr_n_vars+vars.size()-1);
}

add_variables() [2/2]

unsigned int libMesh::System::add_variables ( const std::vector< std::string > &  vars, const Order  order = FIRST, const FEFamily  family = LAGRANGE, const std::set< subdomain_id_type > *const  active_subdomains = nullptr  )

inherited

Adds the variable var to the list of variables for this system.

Same as before, but assumes LAGRANGE as default value for FEType.family. If active_subdomains is either nullptr (the default) or points to an empty set, then it will be assumed that var has no subdomain restrictions

Definition at line 1590 of file system.C.

References libMesh::System::add_variables().

{
  return this->add_variables(vars,
                             FEType(order, family),
                             active_subdomains);
}

add_vector()

NumericVector< Number > & libMesh::System::add_vector ( std::string_view  vec_name, const bool  projections = true, const ParallelType  type = PARALLEL  )

inherited

Adds the additional vector vec_name to this system.

All the additional vectors are similarly distributed, like the solution, and initialized to zero.

By default vectors added by add_vector are projected to changed grids by reinit(). To zero them instead (more efficient), pass "false" as the second argument

If the vector already exists, the existing vector is returned. after any upgrade to the projections or type has been made. We only handle upgrades (projections false->true, or type PARALLEL->GHOSTED) in this fashion, not downgrades, on the theory that if two codes have differing needs we want to support the union of those needs, not the intersection. Downgrades can only be accomplished manually, via set_vector_preservation() or by setting a vector type() and re-initializing.

Definition at line 768 of file system.C.

References libMesh::System::_dof_map, libMesh::System::_is_initialized, libMesh::System::_vector_is_adjoint, libMesh::System::_vector_projections, libMesh::System::_vectors, libMesh::NumericVector< T >::build(), libMesh::NumericVector< T >::close(), libMesh::NumericVector< T >::closed(), libMesh::ParallelObject::comm(), libMesh::default_solver_package(), libMesh::GHOSTED, libMesh::NumericVector< T >::initialized(), libMesh::libmesh_assert(), libMesh::System::n_dofs(), libMesh::System::n_local_dofs(), libMesh::ParallelObject::n_processors(), libMesh::PARALLEL, libMesh::SERIAL, libMesh::NumericVector< T >::set_type(), libMesh::NumericVector< T >::swap(), and libMesh::NumericVector< T >::type().

Referenced by libMesh::System::add_adjoint_rhs(), libMesh::System::add_adjoint_solution(), libMesh::System::add_sensitivity_rhs(), libMesh::System::add_sensitivity_solution(), libMesh::ExplicitSystem::add_system_rhs(), libMesh::System::add_weighted_sensitivity_adjoint_solution(), libMesh::System::add_weighted_sensitivity_solution(), alternative_fe_assembly(), libMesh::AdjointRefinementEstimator::estimate_error(), fe_assembly(), form_functionA(), form_functionB(), libMesh::SecondOrderUnsteadySolver::init(), libMesh::UnsteadySolver::init(), libMesh::UnsteadySolver::init_adjoints(), libMesh::TimeSolver::init_adjoints(), libMesh::OptimizationSystem::init_data(), init_data(), main(), libMesh::NewmarkSystem::NewmarkSystem(), libMesh::System::read_header(), libMesh::FrequencySystem::set_frequencies(), libMesh::FrequencySystem::set_frequencies_by_range(), libMesh::FrequencySystem::set_frequencies_by_steps(), SystemsTest::testAddVectorProjChange(), SystemsTest::testAddVectorTypeChange(), SystemsTest::testPostInitAddVector(), and SystemsTest::testPostInitAddVectorTypeChange().

{
  parallel_object_only();

  libmesh_assert(this->comm().verify(std::string(vec_name)));
  libmesh_assert(this->comm().verify(int(type)));
  libmesh_assert(this->comm().verify(projections));

  // Return the vector if it is already there.
  if (auto it = this->_vectors.find(vec_name);
      it != this->_vectors.end())
    {
      // If the projection setting has *upgraded*, change it.
      if (projections) // only do expensive lookup if needed
        libmesh_map_find(_vector_projections, vec_name) = projections;

      NumericVector<Number> & vec = *it->second;

      // If we're in serial, our vectors are effectively SERIAL, so
      // we'll ignore any type setting.  If we're in parallel, we
      // might have a type change to deal with.

      if (this->n_processors() > 1)
        {
          // If the type setting has changed in a way we can't
          // perceive as an upgrade or a downgrade, scream.
          libmesh_assert_equal_to(type == SERIAL,
                                  vec.type() == SERIAL);

          // If the type setting has *upgraded*, change it.
          if (type == GHOSTED && vec.type() == PARALLEL)
            {
              // A *really* late upgrade is expensive, but better not
              // to risk zeroing data.
              if (vec.initialized())
                {
                  if (!vec.closed())
                    vec.close();

                  // Ideally we'd move parallel coefficients and then
                  // add ghosted coefficients, but copy and swap is
                  // simpler.  If anyone actually ever uses this case
                  // for real we can look into optimizing it.
                  auto new_vec = NumericVector<Number>::build(this->comm());
#ifdef LIBMESH_ENABLE_GHOSTED
                  new_vec->init (this->n_dofs(), this->n_local_dofs(),
                                 _dof_map->get_send_list(), /*fast=*/false,
                                 GHOSTED);
#else
                  libmesh_error_msg("Cannot initialize ghosted vectors when they are not enabled.");
#endif

                  *new_vec = vec;
                  vec.swap(*new_vec);
                }
              else
                // The PARALLEL vec is not yet initialized, so we can
                // just "upgrade" it to GHOSTED.
                vec.set_type(type);
            }
        }

      // Any upgrades are done; we're happy here.
      return vec;
    }

  // Otherwise, build the vector. The following emplace() is
  // guaranteed to succeed because, if we made it here, we don't
  // already have a vector named "vec_name". We pass the user's
  // requested ParallelType directly to NumericVector::build() so
  // that, even if the vector is not initialized now, it will get the
  // right type when it is initialized later.
  auto pr =
    _vectors.emplace(vec_name,
                     NumericVector<Number>::build(this->comm(),
                                                  libMesh::default_solver_package(),
                                                  type));
  auto buf = pr.first->second.get();
  _vector_projections.emplace(vec_name, projections);

  // Vectors are primal by default
  _vector_is_adjoint.emplace(vec_name, -1);

  // Initialize it if necessary
  if (_is_initialized)
    {
      if (type == GHOSTED)
        {
#ifdef LIBMESH_ENABLE_GHOSTED
          buf->init (this->n_dofs(), this->n_local_dofs(),
                     _dof_map->get_send_list(), /*fast=*/false,
                     GHOSTED);
#else
          libmesh_error_msg("Cannot initialize ghosted vectors when they are not enabled.");
#endif
        }
      else
        buf->init (this->n_dofs(), this->n_local_dofs(), false, type);
    }

  return *buf;
}

add_weighted_sensitivity_adjoint_solution()

NumericVector< Number > & libMesh::System::add_weighted_sensitivity_adjoint_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's weighted sensitivity adjoint solution vectors, by default the one corresponding to the first qoi. Creates the vector if it doesn't already exist.

Definition at line 1265 of file system.C.

References libMesh::System::add_vector(), and libMesh::System::set_vector_as_adjoint().

Referenced by libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve().

{
  std::ostringstream adjoint_name;
  adjoint_name << "weighted_sensitivity_adjoint_solution" << i;

  NumericVector<Number> & returnval = this->add_vector(adjoint_name.str());
  this->set_vector_as_adjoint(adjoint_name.str(), i);
  return returnval;
}

add_weighted_sensitivity_solution()

NumericVector< Number > & libMesh::System::add_weighted_sensitivity_solution ( )

inherited

Returns

A reference to the solution of the last weighted sensitivity solve Creates the vector if it doesn't already exist.

Definition at line 1212 of file system.C.

References libMesh::System::add_vector().

Referenced by libMesh::ImplicitSystem::weighted_sensitivity_solve().

{
  return this->add_vector("weighted_sensitivity_solution");
}

adjoint_qoi_parameter_sensitivity()

void libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity ( const QoISet &  qoi_indices, const ParameterVector &  parameters, SensitivityData &  sensitivities  )

overridevirtualinherited

Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j].

Uses adjoint_solve() and the adjoint sensitivity method.

Currently uses finite differenced derivatives (partial q / partial p) and (partial R / partial p).

Reimplemented from libMesh::System.

Definition at line 513 of file implicit_system.C.

References libMesh::ImplicitSystem::adjoint_solve(), libMesh::SensitivityData::allocate_data(), libMesh::ExplicitSystem::assemble_qoi(), libMesh::ImplicitSystem::assemble_residual_derivatives(), libMesh::NumericVector< T >::dot(), libMesh::System::get_qoi_values(), libMesh::System::get_sensitivity_rhs(), libMesh::QoISet::has_index(), libMesh::System::is_adjoint_already_solved(), libMesh::System::n_qois(), libMesh::Real, libMesh::ParameterVector::size(), and libMesh::TOLERANCE.

Referenced by libMesh::UnsteadySolver::integrate_adjoint_sensitivity(), and main().

{
  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  const unsigned int Np = cast_int<unsigned int>
    (parameters_vec.size());
  const unsigned int Nq = this->n_qois();

  // An introduction to the problem:
  //
  // Residual R(u(p),p) = 0
  // partial R / partial u = J = system matrix
  //
  // This implies that:
  // d/dp(R) = 0
  // (partial R / partial p) +
  // (partial R / partial u) * (partial u / partial p) = 0

  // We first do an adjoint solve:
  // J^T * z = (partial q / partial u)
  // if we haven't already or dont have an initial condition for the adjoint
  if (!this->is_adjoint_already_solved())
    {
      this->adjoint_solve(qoi_indices);
    }

  this->assemble_residual_derivatives(parameters_in);

  // Get ready to fill in sensitivities:
  sensitivities.allocate_data(qoi_indices, *this, parameters_vec);

  // We use the identities:
  // dq/dp = (partial q / partial p) + (partial q / partial u) *
  //         (partial u / partial p)
  // dq/dp = (partial q / partial p) + (J^T * z) *
  //         (partial u / partial p)
  // dq/dp = (partial q / partial p) + z * J *
  //         (partial u / partial p)

  // Leading to our final formula:
  // dq/dp = (partial q / partial p) - z * (partial R / partial p)

  // In the case of adjoints with heterogenous Dirichlet boundary
  // function phi, where
  // q :=  S(u) - R(u,phi)
  // the final formula works out to:
  // dq/dp = (partial S / partial p) - z * (partial R / partial p)
  // Because we currently have no direct access to
  // (partial S / partial p), we use the identity
  // (partial S / partial p) = (partial q / partial p) +
  //                           phi * (partial R / partial p)
  // to derive an equivalent equation:
  // dq/dp = (partial q / partial p) - (z-phi) * (partial R / partial p)

  // Since z-phi degrees of freedom are zero for constrained indices,
  // we can use the same constrained -(partial R / partial p) that we
  // use for forward sensitivity solves, taking into account the
  // differing sign convention.
  //
  // Since that vector is constrained, its constrained indices are
  // zero, so its product with phi is zero, so we can neglect the
  // evaluation of phi terms.

  for (unsigned int j=0; j != Np; ++j)
    {
      // We currently get partial derivatives via central differencing

      // (partial q / partial p) ~= (q(p+dp)-q(p-dp))/(2*dp)
      // (partial R / partial p) ~= (rhs(p+dp) - rhs(p-dp))/(2*dp)

      Number old_parameter = *parameters_vec[j];

      const Real delta_p =
        TOLERANCE * std::max(std::abs(old_parameter), 1e-3);

      *parameters_vec[j] = old_parameter - delta_p;
      this->assemble_qoi(qoi_indices);
      const std::vector<Number> qoi_minus = this->get_qoi_values();

      NumericVector<Number> & neg_partialR_partialp = this->get_sensitivity_rhs(j);

      *parameters_vec[j] = old_parameter + delta_p;
      this->assemble_qoi(qoi_indices);
      const std::vector<Number> qoi_plus = this->get_qoi_values();

      std::vector<Number> partialq_partialp(Nq, 0);
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          partialq_partialp[i] = (qoi_plus[i] - qoi_minus[i]) / (2.*delta_p);

      // Don't leave the parameter changed
      *parameters_vec[j] = old_parameter;

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          sensitivities[i][j] = partialq_partialp[i] +
            neg_partialR_partialp.dot(this->get_adjoint_solution(i));
    }

  // All parameters_vec have been reset.
  // Reset the original qoi.

  this->assemble_qoi(qoi_indices);
}

adjoint_solve()

std::pair< unsigned int, Real > libMesh::DifferentiableSystem::adjoint_solve ( const QoISet &  qoi_indices = QoISet() )

overridevirtualinherited

This function sets the _is_adjoint boolean member of TimeSolver to true and then calls the adjoint_solve in implicit system.

Reimplemented from libMesh::ImplicitSystem.

Definition at line 150 of file diff_system.C.

References libMesh::DifferentiableSystem::get_time_solver(), libMesh::TimeSolver::set_is_adjoint(), and libMesh::DifferentiableSystem::time_solver.

Referenced by main().

{
  // Get the time solver object associated with the system, and tell it that
  // we are solving the adjoint problem
  this->get_time_solver().set_is_adjoint(true);

  return time_solver->adjoint_solve(qoi_indices);

  //return this->ImplicitSystem::adjoint_solve(qoi_indices);
}

advance_arcstep()

void libMesh::ContinuationSystem::advance_arcstep

(

)

Call this function after a continuation solve to compute the tangent and get the next initial guess.

Definition at line 936 of file continuation_system.C.

References solve_tangent(), and update_solution().

{
  // Solve for the updated tangent du1/ds, d(lambda1)/ds
  solve_tangent();

  // Advance the solution and the parameter to the next value.
  update_solution();
}

apply_predictor()

void libMesh::ContinuationSystem::apply_predictor ( )

private

Applies the predictor to the current solution to get a guess for the next solution.

Definition at line 1375 of file continuation_system.C.

References AB2, continuation_parameter, dlambda_ds, ds_current, du_ds, Euler, predictor, previous_dlambda_ds, previous_ds, previous_du_ds, libMesh::Real, and libMesh::System::solution.

Referenced by continuation_solve(), and update_solution().

{
  if (predictor == Euler)
    {
      // 1.) Euler Predictor
      // Predict next the solution
      solution->add(ds_current, *du_ds);
      solution->close();

      // Predict next parameter value
      *continuation_parameter += ds_current*dlambda_ds;
    }


  else if (predictor == AB2)
    {
      // 2.) 2nd-order explicit AB predictor
      libmesh_assert_not_equal_to (previous_ds, 0.0);
      const Real stepratio = ds_current/previous_ds;

      // Build up next solution value.
      solution->add( 0.5*ds_current*(2.+stepratio), *du_ds);
      solution->add(-0.5*ds_current*stepratio     , *previous_du_ds);
      solution->close();

      // Next parameter value
      *continuation_parameter +=
        0.5*ds_current*((2.+stepratio)*dlambda_ds -
                        stepratio*previous_dlambda_ds);
    }

  else
    libmesh_error_msg("Unknown predictor!");
}

assemble()

void libMesh::DifferentiableSystem::assemble ( )

overridevirtualinherited

Prepares matrix and rhs for matrix assembly.

Users should not reimplement this. Note that in some cases only current_local_solution is used during assembly, and, therefore, if solution has been altered without update() being called, then the user must call update() before calling this function.

Reimplemented from libMesh::ImplicitSystem.

Definition at line 131 of file diff_system.C.

References libMesh::DifferentiableSystem::assembly().

{
  this->assembly(true, true);
}

assemble_qoi()

void FEMSystem::assemble_qoi ( const QoISet &  indices = QoISet() )

overridevirtualinherited

Runs a qoi assembly loop over all elements, and if assemble_qoi_sides is true over all sides.

Users may have to override this function if they have any quantities of interest that are not expressible as a sum of element qois.

Reimplemented from libMesh::ExplicitSystem.

Definition at line 1147 of file fem_system.C.

References libMesh::ParallelObject::comm(), libMesh::System::get_mesh(), libMesh::DifferentiableSystem::get_qoi(), libMesh::System::get_qoi_values(), libMesh::QoISet::has_index(), mesh, libMesh::System::n_qois(), libMesh::DifferentiableQoI::parallel_op(), libMesh::Threads::parallel_reduce(), libMesh::StoredRange< iterator_type, object_type >::reset(), libMesh::System::set_qoi(), and libMesh::System::update().

{
  LOG_SCOPE("assemble_qoi()", "FEMSystem");

  const MeshBase & mesh = this->get_mesh();

  this->update();

  const unsigned int Nq = this->n_qois();

  // the quantity of interest is assumed to be a sum of element and
  // side terms
  for (unsigned int i=0; i != Nq; ++i)
    if (qoi_indices.has_index(i))
      this->set_qoi(i, 0);

  // Create a non-temporary qoi_contributions object, so we can query
  // its results after the reduction
  QoIContributions qoi_contributions(*this, *(this->get_qoi()), qoi_indices);

  // Loop over every active mesh element on this processor
  Threads::parallel_reduce(elem_range.reset(mesh.active_local_elements_begin(),
                                            mesh.active_local_elements_end()),
                           qoi_contributions);

  std::vector<Number> global_qoi = this->get_qoi_values();
  this->get_qoi()->parallel_op( this->comm(), global_qoi, qoi_contributions.qoi, qoi_indices );
  this->set_qoi(std::move(global_qoi));
}

assemble_qoi_derivative()

void FEMSystem::assemble_qoi_derivative ( const QoISet &  qoi_indices = QoISet(), bool  include_liftfunc = true, bool  apply_constraints = true  )

overridevirtualinherited

Runs a qoi derivative assembly loop over all elements, and if assemble_qoi_sides is true over all sides.

Users may have to override this function for quantities of interest that are not expressible as a sum of element qois.

Reimplemented from libMesh::ExplicitSystem.

Definition at line 1179 of file fem_system.C.

References libMesh::System::add_adjoint_rhs(), libMesh::DifferentiableQoI::finalize_derivative(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_mesh(), libMesh::DifferentiableSystem::get_qoi(), libMesh::QoISet::has_index(), libMesh::make_range(), mesh, libMesh::System::n_qois(), libMesh::Threads::parallel_for(), libMesh::StoredRange< iterator_type, object_type >::reset(), libMesh::System::update(), and libMesh::NumericVector< T >::zero().

{
  LOG_SCOPE("assemble_qoi_derivative()", "FEMSystem");

  const MeshBase & mesh = this->get_mesh();

  this->update();

  // The quantity of interest derivative assembly accumulates on
  // initially zero vectors
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      this->add_adjoint_rhs(i).zero();

  // Loop over every active mesh element on this processor
  Threads::parallel_for (elem_range.reset(mesh.active_local_elements_begin(),
                                          mesh.active_local_elements_end()),
                         QoIDerivativeContributions(*this, qoi_indices,
                                                    *(this->get_qoi()),
                                                    include_liftfunc,
                                                    apply_constraints));

  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      this->get_qoi()->finalize_derivative(this->get_adjoint_rhs(i),i);
}

assemble_residual_derivatives()

void libMesh::ImplicitSystem::assemble_residual_derivatives ( const ParameterVector &  parameters )

overridevirtualinherited

Residual parameter derivative function.

Uses finite differences by default.

This will assemble the sensitivity rhs vectors to hold -(partial R / partial p_i), making them ready to solve the forward sensitivity equation.

Can be overridden in derived classes.

Reimplemented from libMesh::System.

Definition at line 470 of file implicit_system.C.

References libMesh::System::add_sensitivity_rhs(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::ParameterVector::size(), and libMesh::TOLERANCE.

Referenced by libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity(), and libMesh::ImplicitSystem::sensitivity_solve().

{
  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  const unsigned int Np = cast_int<unsigned int>
    (parameters_vec.size());

  for (unsigned int p=0; p != Np; ++p)
    {
      NumericVector<Number> & sensitivity_rhs = this->add_sensitivity_rhs(p);

      // Approximate -(partial R / partial p) by
      // (R(p-dp) - R(p+dp)) / (2*dp)

      Number old_parameter = *parameters_vec[p];

      const Real delta_p =
        TOLERANCE * std::max(std::abs(old_parameter), 1e-3);

      *parameters_vec[p] -= delta_p;

      //      this->assembly(true, false, true);
      this->assembly(true, false, false);
      this->rhs->close();
      sensitivity_rhs = *this->rhs;

      *parameters_vec[p] = old_parameter + delta_p;

      //      this->assembly(true, false, true);
      this->assembly(true, false, false);
      this->rhs->close();

      sensitivity_rhs -= *this->rhs;
      sensitivity_rhs /= (2*delta_p);
      sensitivity_rhs.close();

      *parameters_vec[p] = old_parameter;
    }
}

assembly()

void FEMSystem::assembly ( bool  get_residual, bool  get_jacobian, bool  apply_heterogeneous_constraints = false, bool  apply_no_constraints = false  )

overridevirtualinherited

Prepares matrix or rhs for matrix assembly.

Users may reimplement this to add pre- or post-assembly code before or after calling FEMSystem::assembly(). Note that in some cases only current_local_solution is used during assembly, and, therefore, if solution has been altered without update() being called, then the user must call update() before calling this function.

Implements libMesh::DifferentiableSystem.

Reimplemented in libMesh::VariationalSmootherSystem.

Definition at line 880 of file fem_system.C.

References libMesh::DenseMatrix< T >::add(), libMesh::FEMSystem::build_context(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::err, libMesh::FEType::family, libMesh::DiffContext::get_elem_jacobian(), libMesh::DiffContext::get_elem_residual(), libMesh::System::get_mesh(), libMesh::FEMSystem::init_context(), libMesh::NumericVector< T >::l1_norm(), libMesh::DenseMatrix< T >::l1_norm(), libMesh::SparseMatrix< T >::l1_norm(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::ImplicitSystem::matrix, mesh, libMesh::ParallelObject::n_processors(), libMesh::System::n_variable_groups(), libMesh::FEMSystem::numerical_nonlocal_jacobian(), libMesh::out, libMesh::Threads::parallel_for(), libMesh::FEMContext::pre_fe_reinit(), libMesh::BasicOStreamProxy< charT, traits >::precision(), libMesh::DifferentiableSystem::print_jacobian_norms, libMesh::DifferentiableSystem::print_jacobians, libMesh::DifferentiableSystem::print_residual_norms, libMesh::DifferentiableSystem::print_residuals, libMesh::DifferentiableSystem::print_solution_norms, libMesh::DifferentiableSystem::print_solutions, libMesh::ParallelObject::processor_id(), libMesh::Real, libMesh::StoredRange< iterator_type, object_type >::reset(), libMesh::ExplicitSystem::rhs, libMesh::SCALAR, libMesh::DenseVector< T >::size(), libMesh::System::solution, libMesh::DifferentiableSystem::time_solver, libMesh::Variable::type(), libMesh::System::variable_group(), libMesh::FEMSystem::verify_analytic_jacobians, libMesh::DenseMatrix< T >::zero(), libMesh::NumericVector< T >::zero(), and libMesh::SparseMatrix< T >::zero().

Referenced by libMesh::VariationalSmootherSystem::assembly(), continuation_solve(), HeatSystem::perturb_accumulate_residuals(), and solve_tangent().

{
  libmesh_assert(get_residual || get_jacobian);

  // Log residual and jacobian and combined performance separately
#ifdef LIBMESH_ENABLE_PERFORMANCE_LOGGING
  const char * log_name;
  if (get_residual && get_jacobian)
    log_name = "assembly()";
  else if (get_residual)
    log_name = "assembly(get_residual)";
  else
    log_name = "assembly(get_jacobian)";

  LOG_SCOPE(log_name, "FEMSystem");
#endif

  const MeshBase & mesh = this->get_mesh();

  if (print_solution_norms)
    {
      this->solution->close();

      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "|U| = "
                   << this->solution->l1_norm()
                   << std::endl;
      libMesh::out.precision(old_precision);
    }
  if (print_solutions)
    {
      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "U = [" << *(this->solution)
                   << "];" << std::endl;
      libMesh::out.precision(old_precision);
    }

  // Is this definitely necessary? [RHS]
  // Yes. [RHS 2012]
  if (get_jacobian)
    matrix->zero();
  if (get_residual)
    rhs->zero();

  // Stupid C++ lets you set *Real* verify_analytic_jacobians = true!
  if (verify_analytic_jacobians > 0.5)
    {
      libMesh::err << "WARNING!  verify_analytic_jacobians was set "
                   << "to absurdly large value of "
                   << verify_analytic_jacobians << std::endl;
      libMesh::err << "Resetting to 1e-6!" << std::endl;
      verify_analytic_jacobians = 1e-6;
    }

  // In time-dependent problems, the nonlinear function we're trying
  // to solve at each timestep may depend on the particular solver
  // we're using
  libmesh_assert(time_solver.get());

  // Build the residual and jacobian contributions on every active
  // mesh element on this processor
  Threads::parallel_for
    (elem_range.reset(mesh.active_local_elements_begin(),
                      mesh.active_local_elements_end()),
     AssemblyContributions(*this, get_residual, get_jacobian,
                           apply_heterogeneous_constraints,
                           apply_no_constraints));

  // Check and see if we have SCALAR variables
  bool have_scalar = false;
  for (auto i : make_range(this->n_variable_groups()))
    {
      if (this->variable_group(i).type().family == SCALAR)
        {
          have_scalar = true;
          break;
        }
    }

  // SCALAR dofs are stored on the last processor, so we'll evaluate
  // their equation terms there and only if we have a SCALAR variable
  if (this->processor_id() == (this->n_processors()-1) && have_scalar)
    {
      std::unique_ptr<DiffContext> con = this->build_context();
      FEMContext & _femcontext = cast_ref<FEMContext &>(*con);
      this->init_context(_femcontext);
      _femcontext.pre_fe_reinit(*this, nullptr);

      bool jacobian_computed =
        this->time_solver->nonlocal_residual(get_jacobian, _femcontext);

      // Nonlocal residuals are likely to be length 0, in which case we
      // don't need to do any more.  And we shouldn't try to do any
      // more; lots of DenseVector/DenseMatrix code assumes rank>0.
      if (_femcontext.get_elem_residual().size())
        {
          // Compute a numeric jacobian if we have to
          if (get_jacobian && !jacobian_computed)
            {
              // Make sure we didn't compute a jacobian and lie about it
              libmesh_assert_equal_to (_femcontext.get_elem_jacobian().l1_norm(), 0.0);
              // Logging of numerical jacobians is done separately
              this->numerical_nonlocal_jacobian(_femcontext);
            }

          // Compute a numeric jacobian if we're asked to verify the
          // analytic jacobian we got
          if (get_jacobian && jacobian_computed &&
              this->verify_analytic_jacobians != 0.0)
            {
              DenseMatrix<Number> analytic_jacobian(_femcontext.get_elem_jacobian());

              _femcontext.get_elem_jacobian().zero();
              // Logging of numerical jacobians is done separately
              this->numerical_nonlocal_jacobian(_femcontext);

              Real analytic_norm = analytic_jacobian.l1_norm();
              Real numerical_norm = _femcontext.get_elem_jacobian().l1_norm();

              // If we can continue, we'll probably prefer the analytic jacobian
              analytic_jacobian.swap(_femcontext.get_elem_jacobian());

              // The matrix "analytic_jacobian" will now hold the error matrix
              analytic_jacobian.add(-1.0, _femcontext.get_elem_jacobian());
              Real error_norm = analytic_jacobian.l1_norm();

              Real relative_error = error_norm /
                std::max(analytic_norm, numerical_norm);

              if (relative_error > this->verify_analytic_jacobians)
                {
                  libMesh::err << "Relative error " << relative_error
                               << " detected in analytic jacobian on nonlocal dofs!"
                               << std::endl;

                  std::streamsize old_precision = libMesh::out.precision();
                  libMesh::out.precision(16);
                  libMesh::out << "J_analytic nonlocal = "
                               << _femcontext.get_elem_jacobian() << std::endl;
                  analytic_jacobian.add(1.0, _femcontext.get_elem_jacobian());
                  libMesh::out << "J_numeric nonlocal = "
                               << analytic_jacobian << std::endl;

                  libMesh::out.precision(old_precision);

                  libmesh_error_msg("Relative error too large, exiting!");
                }
            }

          add_element_system
            (*this, get_residual, get_jacobian,
             apply_heterogeneous_constraints, apply_no_constraints, _femcontext);
        }
    }

  if (get_residual && (print_residual_norms || print_residuals))
    this->rhs->close();
  if (get_residual && print_residual_norms)
    {
      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "|F| = " << this->rhs->l1_norm() << std::endl;
      libMesh::out.precision(old_precision);
    }
  if (get_residual && print_residuals)
    {
      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "F = [" << *(this->rhs) << "];" << std::endl;
      libMesh::out.precision(old_precision);
    }

  if (get_jacobian && (print_jacobian_norms || print_jacobians))
    this->matrix->close();
  if (get_jacobian && print_jacobian_norms)
    {
      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "|J| = " << this->matrix->l1_norm() << std::endl;
      libMesh::out.precision(old_precision);
    }
  if (get_jacobian && print_jacobians)
    {
      std::streamsize old_precision = libMesh::out.precision();
      libMesh::out.precision(16);
      libMesh::out << "J = [" << *(this->matrix) << "];" << std::endl;
      libMesh::out.precision(old_precision);
    }
}

attach_assemble_function()

void libMesh::System::attach_assemble_function ( void   fptrEquationSystems &es, const std::string &name )

inherited

Register a user function to use in assembling the system matrix and RHS.

Definition at line 2161 of file system.C.

References libMesh::System::_assemble_system_function, libMesh::System::_assemble_system_object, fptr(), and libMesh::libmesh_assert().

Referenced by assemble_and_solve(), main(), ConstraintOperatorTest::test1DCoarseningNewNodes(), ConstraintOperatorTest::test1DCoarseningOperator(), SystemsTest::testAssemblyWithDgFemContext(), ConstraintOperatorTest::testCoreform(), SystemsTest::testDofCouplingWithVarGroups(), and PeriodicBCTest::testPeriodicBC().

{
  libmesh_assert(fptr);

  if (_assemble_system_object != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both assembly function and object!");

      _assemble_system_object = nullptr;
    }

  _assemble_system_function = fptr;
}

attach_assemble_object()

void libMesh::System::attach_assemble_object ( System::Assembly &  assemble_in )

inherited

Register a user object to use in assembling the system matrix and RHS.

Definition at line 2178 of file system.C.

References libMesh::System::_assemble_system_function, and libMesh::System::_assemble_system_object.

Referenced by main().

{
  if (_assemble_system_function != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both assembly object and function!");

      _assemble_system_function = nullptr;
    }

  _assemble_system_object = &assemble_in;
}

attach_constraint_function()

void libMesh::System::attach_constraint_function ( void   fptrEquationSystems &es, const std::string &name )

inherited

Register a user function for imposing constraints.

Definition at line 2192 of file system.C.

References libMesh::System::_constrain_system_function, libMesh::System::_constrain_system_object, fptr(), and libMesh::libmesh_assert().

{
  libmesh_assert(fptr);

  if (_constrain_system_object != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both constraint function and object!");

      _constrain_system_object = nullptr;
    }

  _constrain_system_function = fptr;
}

attach_constraint_object()

void libMesh::System::attach_constraint_object ( System::Constraint &  constrain )

inherited

Register a user object for imposing constraints.

Definition at line 2209 of file system.C.

References libMesh::System::_constrain_system_function, and libMesh::System::_constrain_system_object.

Referenced by libMesh::VariationalMeshSmoother::smooth(), and DofMapTest::testConstraintLoopDetection().

{
  if (_constrain_system_function != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both constraint object and function!");

      _constrain_system_function = nullptr;
    }

  _constrain_system_object = &constrain;
}

attach_init_function()

void libMesh::System::attach_init_function ( void   fptrEquationSystems &es, const std::string &name )

inherited

Register a user function to use in initializing the system.

Definition at line 2130 of file system.C.

References libMesh::System::_init_system_function, libMesh::System::_init_system_object, fptr(), and libMesh::libmesh_assert().

Referenced by main().

{
  libmesh_assert(fptr);

  if (_init_system_object != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both initialization function and object!");

      _init_system_object = nullptr;
    }

  _init_system_function = fptr;
}

attach_init_object()

void libMesh::System::attach_init_object ( System::Initialization &  init_in )

inherited

Register a user class to use to initialize the system.

Note

This is exclusive with the attach_init_function.

Definition at line 2147 of file system.C.

References libMesh::System::_init_system_function, and libMesh::System::_init_system_object.

{
  if (_init_system_function != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both initialization object and function!");

      _init_system_function = nullptr;
    }

  _init_system_object = &init_in;
}

attach_physics()

void libMesh::DifferentiableSystem::attach_physics ( DifferentiablePhysics *  physics_in )

inlineinherited

Attach external Physics object.

Definition at line 200 of file diff_system.h.

References libMesh::DifferentiableSystem::_diff_physics, and libMesh::DifferentiablePhysics::clone_physics().

  { this->_diff_physics.push(physics_in->clone_physics());
    this->_diff_physics.top()->init_physics(*this);}

attach_qoi()

void libMesh::DifferentiableSystem::attach_qoi ( DifferentiableQoI *  qoi_in )

inherited

Attach external QoI object.

Definition at line 279 of file diff_system.C.

References libMesh::DifferentiableSystem::_diff_qoi, libMesh::DifferentiableQoI::clone(), libMesh::libmesh_assert(), and libMesh::System::qoi.

Referenced by main().

{
  this->_diff_qoi = {};
  this->_diff_qoi.push(qoi_in->clone());

  auto & dq = this->_diff_qoi.top();
  // User needs to resize qoi system qoi accordingly
#ifdef LIBMESH_ENABLE_DEPRECATED
  // Call the old API for backwards compatibility
  dq->init_qoi( this->qoi );

  // Then the new API for forwards compatibility
  dq->init_qoi_count( *this );
#else
#ifndef NDEBUG
  // Make sure the user has updated their QoI subclass - call the old
  // API and make sure it does nothing
  std::vector<Number> deprecated_vector;
  dq->init_qoi( deprecated_vector );
  libmesh_assert(deprecated_vector.empty());
#endif

  // Then the new API
  dq->init_qoi_count( *this );
#endif
}

attach_QOI_derivative()

void libMesh::System::attach_QOI_derivative ( void   fptrEquationSystems &es, const std::string &name, const QoISet &qoi_indices, bool include_liftfunc, bool apply_constraints )

inherited

Register a user function for evaluating derivatives of a quantity of interest with respect to test functions, whose values should be placed in System::rhs.

Definition at line 2266 of file system.C.

References libMesh::System::_qoi_evaluate_derivative_function, libMesh::System::_qoi_evaluate_derivative_object, fptr(), and libMesh::libmesh_assert().

{
  libmesh_assert(fptr);

  if (_qoi_evaluate_derivative_object != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both QOI derivative function and object!");

      _qoi_evaluate_derivative_object = nullptr;
    }

  _qoi_evaluate_derivative_function = fptr;
}

attach_QOI_derivative_object()

void libMesh::System::attach_QOI_derivative_object ( QOIDerivative &  qoi_derivative )

inherited

Register a user object for evaluating derivatives of a quantity of interest with respect to test functions, whose values should be placed in System::rhs.

Definition at line 2283 of file system.C.

References libMesh::System::_qoi_evaluate_derivative_function, and libMesh::System::_qoi_evaluate_derivative_object.

{
  if (_qoi_evaluate_derivative_function != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both QOI derivative object and function!");

      _qoi_evaluate_derivative_function = nullptr;
    }

  _qoi_evaluate_derivative_object = &qoi_derivative;
}

attach_QOI_function()

void libMesh::System::attach_QOI_function ( void   fptrEquationSystems &es, const std::string &name, const QoISet &qoi_indices )

inherited

Register a user function for evaluating the quantities of interest, whose values should be placed in System::qoi.

Definition at line 2234 of file system.C.

References libMesh::System::_qoi_evaluate_function, libMesh::System::_qoi_evaluate_object, fptr(), and libMesh::libmesh_assert().

{
  libmesh_assert(fptr);

  if (_qoi_evaluate_object != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both QOI function and object!");

      _qoi_evaluate_object = nullptr;
    }

  _qoi_evaluate_function = fptr;
}

attach_QOI_object()

void libMesh::System::attach_QOI_object ( QOI &  qoi )

inherited

Register a user object for evaluating the quantities of interest, whose values should be placed in System::qoi.

Definition at line 2252 of file system.C.

References libMesh::System::_qoi_evaluate_function, and libMesh::System::_qoi_evaluate_object.

{
  if (_qoi_evaluate_function != nullptr)
    {
      libmesh_warning("WARNING:  Cannot specify both QOI object and function!");

      _qoi_evaluate_function = nullptr;
    }

  _qoi_evaluate_object = &qoi_in;
}

boundary_project_solution() [1/2]

void libMesh::System::boundary_project_solution ( const std::set< boundary_id_type > &  b, const std::vector< unsigned int > &  variables, FunctionBase< Number > *  f, FunctionBase< Gradient > *  g = nullptr  )

inherited

Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary boundary function onto the solution via L2 projections and nodal interpolations on each element.

Only degrees of freedom which affect the function's trace on a boundary in the set b are affected. Only degrees of freedom associated with the variables listed in the vector variables are projected. The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Definition at line 1253 of file system_projection.C.

Referenced by SystemsTest::testBoundaryProjectCube().

{
  this->boundary_project_vector(b, variables, *solution, f, g);

  solution->localize(*current_local_solution);
}

boundary_project_solution() [2/2]

void libMesh::System::boundary_project_solution ( const std::set< boundary_id_type > &  b, const std::vector< unsigned int > &  variables, ValueFunctionPointer  fptr, GradientFunctionPointer  gptr, const Parameters &  parameters  )

inherited

Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system.

This method projects components of an arbitrary boundary function onto the solution via L2 projections and nodal interpolations on each element.

Only degrees of freedom which affect the function's trace on a boundary in the set b are affected. Only degrees of freedom associated with the variables listed in the vector variables are projected. The function value fptr and its gradient gptr are represented by function pointers. A gradient gptr is only required/used for projecting onto finite element spaces with continuous derivatives.

Definition at line 1236 of file system_projection.C.

References fptr(), and gptr().

{
  WrappedFunction<Number> f(*this, fptr, &function_parameters);
  WrappedFunction<Gradient> g(*this, gptr, &function_parameters);
  this->boundary_project_solution(b, variables, &f, &g);
}

boundary_project_vector() [1/2]

void libMesh::System::boundary_project_vector ( const std::set< boundary_id_type > &  b, const std::vector< unsigned int > &  variables, NumericVector< Number > &  new_vector, FunctionBase< Number > *  f, FunctionBase< Gradient > *  g = nullptr, int  is_adjoint = -1  ) const

inherited

Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary function via L2 projections and nodal interpolations on each element.

Only degrees of freedom which affect the function's trace on a boundary in the set b are affected. Only degrees of freedom associated with the variables listed in the vector variables are projected. The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 1289 of file system_projection.C.

References libMesh::NumericVector< T >::close(), libMesh::libmesh_ignore(), and libMesh::Threads::parallel_for().

{
  LOG_SCOPE ("boundary_project_vector()", "System");

  Threads::parallel_for
    (ConstElemRange (this->get_mesh().active_local_elements_begin(),
                     this->get_mesh().active_local_elements_end() ),
     BoundaryProjectSolution(b, variables, *this, f, g,
                             this->get_equation_systems().parameters,
                             new_vector)
     );

  // We don't do SCALAR dofs when just projecting the boundary, so
  // we're done here.

  new_vector.close();

#ifdef LIBMESH_ENABLE_CONSTRAINTS
  if (is_adjoint == -1)
    this->get_dof_map().enforce_constraints_exactly(*this, &new_vector);
  else if (is_adjoint >= 0)
    this->get_dof_map().enforce_adjoint_constraints_exactly(new_vector,
                                                            is_adjoint);
#else
  libmesh_ignore(is_adjoint);
#endif
}

boundary_project_vector() [2/2]

void libMesh::System::boundary_project_vector ( const std::set< boundary_id_type > &  b, const std::vector< unsigned int > &  variables, ValueFunctionPointer  fptr, GradientFunctionPointer  gptr, const Parameters &  parameters, NumericVector< Number > &  new_vector, int  is_adjoint = -1  ) const

inherited

Projects arbitrary boundary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary boundary function via L2 projections and nodal interpolations on each element.

Only degrees of freedom which affect the function's trace on a boundary in the set b are affected. Only degrees of freedom associated with the variables listed in the vector variables are projected. The function value fptr and its gradient gptr are represented by function pointers. A gradient gptr is only required/used for projecting onto finite element spaces with continuous derivatives.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 1271 of file system_projection.C.

References fptr(), and gptr().

{
  WrappedFunction<Number> f(*this, fptr, &function_parameters);
  WrappedFunction<Gradient> g(*this, gptr, &function_parameters);
  this->boundary_project_vector(b, variables, new_vector, &f, &g,
                                is_adjoint);
}

build_context()

std::unique_ptr< DiffContext > FEMSystem::build_context ( )

overridevirtualinherited

Builds a FEMContext object with enough information to do evaluations on each element.

For most problems, the default FEMSystem implementation is correct; users who subclass FEMContext will need to also reimplement this method to build it.

Reimplemented from libMesh::DifferentiableSystem.

Definition at line 1346 of file fem_system.C.

References libMesh::DifferentiableSystem::deltat, libMesh::DifferentiablePhysics::get_mesh_system(), libMesh::DifferentiablePhysics::get_mesh_x_var(), libMesh::DifferentiablePhysics::get_mesh_y_var(), libMesh::DifferentiablePhysics::get_mesh_z_var(), libMesh::DifferentiableSystem::get_physics(), libMesh::DifferentiableSystem::get_time_solver(), libMesh::TimeSolver::is_adjoint(), and libMesh::libmesh_assert().

Referenced by libMesh::FEMSystem::assembly(), libMesh::VariationalSmootherSystem::compute_element_reference_volume(), libMesh::FEMSystem::mesh_position_get(), and libMesh::FEMSystem::mesh_position_set().

{
  auto fc = std::make_unique<FEMContext>(*this);

  DifferentiablePhysics * phys = this->get_physics();

  libmesh_assert (phys);

  // If we are solving a moving mesh problem, tell that to the Context
  fc->set_mesh_system(phys->get_mesh_system());
  fc->set_mesh_x_var(phys->get_mesh_x_var());
  fc->set_mesh_y_var(phys->get_mesh_y_var());
  fc->set_mesh_z_var(phys->get_mesh_z_var());

  fc->set_deltat_pointer( &deltat );

  // If we are solving the adjoint problem, tell that to the Context
  fc->is_adjoint() = this->get_time_solver().is_adjoint();

  return fc;
}

calculate_norm() [1/2]

Real libMesh::System::calculate_norm ( const NumericVector< Number > &  v, unsigned int  var, FEMNormType  norm_type, std::set< unsigned int > *  skip_dimensions = nullptr  ) const

inherited

Returns

A norm of variable var in the vector v, in the specified norm (e.g. L2, L_INF, H1)

Definition at line 1724 of file system.C.

References libMesh::DISCRETE_L1, libMesh::DISCRETE_L2, libMesh::DISCRETE_L_INF, libMesh::System::discrete_var_norm(), libMesh::L2, libMesh::System::n_vars(), and libMesh::Real.

Referenced by libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::AdaptiveTimeSolver::calculate_norm(), libMesh::UnsteadySolver::du(), main(), output_norms(), ConstraintOperatorTest::testCoreform(), and MeshInputTest::testProjectionRegression().

{
  //short circuit to save time
  if (norm_type == DISCRETE_L1 ||
      norm_type == DISCRETE_L2 ||
      norm_type == DISCRETE_L_INF)
    return discrete_var_norm(v,var,norm_type);

  // Not a discrete norm
  std::vector<FEMNormType> norms(this->n_vars(), L2);
  std::vector<Real> weights(this->n_vars(), 0.0);
  norms[var] = norm_type;
  weights[var] = 1.0;
  Real val = this->calculate_norm(v, SystemNorm(norms, weights), skip_dimensions);
  return val;
}

calculate_norm() [2/2]

Real libMesh::System::calculate_norm ( const NumericVector< Number > &  v, const SystemNorm &  norm, std::set< unsigned int > *  skip_dimensions = nullptr  ) const

inherited

Returns

A norm of the vector v, using component_norm and component_scale to choose and weight the norms of each variable.

Definition at line 1746 of file system.C.

References libMesh::System::_dof_map, libMesh::System::_mesh, libMesh::FEGenericBase< OutputType >::build(), libMesh::NumericVector< T >::build(), libMesh::ParallelObject::comm(), libMesh::FEType::default_quadrature_rule(), dim, libMesh::DISCRETE_L1, libMesh::DISCRETE_L2, libMesh::DISCRETE_L_INF, libMesh::System::discrete_var_norm(), libMesh::DofMap::dof_indices(), libMesh::MeshBase::elem_dimensions(), libMesh::Utility::enum_to_string(), libMesh::FEInterface::field_type(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::GHOSTED, libMesh::H1, libMesh::H1_SEMINORM, libMesh::H2, libMesh::H2_SEMINORM, libMesh::L1, libMesh::NumericVector< T >::l1_norm(), libMesh::L2, libMesh::NumericVector< T >::l2_norm(), libMesh::L_INF, libMesh::libmesh_assert(), libMesh::NumericVector< T >::linfty_norm(), libMesh::NumericVector< T >::local_size(), libMesh::NumericVector< T >::localize(), libMesh::make_range(), TIMPI::Communicator::max(), libMesh::System::n_vars(), libMesh::TensorTools::norm(), libMesh::TensorTools::norm_sq(), libMesh::Real, libMesh::NumericVector< T >::size(), TIMPI::Communicator::sum(), libMesh::TYPE_SCALAR, libMesh::TYPE_VECTOR, libMesh::DofMap::variable_type(), libMesh::W1_INF_SEMINORM, libMesh::W2_INF_SEMINORM, and libMesh::SystemNorm::weight().

{
  // This function must be run on all processors at once
  parallel_object_only();

  LOG_SCOPE ("calculate_norm()", "System");

  // Zero the norm before summation
  Real v_norm = 0.;

  if (norm.is_discrete())
    {
      //Check to see if all weights are 1.0 and all types are equal
      FEMNormType norm_type0 = norm.type(0);
      unsigned int check_var = 0, check_end = this->n_vars();
      for (; check_var != check_end; ++check_var)
        if ((norm.weight(check_var) != 1.0) || (norm.type(check_var) != norm_type0))
          break;

      //All weights were 1.0 so just do the full vector discrete norm
      if (check_var == this->n_vars())
        {
          if (norm_type0 == DISCRETE_L1)
            return v.l1_norm();
          if (norm_type0 == DISCRETE_L2)
            return v.l2_norm();
          if (norm_type0 == DISCRETE_L_INF)
            return v.linfty_norm();
          else
            libmesh_error_msg("Invalid norm_type0 = " << Utility::enum_to_string(norm_type0));
        }

      for (auto var : make_range(this->n_vars()))
        {
          // Skip any variables we don't need to integrate
          if (norm.weight(var) == 0.0)
            continue;

          v_norm += norm.weight(var) * discrete_var_norm(v, var, norm.type(var));
        }

      return v_norm;
    }

  // Localize the potentially parallel vector
  std::unique_ptr<NumericVector<Number>> local_v = NumericVector<Number>::build(this->comm());
  local_v->init(v.size(), v.local_size(), _dof_map->get_send_list(),
                true, GHOSTED);
  v.localize (*local_v, _dof_map->get_send_list());

  // I'm not sure how best to mix Hilbert norms on some variables (for
  // which we'll want to square then sum then square root) with norms
  // like L_inf (for which we'll just want to take an absolute value
  // and then sum).
  bool using_hilbert_norm = true,
    using_nonhilbert_norm = true;

  // Loop over all variables
  for (auto var : make_range(this->n_vars()))
    {
      // Skip any variables we don't need to integrate
      Real norm_weight_sq = norm.weight_sq(var);
      if (norm_weight_sq == 0.0)
        continue;
      Real norm_weight = norm.weight(var);

      // Check for unimplemented norms (rather than just returning 0).
      FEMNormType norm_type = norm.type(var);
      if ((norm_type==H1) ||
          (norm_type==H2) ||
          (norm_type==L2) ||
          (norm_type==H1_SEMINORM) ||
          (norm_type==H2_SEMINORM))
        {
          if (!using_hilbert_norm)
            libmesh_not_implemented();
          using_nonhilbert_norm = false;
        }
      else if ((norm_type==L1) ||
               (norm_type==L_INF) ||
               (norm_type==W1_INF_SEMINORM) ||
               (norm_type==W2_INF_SEMINORM))
        {
          if (!using_nonhilbert_norm)
            libmesh_not_implemented();
          using_hilbert_norm = false;
        }
      else
        libmesh_not_implemented();

      const FEType & fe_type = this->get_dof_map().variable_type(var);

      // Allow space for dims 0-3, and for both scalar and vector
      // elements, even if we don't use them all
      std::vector<std::unique_ptr<FEBase>> fe_ptrs(4);
      std::vector<std::unique_ptr<FEVectorBase>> vec_fe_ptrs(4);
      std::vector<std::unique_ptr<QBase>> q_rules(4);

      const std::set<unsigned char> & elem_dims = _mesh.elem_dimensions();

      // Prepare finite elements for each dimension present in the mesh
      for (const auto & dim : elem_dims)
        {
          if (skip_dimensions && skip_dimensions->find(dim) != skip_dimensions->end())
            continue;

          // Construct quadrature and finite element objects
          q_rules[dim] = fe_type.default_quadrature_rule (dim);

          const FEFieldType field_type = FEInterface::field_type(fe_type);
          if (field_type == TYPE_SCALAR)
            {
              fe_ptrs[dim] = FEBase::build(dim, fe_type);
              fe_ptrs[dim]->attach_quadrature_rule (q_rules[dim].get());
            }
          else
            {
              vec_fe_ptrs[dim] = FEVectorBase::build(dim, fe_type);
              vec_fe_ptrs[dim]->attach_quadrature_rule (q_rules[dim].get());
              libmesh_assert_equal_to(field_type, TYPE_VECTOR);
            }

        }

      std::vector<dof_id_type> dof_indices;

      // Begin the loop over the elements
      for (const auto & elem : this->get_mesh().active_local_element_ptr_range())
        {
          const unsigned int dim = elem->dim();

          // One way for implementing this would be to exchange the fe with the FEInterface- class.
          // However, it needs to be discussed whether integral-norms make sense for infinite elements.
          // or in which sense they could make sense.
          if (elem->infinite() )
            libmesh_not_implemented();

          if (skip_dimensions && skip_dimensions->find(dim) != skip_dimensions->end())
            continue;

          QBase * qrule = q_rules[dim].get();
          libmesh_assert(qrule);

          this->get_dof_map().dof_indices (elem, dof_indices, var);

          auto element_calculation = [&dof_indices, &elem,
               norm_type, norm_weight, norm_weight_sq, &qrule,
               &local_v, &v_norm](auto & fe) {
          typedef typename std::remove_reference<decltype(fe)>::type::OutputShape OutputShape;
          typedef typename TensorTools::MakeNumber<OutputShape>::type OutputNumberShape;
          typedef typename std::remove_reference<decltype(fe)>::type::OutputGradient OutputGradient;
          typedef typename TensorTools::MakeNumber<OutputGradient>::type OutputNumberGradient;

          const std::vector<Real> &                     JxW = fe.get_JxW();
          const std::vector<std::vector<OutputShape>> * phi = nullptr;
          if (norm_type == H1 ||
              norm_type == H2 ||
              norm_type == L2 ||
              norm_type == L1 ||
              norm_type == L_INF)
            phi = &(fe.get_phi());

          const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
          if (norm_type == H1 ||
              norm_type == H2 ||
              norm_type == H1_SEMINORM ||
              norm_type == W1_INF_SEMINORM)
            dphi = &(fe.get_dphi());

#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
          typedef typename std::remove_reference<decltype(fe)>::type::OutputTensor OutputTensor;

          const std::vector<std::vector<OutputTensor>> *  d2phi = nullptr;
          if (norm_type == H2 ||
              norm_type == H2_SEMINORM ||
              norm_type == W2_INF_SEMINORM)
            d2phi = &(fe.get_d2phi());
#endif

          fe.reinit (elem);

          const unsigned int n_qp = qrule->n_points();

          const unsigned int n_sf = cast_int<unsigned int>
            (dof_indices.size());

          // Begin the loop over the Quadrature points.
          for (unsigned int qp=0; qp<n_qp; qp++)
            {
              if (norm_type == L1)
                {
                  OutputNumberShape u_h = 0.;
                  for (unsigned int i=0; i != n_sf; ++i)
                    u_h += (*phi)[i][qp] * (*local_v)(dof_indices[i]);
                  v_norm += norm_weight *
                    JxW[qp] * TensorTools::norm(u_h);
                }

              if (norm_type == L_INF)
                {
                  OutputNumberShape u_h = 0.;
                  for (unsigned int i=0; i != n_sf; ++i)
                    u_h += (*phi)[i][qp] * (*local_v)(dof_indices[i]);
                  v_norm = std::max(v_norm, norm_weight * TensorTools::norm(u_h));
                }

              if (norm_type == H1 ||
                  norm_type == H2 ||
                  norm_type == L2)
                {
                  OutputNumberShape u_h = 0.;
                  for (unsigned int i=0; i != n_sf; ++i)
                    u_h += (*phi)[i][qp] * (*local_v)(dof_indices[i]);
                  v_norm += norm_weight_sq *
                    JxW[qp] * TensorTools::norm_sq(u_h);
                }

              if (norm_type == H1 ||
                  norm_type == H2 ||
                  norm_type == H1_SEMINORM)
                {
                  OutputNumberGradient grad_u_h;
                  for (unsigned int i=0; i != n_sf; ++i)
                    grad_u_h.add_scaled((*dphi)[i][qp], (*local_v)(dof_indices[i]));
                  v_norm += norm_weight_sq *
                    JxW[qp] * grad_u_h.norm_sq();
                }

              if (norm_type == W1_INF_SEMINORM)
                {
                  OutputNumberGradient grad_u_h;
                  for (unsigned int i=0; i != n_sf; ++i)
                    grad_u_h.add_scaled((*dphi)[i][qp], (*local_v)(dof_indices[i]));
                  v_norm = std::max(v_norm, norm_weight * grad_u_h.norm());
                }

#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
              typedef typename TensorTools::MakeNumber<OutputTensor>::type OutputNumberTensor;

              if (norm_type == H2 ||
                  norm_type == H2_SEMINORM)
                {
                  OutputNumberTensor hess_u_h;
                  for (unsigned int i=0; i != n_sf; ++i)
                    hess_u_h.add_scaled((*d2phi)[i][qp], (*local_v)(dof_indices[i]));
                  v_norm += norm_weight_sq *
                    JxW[qp] * hess_u_h.norm_sq();
                }

              if (norm_type == W2_INF_SEMINORM)
                {
                  OutputNumberTensor hess_u_h;
                  for (unsigned int i=0; i != n_sf; ++i)
                    hess_u_h.add_scaled((*d2phi)[i][qp], (*local_v)(dof_indices[i]));
                  v_norm = std::max(v_norm, norm_weight * hess_u_h.norm());
                }
#endif
            }
          };

          FEBase * scalar_fe = fe_ptrs[dim].get();
          FEVectorBase * vec_fe = vec_fe_ptrs[dim].get();

          if (scalar_fe)
            {
              libmesh_assert(!vec_fe);
              element_calculation(*scalar_fe);
            }

          if (vec_fe)
            {
              libmesh_assert(!scalar_fe);
              element_calculation(*vec_fe);
            }
        }
    }

  if (using_hilbert_norm)
    {
      this->comm().sum(v_norm);
      v_norm = std::sqrt(v_norm);
    }
  else
    {
      this->comm().max(v_norm);
    }

  return v_norm;
}

can_add_matrices()

bool libMesh::System::can_add_matrices ( ) const

inlineprotectedinherited

Returns

Whether or not matrices can still be added without expensive per-matrix initialization.

Definition at line 1975 of file system.h.

References libMesh::System::_matrices_initialized.

Referenced by libMesh::EigenSystem::set_eigenproblem_type().

{ return !_matrices_initialized; }

clear()

void libMesh::ContinuationSystem::clear ( )

overridevirtual

Clear all the data structures associated with the system.

Reimplemented from libMesh::DifferentiableSystem.

Definition at line 83 of file continuation_system.C.

References libMesh::DifferentiableSystem::clear().

{
  // Call the Parent's clear function
  Parent::clear();
}

clear_physics()

void libMesh::DifferentiablePhysics::clear_physics ( )

virtualinherited

Clear any data structures associated with the physics.

Definition at line 28 of file diff_physics.C.

References libMesh::DifferentiablePhysics::_time_evolving.

Referenced by libMesh::DifferentiableSystem::clear().

{
  _time_evolving.resize(0);
}

clear_qoi()

virtual void libMesh::DifferentiableQoI::clear_qoi ( )

inlinevirtualinherited

Clear all the data structures associated with the QoI.

Definition at line 91 of file diff_qoi.h.

Referenced by libMesh::DifferentiableSystem::clear().

{}

clone()

virtual std::unique_ptr<DifferentiableQoI> libMesh::DifferentiableSystem::clone ( )

inlineoverridevirtualinherited

We don't allow systems to be attached to each other.

Implements libMesh::DifferentiableQoI.

Definition at line 168 of file diff_system.h.

Referenced by libMesh::AdjointRefinementEstimator::estimate_error().

  {
    libmesh_not_implemented();
    // dummy to avoid compiler warnings, not a real implementation
    return std::unique_ptr<DifferentiableQoI>(nullptr);
  }

clone_physics()

virtual std::unique_ptr<DifferentiablePhysics> libMesh::DifferentiableSystem::clone_physics ( )

inlineoverridevirtualinherited

We don't allow systems to be attached to each other.

Implements libMesh::DifferentiablePhysics.

Definition at line 158 of file diff_system.h.

  {
    libmesh_not_implemented();
    // dummy to avoid compiler warnings, not a real implementation
    return std::unique_ptr<DifferentiablePhysics>(nullptr);
  }

comm()

const Parallel::Communicator& libMesh::ParallelObject::comm ( ) const

inlineinherited

Returns

A reference to the Parallel::Communicator object used by this mesh.

Definition at line 97 of file parallel_object.h.

References libMesh::ParallelObject::_communicator.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), libMesh::__libmesh_petsc_diff_solver_monitor(), libMesh::__libmesh_petsc_diff_solver_residual(), libMesh::__libmesh_tao_equality_constraints(), libMesh::__libmesh_tao_equality_constraints_jacobian(), libMesh::__libmesh_tao_gradient(), libMesh::__libmesh_tao_hessian(), libMesh::__libmesh_tao_inequality_constraints(), libMesh::__libmesh_tao_inequality_constraints_jacobian(), libMesh::__libmesh_tao_objective(), libMesh::MeshRefinement::_coarsen_elements(), libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::Partitioner::_find_global_index_by_pid_map(), libMesh::BoundaryInfo::_find_id_maps(), libMesh::PetscLinearSolver< Number >::_petsc_shell_matrix_get_diagonal(), libMesh::SlepcEigenSolver< libMesh::Number >::_petsc_shell_matrix_get_diagonal(), libMesh::PetscLinearSolver< Number >::_petsc_shell_matrix_mult(), libMesh::SlepcEigenSolver< libMesh::Number >::_petsc_shell_matrix_mult(), libMesh::PetscLinearSolver< Number >::_petsc_shell_matrix_mult_add(), libMesh::MeshRefinement::_refine_elements(), libMesh::MeshRefinement::_smooth_flags(), libMesh::DofMap::add_constraints_to_send_list(), add_cube_convex_hull_to_mesh(), libMesh::PetscDMWrapper::add_dofs_helper(), libMesh::PetscDMWrapper::add_dofs_to_section(), libMesh::TransientRBConstruction::add_IC_to_RB_space(), libMesh::RBEIMEvaluation::add_interpolation_data(), libMesh::CondensedEigenSystem::add_matrices(), libMesh::EigenSystem::add_matrices(), libMesh::System::add_matrix(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::System::add_variable(), libMesh::System::add_variables(), libMesh::System::add_vector(), libMesh::MeshTools::Modification::all_tri(), libMesh::LaplaceMeshSmoother::allgather_graph(), libMesh::DofMap::allgather_recursive_constraints(), libMesh::TransientRBConstruction::allocate_data_structures(), libMesh::RBConstruction::allocate_data_structures(), libMesh::TransientRBConstruction::assemble_affine_expansion(), libMesh::AdvectionSystem::assemble_claw_rhs(), libMesh::FEMSystem::assemble_qoi(), libMesh::Nemesis_IO::assert_symmetric_cmaps(), libMesh::MeshCommunication::assign_global_indices(), libMesh::Partitioner::assign_partitioning(), libMesh::MeshTools::Generation::build_extrusion(), libMesh::Partitioner::build_graph(), libMesh::BoundaryInfo::build_node_list_from_side_list(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::PetscDMWrapper::build_section(), libMesh::PetscDMWrapper::build_sf(), libMesh::MeshBase::cache_elem_data(), libMesh::System::calculate_norm(), libMesh::DofMap::check_dirichlet_bcid_consistency(), libMesh::RBConstruction::compute_Fq_representor_innerprods(), libMesh::RBConstruction::compute_max_error_bound(), libMesh::Nemesis_IO_Helper::compute_num_global_elem_blocks(), libMesh::Nemesis_IO_Helper::compute_num_global_nodesets(), libMesh::Nemesis_IO_Helper::compute_num_global_sidesets(), libMesh::RBConstruction::compute_output_dual_innerprods(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), libMesh::RBSCMConstruction::compute_SCM_bounds_on_training_set(), libMesh::DofMap::computed_sparsity_already(), libMesh::Problem_Interface::computeF(), libMesh::Problem_Interface::computeJacobian(), libMesh::Problem_Interface::computePreconditioner(), ContinuationSystem(), libMesh::MeshBase::copy_constraint_rows(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::CondensedEigenSystem::copy_super_to_sub(), libMesh::MeshTools::correct_node_proc_ids(), libMesh::MeshTools::create_bounding_box(), libMesh::DofMap::create_dof_constraints(), libMesh::MeshTools::create_nodal_bounding_box(), libMesh::MeshRefinement::create_parent_error_vector(), libMesh::MeshTools::create_processor_bounding_box(), libMesh::MeshTools::create_subdomain_bounding_box(), libMesh::PetscMatrix< T >::create_submatrix_nosort(), create_wrapped_function(), libMesh::MeshCommunication::delete_remote_elements(), libMesh::RBEIMEvaluation::distribute_bfs(), DMlibMeshFunction(), DMlibMeshJacobian(), DMlibMeshSetSystem_libMesh(), DMVariableBounds_libMesh(), libMesh::DTKSolutionTransfer::DTKSolutionTransfer(), libMesh::MeshRefinement::eliminate_unrefined_patches(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_interiors(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_nodes(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_sides(), libMesh::TransientRBConstruction::enrich_RB_space(), libMesh::EpetraVector< T >::EpetraVector(), AssembleOptimization::equality_constraints(), libMesh::PatchRecoveryErrorEstimator::estimate_error(), libMesh::WeightedPatchRecoveryErrorEstimator::estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::MeshRefinement::flag_elements_by_elem_fraction(), libMesh::MeshRefinement::flag_elements_by_error_fraction(), libMesh::MeshRefinement::flag_elements_by_error_tolerance(), libMesh::MeshRefinement::flag_elements_by_mean_stddev(), libMesh::MeshRefinement::flag_elements_by_nelem_target(), libMesh::RBEIMEvaluation::gather_bfs(), libMesh::DofMap::gather_constraints(), libMesh::MeshfreeInterpolation::gather_remote_data(), libMesh::CondensedEigenSystem::get_eigenpair(), libMesh::RBEIMEvaluation::get_eim_basis_function_node_value(), libMesh::RBEIMEvaluation::get_eim_basis_function_side_value(), libMesh::RBEIMEvaluation::get_eim_basis_function_value(), libMesh::MeshBase::get_info(), libMesh::System::get_info(), libMesh::DofMap::get_info(), libMesh::RBEIMEvaluation::get_interior_basis_functions_as_vecs(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::RBEIMConstruction::get_max_abs_value(), libMesh::RBEIMConstruction::get_node_max_abs_value(), libMesh::RBEIMEvaluation::get_parametrized_function_node_value(), libMesh::RBEIMEvaluation::get_parametrized_function_side_value(), libMesh::RBEIMEvaluation::get_parametrized_function_value(), libMesh::RBEIMConstruction::get_random_point(), AssembleOptimization::inequality_constraints(), AssembleOptimization::inequality_constraints_jacobian(), libMesh::LocationMap< T >::init(), libMesh::TimeSolver::init(), libMesh::StaticCondensation::init(), libMesh::SystemSubsetBySubdomain::init(), libMesh::PetscDMWrapper::init_and_attach_petscdm(), libMesh::AdvectionSystem::init_data(), libMesh::ClawSystem::init_data(), libMesh::PetscDMWrapper::init_petscdm(), libMesh::ExodusII_IO_Helper::initialize(), libMesh::OptimizationSystem::initialize_equality_constraints_storage(), libMesh::OptimizationSystem::initialize_inequality_constraints_storage(), libMesh::RBEIMConstruction::initialize_parametrized_functions_in_training_set(), libMesh::RBEIMConstruction::inner_product(), integrate_function(), libMesh::MeshTools::libmesh_assert_consistent_distributed(), libMesh::MeshTools::libmesh_assert_consistent_distributed_nodes(), libMesh::MeshTools::libmesh_assert_contiguous_dof_ids(), libMesh::MeshTools::libmesh_assert_equal_connectivity(), libMesh::MeshTools::libmesh_assert_equal_points(), libMesh::MeshTools::libmesh_assert_parallel_consistent_new_node_procids(), libMesh::MeshTools::libmesh_assert_parallel_consistent_procids< Elem >(), libMesh::MeshTools::libmesh_assert_parallel_consistent_procids< Node >(), libMesh::MeshTools::libmesh_assert_topology_consistent_procids< Node >(), libMesh::MeshTools::libmesh_assert_valid_boundary_ids(), libMesh::MeshTools::libmesh_assert_valid_constraint_rows(), libMesh::MeshTools::libmesh_assert_valid_dof_ids(), libMesh::MeshTools::libmesh_assert_valid_neighbors(), libMesh::DistributedMesh::libmesh_assert_valid_parallel_flags(), libMesh::DistributedMesh::libmesh_assert_valid_parallel_object_ids(), libMesh::DistributedMesh::libmesh_assert_valid_parallel_p_levels(), libMesh::MeshTools::libmesh_assert_valid_refinement_flags(), libMesh::MeshTools::libmesh_assert_valid_unique_ids(), libMesh::libmesh_petsc_linesearch_shellfunc(), libMesh::libmesh_petsc_preconditioner_apply(), libMesh::libmesh_petsc_recalculate_monitor(), libMesh::libmesh_petsc_snes_fd_residual(), libMesh::libmesh_petsc_snes_jacobian(), libMesh::libmesh_petsc_snes_mffd_interface(), libMesh::libmesh_petsc_snes_mffd_residual(), libMesh::libmesh_petsc_snes_postcheck(), libMesh::libmesh_petsc_snes_precheck(), libMesh::libmesh_petsc_snes_residual(), libMesh::libmesh_petsc_snes_residual_helper(), libMesh::MeshRefinement::limit_level_mismatch_at_edge(), libMesh::MeshRefinement::limit_level_mismatch_at_node(), libMesh::MeshRefinement::limit_overrefined_boundary(), libMesh::MeshRefinement::limit_underrefined_boundary(), libMesh::LinearImplicitSystem::LinearImplicitSystem(), main(), libMesh::MeshRefinement::make_coarsening_compatible(), libMesh::MeshCommunication::make_elems_parallel_consistent(), libMesh::MeshRefinement::make_flags_parallel_consistent(), libMesh::MeshCommunication::make_new_node_proc_ids_parallel_consistent(), libMesh::MeshCommunication::make_new_nodes_parallel_consistent(), libMesh::MeshCommunication::make_node_bcids_parallel_consistent(), libMesh::MeshCommunication::make_node_ids_parallel_consistent(), libMesh::MeshCommunication::make_node_proc_ids_parallel_consistent(), libMesh::MeshCommunication::make_node_unique_ids_parallel_consistent(), libMesh::MeshCommunication::make_nodes_parallel_consistent(), libMesh::MeshCommunication::make_p_levels_parallel_consistent(), libMesh::MeshRefinement::make_refinement_compatible(), libMesh::TransientRBConstruction::mass_matrix_scaled_matvec(), libMesh::FEMSystem::mesh_position_set(), libMesh::TriangulatorInterface::MeshedHole::MeshedHole(), LinearElasticityWithContact::move_mesh(), libMesh::DistributedMesh::n_active_elem(), libMesh::MeshTools::n_active_levels(), libMesh::BoundaryInfo::n_boundary_conds(), libMesh::MeshTools::n_connected_components(), libMesh::DofMap::n_constrained_dofs(), libMesh::MeshBase::n_constraint_rows(), libMesh::DofMap::n_dofs(), libMesh::DofMap::n_dofs_per_processor(), libMesh::BoundaryInfo::n_edge_conds(), libMesh::CondensedEigenSystem::n_global_non_condensed_dofs(), libMesh::MeshTools::n_levels(), MixedOrderTest::n_neighbor_links(), libMesh::BoundaryInfo::n_nodeset_conds(), libMesh::SparsityPattern::Build::n_nonzeros(), libMesh::MeshTools::n_p_levels(), libMesh::BoundaryInfo::n_shellface_conds(), libMesh::RBEIMEvaluation::node_distribute_bfs(), libMesh::RBEIMEvaluation::node_gather_bfs(), libMesh::RBEIMConstruction::node_inner_product(), libMesh::MeshBase::operator==(), libMesh::DistributedMesh::parallel_max_elem_id(), libMesh::DistributedMesh::parallel_max_node_id(), libMesh::ReplicatedMesh::parallel_max_unique_id(), libMesh::DistributedMesh::parallel_max_unique_id(), libMesh::DistributedMesh::parallel_n_elem(), libMesh::DistributedMesh::parallel_n_nodes(), libMesh::SparsityPattern::Build::parallel_sync(), libMesh::BoundaryInfo::parallel_sync_node_ids(), libMesh::BoundaryInfo::parallel_sync_side_ids(), libMesh::MeshTools::paranoid_n_levels(), libMesh::Partitioner::partition(), libMesh::Partitioner::partition_unpartitioned_elements(), libMesh::petsc_auto_fieldsplit(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::MeshBase::prepare_for_use(), libMesh::MeshBase::print_constraint_rows(), libMesh::DofMap::print_dof_constraints(), libMesh::DofMap::process_mesh_constraint_rows(), libMesh::Partitioner::processor_pairs_to_interface_nodes(), libMesh::InterMeshProjection::project_system_vectors(), FEMParameters::read(), libMesh::Nemesis_IO::read(), libMesh::XdrIO::read(), libMesh::EquationSystems::read(), libMesh::ExodusII_IO::read_header(), libMesh::CheckpointIO::read_header(), libMesh::XdrIO::read_header(), libMesh::System::read_header(), libMesh::RBEIMEvaluation::read_in_interior_basis_functions(), libMesh::RBEIMEvaluation::read_in_node_basis_functions(), libMesh::RBEIMEvaluation::read_in_side_basis_functions(), libMesh::RBEvaluation::read_in_vectors_from_multiple_files(), libMesh::System::read_legacy_data(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), libMesh::RBConstruction::read_riesz_representors_from_files(), libMesh::System::read_SCALAR_dofs(), libMesh::XdrIO::read_serialized_bc_names(), libMesh::XdrIO::read_serialized_bcs_helper(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::XdrIO::read_serialized_connectivity(), libMesh::XdrIO::read_serialized_nodes(), libMesh::XdrIO::read_serialized_nodesets(), libMesh::XdrIO::read_serialized_subdomain_names(), libMesh::System::read_serialized_vector(), libMesh::Nemesis_IO_Helper::read_var_names_impl(), libMesh::MeshBase::recalculate_n_partitions(), libMesh::MeshRefinement::refine_and_coarsen_elements(), libMesh::SimplexRefiner::refine_via_edges(), libMesh::StaticCondensationDofMap::reinit(), libMesh::DistributedMesh::renumber_dof_objects(), libMesh::DistributedMesh::renumber_nodes_and_elements(), LinearElasticityWithContact::residual_and_jacobian(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), scale_mesh_and_plot(), libMesh::DofMap::scatter_constraints(), libMesh::CheckpointIO::select_split_config(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::send_and_insert_dof_values(), libMesh::TransientRBConstruction::set_error_temporal_data(), libMesh::Partitioner::set_interface_node_processor_ids_BFS(), libMesh::Partitioner::set_interface_node_processor_ids_linear(), libMesh::Partitioner::set_interface_node_processor_ids_petscpartitioner(), libMesh::Partitioner::set_node_processor_ids(), libMesh::DofMap::set_nonlocal_dof_objects(), libMesh::Partitioner::set_parent_processor_ids(), libMesh::PetscDMWrapper::set_point_range_in_section(), libMesh::PetscDiffSolver::setup_petsc_data(), libMesh::RBEIMEvaluation::side_distribute_bfs(), libMesh::RBEIMEvaluation::side_gather_bfs(), libMesh::RBEIMConstruction::side_inner_product(), libMesh::Partitioner::single_partition(), libMesh::LaplaceMeshSmoother::smooth(), libMesh::VariationalMeshSmoother::smooth(), libMesh::ClawSystem::solve_conservation_law(), libMesh::split_mesh(), libMesh::RBEIMConstruction::store_eim_solutions_for_training_set(), libMesh::MeshBase::subdomain_ids(), libMesh::BoundaryInfo::sync(), ConstraintOperatorTest::test1DCoarseningNewNodes(), ConstraintOperatorTest::test1DCoarseningOperator(), libMesh::MeshRefinement::test_level_one(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), libMesh::MeshRefinement::test_unflagged(), DofMapTest::testBadElemFECombo(), SystemsTest::testBlockRestrictedVarNDofs(), BoundaryInfoTest::testBoundaryOnChildrenErrors(), VolumeTest::testC0PolygonMethods(), VolumeTest::testC0PolyhedronMethods(), ConstraintOperatorTest::testCoreform(), ConnectedComponentsTest::testEdge(), MeshInputTest::testExodusIGASidesets(), MeshTriangulationTest::testFoundCenters(), PointLocatorTest::testLocator(), BoundaryInfoTest::testMesh(), PointLocatorTest::testPlanar(), MeshTriangulationTest::testPoly2TriRefinementBase(), SystemsTest::testProjectCubeWithMeshFunction(), BoundaryInfoTest::testRenumber(), CheckpointIOTest::testSplitter(), MeshInputTest::testTetgenIO(), MeshTriangulationTest::testTriangulatorInterp(), MeshTriangulationTest::testTriangulatorMeshedHoles(), MeshTriangulationTest::testTriangulatorRoundHole(), libMesh::MeshTools::total_weight(), libMesh::RBConstruction::train_reduced_basis_with_POD(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::MeshfreeSolutionTransfer::transfer(), libMesh::Poly2TriTriangulator::triangulate(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::RBConstruction::truth_assembly(), libMesh::MeshRefinement::uniformly_coarsen(), update_current_local_solution(), libMesh::TransientRBConstruction::update_RB_initial_condition_all_N(), libMesh::TransientRBConstruction::update_RB_system_matrices(), libMesh::RBConstruction::update_RB_system_matrices(), libMesh::TransientRBConstruction::update_residual_terms(), libMesh::RBConstruction::update_residual_terms(), libMesh::MeshTools::volume(), libMesh::STLIO::write(), libMesh::NameBasedIO::write(), libMesh::XdrIO::write(), libMesh::VTKIO::write_nodal_data(), libMesh::RBEIMEvaluation::write_out_interior_basis_functions(), libMesh::RBEIMEvaluation::write_out_node_basis_functions(), libMesh::RBEIMEvaluation::write_out_side_basis_functions(), libMesh::RBEvaluation::write_out_vectors(), libMesh::TransientRBConstruction::write_riesz_representors_to_files(), libMesh::RBConstruction::write_riesz_representors_to_files(), libMesh::System::write_SCALAR_dofs(), libMesh::XdrIO::write_serialized_bcs_helper(), libMesh::System::write_serialized_blocked_dof_objects(), libMesh::XdrIO::write_serialized_connectivity(), libMesh::XdrIO::write_serialized_nodes(), libMesh::XdrIO::write_serialized_nodesets(), libMesh::RBDataSerialization::RBEvaluationSerialization::write_to_file(), libMesh::RBDataSerialization::TransientRBEvaluationSerialization::write_to_file(), libMesh::RBDataSerialization::RBEIMEvaluationSerialization::write_to_file(), and libMesh::RBDataSerialization::RBSCMEvaluationSerialization::write_to_file().

  { return _communicator; }

compare()

bool libMesh::System::compare ( const System &  other_system, const Real  threshold, const bool  verbose  ) const

virtualinherited

Returns

true when the other system contains identical data, up to the given threshold. Outputs some diagnostic info when verbose is set.

Definition at line 618 of file system.C.

References libMesh::System::_is_initialized, libMesh::System::_sys_name, libMesh::System::_vectors, libMesh::System::get_vector(), libMesh::libmesh_assert(), libMesh::System::n_vectors(), libMesh::System::name(), libMesh::out, and libMesh::System::solution.

{
  // we do not care for matrices, but for vectors
  libmesh_assert (_is_initialized);
  libmesh_assert (other_system._is_initialized);

  if (verbose)
    {
      libMesh::out << "  Systems \"" << _sys_name << "\"" << std::endl;
      libMesh::out << "   comparing matrices not supported." << std::endl;
      libMesh::out << "   comparing names...";
    }

  // compare the name: 0 means identical
  const int name_result = _sys_name.compare(other_system.name());
  if (verbose)
    {
      if (name_result == 0)
        libMesh::out << " identical." << std::endl;
      else
        libMesh::out << "  names not identical." << std::endl;
      libMesh::out << "   comparing solution vector...";
    }


  // compare the solution: -1 means identical
  const int solu_result = solution->compare (*other_system.solution.get(),
                                             threshold);

  if (verbose)
    {
      if (solu_result == -1)
        libMesh::out << " identical up to threshold." << std::endl;
      else
        libMesh::out << "  first difference occurred at index = "
                     << solu_result << "." << std::endl;
    }


  // safety check, whether we handle at least the same number
  // of vectors
  std::vector<int> ov_result;

  if (this->n_vectors() != other_system.n_vectors())
    {
      if (verbose)
        {
          libMesh::out << "   Fatal difference. This system handles "
                       << this->n_vectors() << " add'l vectors," << std::endl
                       << "   while the other system handles "
                       << other_system.n_vectors()
                       << " add'l vectors." << std::endl
                       << "   Aborting comparison." << std::endl;
        }
      return false;
    }
  else if (this->n_vectors() == 0)
    {
      // there are no additional vectors...
      ov_result.clear ();
    }
  else
    {
      // compare other vectors
      for (auto & [vec_name, vec] : _vectors)
        {
          if (verbose)
            libMesh::out << "   comparing vector \""
                         << vec_name << "\" ...";

          // assume they have the same name
          const NumericVector<Number> & other_system_vector =
            other_system.get_vector(vec_name);

          ov_result.push_back(vec->compare(other_system_vector, threshold));

          if (verbose)
            {
              if (ov_result[ov_result.size()-1] == -1)
                libMesh::out << " identical up to threshold." << std::endl;
              else
                libMesh::out << " first difference occurred at" << std::endl
                             << "   index = " << ov_result[ov_result.size()-1] << "." << std::endl;
            }
        }
    } // finished comparing additional vectors


  bool overall_result;

  // sum up the results
  if ((name_result==0) && (solu_result==-1))
    {
      if (ov_result.size()==0)
        overall_result = true;
      else
        {
          bool ov_identical;
          unsigned int n    = 0;
          do
            {
              ov_identical = (ov_result[n]==-1);
              n++;
            }
          while (ov_identical && n<ov_result.size());
          overall_result = ov_identical;
        }
    }
  else
    overall_result = false;

  if (verbose)
    {
      libMesh::out << "   finished comparisons, ";
      if (overall_result)
        libMesh::out << "found no differences." << std::endl << std::endl;
      else
        libMesh::out << "found differences." << std::endl << std::endl;
    }

  return overall_result;
}

condense_constrained_dofs()

virtual bool libMesh::System::condense_constrained_dofs ( ) const

inlineprotectedvirtualinherited

Whether this object should condense out constrained degrees of freedom.

Reimplemented in libMesh::CondensedEigenSystem.

Definition at line 2013 of file system.h.

Referenced by libMesh::EigenSystem::init_matrices().

{ return false; }

continuation_solve()

void libMesh::ContinuationSystem::continuation_solve

(

)

Perform a continuation solve of the system.

In general, you can only begin the continuation solves after either reading in or solving for two previous values of the control parameter. The prior two solutions are required for starting up the continuation method.

Definition at line 359 of file continuation_system.C.

References libMesh::NumericVector< T >::add(), apply_predictor(), libMesh::FEMSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), continuation_parameter, continuation_parameter_tolerance, delta_u, dlambda_ds, libMesh::NumericVector< T >::dot(), ds_current, du_ds, G_Lambda, initial_newton_tolerance, initialize_tangent(), libMesh::NumericVector< T >::l2_norm(), libMesh::libmesh_real(), libMesh::ImplicitSystem::linear_solver, libMesh::ImplicitSystem::matrix, max_continuation_parameter, libMesh::DiffSolver::max_linear_iterations, libMesh::DiffSolver::max_nonlinear_iterations, min_continuation_parameter, n_arclength_reductions, n_backtrack_steps, newton_progress_check, newton_solver, newton_step, old_continuation_parameter, libMesh::out, libMesh::Utility::pow(), libMesh::BasicOStreamProxy< charT, traits >::precision(), previous_u, quiet, libMesh::Real, Residual, libMesh::ExplicitSystem::rhs, rhs_mode, libMesh::NumericVector< T >::scale(), libMesh::BasicOStreamProxy< charT, traits >::setf(), libMesh::System::solution, solution_tolerance, tangent_initialized, Theta, Theta_LOCA, libMesh::DifferentiableSystem::time_solver, libMesh::BasicOStreamProxy< charT, traits >::unsetf(), y, y_old, z, and libMesh::NumericVector< T >::zero().

{
  // Be sure the user has set the continuation parameter pointer
  libmesh_error_msg_if(!continuation_parameter,
                       "You must set the continuation_parameter pointer "
                       "to a member variable of the derived class, preferably in the "
                       "Derived class's init_data function.  This is how the ContinuationSystem "
                       "updates the continuation parameter.");

  // Use extra precision for all the numbers printed in this function.
  std::streamsize old_precision = libMesh::out.precision();
  libMesh::out.precision(16);
  libMesh::out.setf(std::ios_base::scientific);

  // We can't start solving the augmented PDE system unless the tangent
  // vectors have been initialized.  This only needs to occur once.
  if (!tangent_initialized)
    initialize_tangent();

  // Save the old value of -du/dlambda.  This will be used after the Newton iterations
  // to compute the angle between previous tangent vectors.  This cosine of this angle is
  //
  // tau := abs( (du/d(lambda)_i , du/d(lambda)_{i-1}) / (||du/d(lambda)_i|| * ||du/d(lambda)_{i-1}||) )
  //
  // The scaling factor tau (which should vary between 0 and 1) is used to shrink the step-size ds
  // when we are approaching a turning point.  Note that it can only shrink the step size.
  *y_old = *y;

  // Set pointer to underlying Newton solver
  if (!newton_solver)
    newton_solver = cast_ptr<NewtonSolver *> (this->time_solver->diff_solver().get());

  // A pair for catching return values from linear system solves.
  std::pair<unsigned int, Real> rval;

  // Convergence flag for the entire arcstep
  bool arcstep_converged = false;

  // Begin loop over arcstep reductions.
  for (unsigned int ns=0; ns<n_arclength_reductions; ++ns)
    {
      if (!quiet)
        {
          libMesh::out << "Current arclength stepsize, ds_current=" << ds_current << std::endl;
          libMesh::out << "Current parameter value, lambda=" << *continuation_parameter << std::endl;
        }

      // Upon exit from the nonlinear loop, the newton_converged flag
      // will tell us the convergence status of Newton's method.
      bool newton_converged = false;

      // The nonlinear residual before *any* nonlinear steps have been taken.
      Real nonlinear_residual_firststep = 0.;

      // The nonlinear residual from the current "k" Newton step, before the Newton step
      Real nonlinear_residual_beforestep = 0.;

      // The nonlinear residual from the current "k" Newton step, after the Newton step
      Real nonlinear_residual_afterstep = 0.;

      // The linear solver tolerance, can be updated dynamically at each Newton step.
      double current_linear_tolerance = 0.;

      // The nonlinear loop
      for (newton_step=0; newton_step<newton_solver->max_nonlinear_iterations; ++newton_step)
        {
          libMesh::out << "\n === Starting Newton step " << newton_step << " ===" << std::endl;

          // Set the linear system solver tolerance
          //   // 1.) Set the current linear tolerance based as a multiple of the current residual of the system.
          //   const Real residual_multiple = 1.e-4;
          //   Real current_linear_tolerance = residual_multiple*nonlinear_residual_beforestep;

          //   // But if the current residual isn't small, don't let the solver exit with zero iterations!
          //   if (current_linear_tolerance > 1.)
          //     current_linear_tolerance = residual_multiple;

          // 2.) Set the current linear tolerance based on the method based on technique of Eisenstat & Walker.
          if (newton_step==0)
            {
              // At first step, only try reducing the residual by a small amount
              current_linear_tolerance = initial_newton_tolerance;//0.01;
            }

          else
            {
              // The new tolerance is based on the ratio of the most recent tolerances
              const Real alp=0.5*(1.+std::sqrt(5.));
              const Real gam=0.9;

              libmesh_assert_not_equal_to (nonlinear_residual_beforestep, 0.0);
              libmesh_assert_not_equal_to (nonlinear_residual_afterstep, 0.0);

              current_linear_tolerance =
                double(std::min(gam*std::pow(nonlinear_residual_afterstep/nonlinear_residual_beforestep, alp),
                                current_linear_tolerance*current_linear_tolerance));

              // Don't let it get ridiculously small!!
              if (current_linear_tolerance < 1.e-12)
                current_linear_tolerance = 1.e-12;
            }

          if (!quiet)
            libMesh::out << "Using current_linear_tolerance=" << current_linear_tolerance << std::endl;


          // Assemble the residual (and Jacobian).
          rhs_mode = Residual;
          assembly(true,   // Residual
                   true); // Jacobian
          rhs->close();

          // Save the current nonlinear residual.  We don't need to recompute the residual unless
          // this is the first step, since it was already computed as part of the convergence check
          // at the end of the last loop iteration.
          if (newton_step==0)
            {
              nonlinear_residual_beforestep = rhs->l2_norm();

              // Store the residual before any steps have been taken.  This will *not*
              // be updated at each step, and can be used to see if any progress has
              // been made from the initial residual at later steps.
              nonlinear_residual_firststep = nonlinear_residual_beforestep;

              const Real old_norm_u = solution->l2_norm();
              libMesh::out << "  (before step) ||R||_{L2} = " << nonlinear_residual_beforestep << std::endl;
              libMesh::out << "  (before step) ||R||_{L2}/||u|| = " << nonlinear_residual_beforestep / old_norm_u << std::endl;

              // In rare cases (very small arcsteps), it's possible that the residual is
              // already below our absolute linear tolerance.
              if (nonlinear_residual_beforestep  < solution_tolerance)
                {
                  if (!quiet)
                    libMesh::out << "Initial guess satisfied linear tolerance, exiting with zero Newton iterations!" << std::endl;

                  // Since we go straight from here to the solve of the next tangent, we
                  // have to close the matrix before it can be assembled again.
                  matrix->close();
                  newton_converged=true;
                  break; // out of Newton iterations, with newton_converged=true
                }
            }

          else
            {
              nonlinear_residual_beforestep = nonlinear_residual_afterstep;
            }


          // Solve the linear system G_u*z = G
          // Initial guess?
          z->zero(); // It seems to be extremely important to zero z here, otherwise the solver quits early.
          z->close();

          // It's possible that we have selected the current_linear_tolerance so large that
          // a guess of z=zero yields a linear system residual |Az + R| small enough that the
          // linear solver exits in zero iterations.  If this happens, we will reduce the
          // current_linear_tolerance until the linear solver does at least 1 iteration.
          do
            {
              rval =
                linear_solver->solve(*matrix,
                                     *z,
                                     *rhs,
                                     //1.e-12,
                                     current_linear_tolerance,
                                     newton_solver->max_linear_iterations);   // max linear iterations

              if (rval.first==0)
                {
                  if (newton_step==0)
                    {
                      libMesh::out << "Repeating initial solve with smaller linear tolerance!" << std::endl;
                      current_linear_tolerance *= initial_newton_tolerance; // reduce the linear tolerance to force the solver to do some work
                    }
                  else
                    // We shouldn't get here ... it means the linear solver did no work on a Newton
                    // step other than the first one.  If this happens, we need to think more about our
                    // tolerance selection.
                    libmesh_error_msg("Linear solver did no work!");
                }

            } while (rval.first==0);


          if (!quiet)
            libMesh::out << "  G_u*z = G solver converged at step "
                         << rval.first
                         << " linear tolerance = "
                         << rval.second
                         << "."
                         << std::endl;

          // Sometimes (I am not sure why) the linear solver exits after zero iterations.
          // Perhaps it is hitting PETSc's divergence tolerance dtol???  If this occurs,
          // we should break out of the Newton iteration loop because nothing further is
          // going to happen...  Of course if the tolerance is already small enough after
          // zero iterations (how can this happen?!) we should not quit.
          if ((rval.first == 0) && (rval.second > current_linear_tolerance*nonlinear_residual_beforestep))
            {
              if (!quiet)
                libMesh::out << "Linear solver exited in zero iterations!" << std::endl;

              // Try to find out the reason for convergence/divergence
              linear_solver->print_converged_reason();

              break; // out of Newton iterations
            }

          // Note: need to scale z by -1 since our code always solves Jx=R
          // instead of Jx=-R.
          z->scale(-1.);
          z->close();






          // Assemble the G_Lambda vector, skip residual.
          rhs_mode = G_Lambda;

          // Assemble both rhs and Jacobian
          assembly(true,  // Residual
                   false); // Jacobian

          // Not sure if this is really necessary
          rhs->close();
          const Real yrhsnorm=rhs->l2_norm();
          libmesh_error_msg_if(yrhsnorm == 0.0, "||G_Lambda|| = 0");

          // We select a tolerance for the y-system which is based on the inexact Newton
          // tolerance but scaled by an extra term proportional to the RHS (which is not -> 0 in this case)
          const double ysystemtol =
            double(current_linear_tolerance*(nonlinear_residual_beforestep/yrhsnorm));
          if (!quiet)
            libMesh::out << "ysystemtol=" << ysystemtol << std::endl;

          // Solve G_u*y = G_{\lambda}
          // FIXME: Initial guess?  This is really a solve for -du/dlambda so we could try
          // initializing it with the latest approximation to that... du/dlambda ~ du/ds * ds/dlambda
          //*y = *solution;
          //y->add(-1., *previous_u);
          //y->scale(-1. / (*continuation_parameter - old_continuation_parameter)); // Be careful of divide by zero...
          //y->close();

          //  const unsigned int max_attempts=1;
          // unsigned int attempt=0;
          //   do
          //     {
          //       if (!quiet)
          // libMesh::out << "Trying to solve tangent system, attempt " << attempt << std::endl;

          rval =
            linear_solver->solve(*matrix,
                                 *y,
                                 *rhs,
                                 //1.e-12,
                                 ysystemtol,
                                 newton_solver->max_linear_iterations);   // max linear iterations

          if (!quiet)
            libMesh::out << "  G_u*y = G_{lambda} solver converged at step "
                         << rval.first
                         << ", linear tolerance = "
                         << rval.second
                         << "."
                         << std::endl;

          // Sometimes (I am not sure why) the linear solver exits after zero iterations.
          // Perhaps it is hitting PETSc's divergence tolerance dtol???  If this occurs,
          // we should break out of the Newton iteration loop because nothing further is
          // going to happen...
          if ((rval.first == 0) && (rval.second > ysystemtol))
            {
              if (!quiet)
                libMesh::out << "Linear solver exited in zero iterations!" << std::endl;

              break; // out of Newton iterations
            }

          //       ++attempt;
          //     } while ((attempt<max_attempts) && (rval.first==newton_solver->max_linear_iterations));





          // Compute N, the residual of the arclength constraint eqn.
          // Note 1: N(u,lambda,s) := (u-u_{old}, du_ds) + (lambda-lambda_{old}, dlambda_ds) - _ds
          // We temporarily use the delta_u vector as a temporary vector for this calculation.
          *delta_u = *solution;
          delta_u->add(-1., *previous_u);

          // First part of the arclength constraint
          const Number N1 = Theta_LOCA*Theta_LOCA*Theta*delta_u->dot(*du_ds);
          const Number N2 = ((*continuation_parameter) - old_continuation_parameter)*dlambda_ds;
          const Number N3 = ds_current;

          if (!quiet)
            {
              libMesh::out << "  N1=" << N1 << std::endl;
              libMesh::out << "  N2=" << N2 << std::endl;
              libMesh::out << "  N3=" << N3 << std::endl;
            }

          // The arclength constraint value
          const Number N = N1+N2-N3;

          if (!quiet)
            libMesh::out << "  N=" << N << std::endl;

          const Number duds_dot_z = du_ds->dot(*z);
          const Number duds_dot_y = du_ds->dot(*y);

          //libMesh::out << "duds_dot_z=" << duds_dot_z << std::endl;
          //libMesh::out << "duds_dot_y=" << duds_dot_y << std::endl;
          //libMesh::out << "dlambda_ds=" << dlambda_ds << std::endl;

          const Number delta_lambda_numerator   = -(N          + Theta_LOCA*Theta_LOCA*Theta*duds_dot_z);
          const Number delta_lambda_denominator =  (dlambda_ds - Theta_LOCA*Theta_LOCA*Theta*duds_dot_y);

          libmesh_assert_not_equal_to (delta_lambda_denominator, 0.0);

          // Now, we are ready to compute the step delta_lambda
          const Number delta_lambda_comp = delta_lambda_numerator /
            delta_lambda_denominator;
          // Lambda is real-valued
          const Real delta_lambda = libmesh_real(delta_lambda_comp);

          // Knowing delta_lambda, we are ready to update delta_u
          // delta_u = z - delta_lambda*y
          delta_u->zero();
          delta_u->add(1., *z);
          delta_u->add(-delta_lambda, *y);
          delta_u->close();

          // Update the system solution and the continuation parameter.
          solution->add(1., *delta_u);
          solution->close();
          *continuation_parameter += delta_lambda;

          // Did the Newton step actually reduce the residual?
          rhs_mode = Residual;
          assembly(true,   // Residual
                   false); // Jacobian
          rhs->close();
          nonlinear_residual_afterstep = rhs->l2_norm();


          // In a "normal" Newton step, ||du||/||R|| > 1 since the most recent
          // step is where you "just were" and the current residual is where
          // you are now.  It can occur that ||du||/||R|| < 1, but these are
          // likely not good cases to attempt backtracking (?).
          const Real norm_du_norm_R = delta_u->l2_norm() / nonlinear_residual_afterstep;
          if (!quiet)
            libMesh::out << "  norm_du_norm_R=" << norm_du_norm_R << std::endl;


          // Factor to decrease the stepsize by for backtracking
          Real newton_stepfactor = 1.;

          const bool attempt_backtracking =
            (nonlinear_residual_afterstep > solution_tolerance)
            && (nonlinear_residual_afterstep > nonlinear_residual_beforestep)
            && (n_backtrack_steps>0)
            && (norm_du_norm_R > 1.)
            ;

          // If residual is not reduced, do Newton back tracking.
          if (attempt_backtracking)
            {
              if (!quiet)
                libMesh::out << "Newton step did not reduce residual." << std::endl;

              // back off the previous step.
              solution->add(-1., *delta_u);
              solution->close();
              *continuation_parameter -= delta_lambda;

              // Backtracking: start cutting the Newton stepsize by halves until
              // the new residual is actually smaller...
              for (unsigned int backtrack_step=0; backtrack_step<n_backtrack_steps; ++backtrack_step)
                {
                  newton_stepfactor *= 0.5;

                  if (!quiet)
                    libMesh::out << "Shrinking step size by " << newton_stepfactor << std::endl;

                  // Take fractional step
                  solution->add(newton_stepfactor, *delta_u);
                  solution->close();
                  *continuation_parameter += newton_stepfactor*delta_lambda;

                  rhs_mode = Residual;
                  assembly(true,   // Residual
                           false); // Jacobian
                  rhs->close();
                  nonlinear_residual_afterstep = rhs->l2_norm();

                  if (!quiet)
                    libMesh::out << "At shrink step "
                                 << backtrack_step
                                 << ", nonlinear_residual_afterstep="
                                 << nonlinear_residual_afterstep
                                 << std::endl;

                  if (nonlinear_residual_afterstep < nonlinear_residual_beforestep)
                    {
                      if (!quiet)
                        libMesh::out << "Backtracking succeeded!" << std::endl;

                      break; // out of backtracking loop
                    }

                  else
                    {
                      // Back off that step
                      solution->add(-newton_stepfactor, *delta_u);
                      solution->close();
                      *continuation_parameter -= newton_stepfactor*delta_lambda;
                    }

                  // Save a copy of the solution from before the Newton step.
                  //std::unique_ptr<NumericVector<Number>> prior_iterate = solution->clone();
                }
            } // end if (attempte_backtracking)


          // If we tried backtracking but the residual is still not reduced, print message.
          if ((attempt_backtracking) && (nonlinear_residual_afterstep > nonlinear_residual_beforestep))
            {
              //libMesh::err << "Backtracking failed." << std::endl;
              libMesh::out << "Backtracking failed." << std::endl;

              // 1.) Quit, exit program.
              //libmesh_error_msg("Backtracking failed!");

              // 2.) Continue with last newton_stepfactor
              if (newton_step<3)
                {
                  solution->add(newton_stepfactor, *delta_u);
                  solution->close();
                  *continuation_parameter += newton_stepfactor*delta_lambda;
                  if (!quiet)
                    libMesh::out << "Backtracking could not reduce residual ... continuing anyway!" << std::endl;
                }

              // 3.) Break out of Newton iteration loop with newton_converged = false,
              //     reduce the arclength stepsize, and try again.
              else
                {
                  break; // out of Newton iteration loop, with newton_converged=false
                }
            }

          // Another type of convergence check: suppose the residual has not been reduced
          // from its initial value after half of the allowed Newton steps have occurred.
          // In our experience, this typically means that it isn't going to converge and
          // we could probably save time by dropping out of the Newton iteration loop and
          // trying a smaller arcstep.
          if (this->newton_progress_check)
            {
              if ((nonlinear_residual_afterstep > nonlinear_residual_firststep) &&
                  (newton_step+1 > static_cast<unsigned int>(0.5*newton_solver->max_nonlinear_iterations)))
                {
                  libMesh::out << "Progress check failed: the current residual: "
                               << nonlinear_residual_afterstep
                               << ", is\n"
                               << "larger than the initial residual, and half of the allowed\n"
                               << "number of Newton iterations have elapsed.\n"
                               << "Exiting Newton iterations with converged==false." << std::endl;

                  break; // out of Newton iteration loop, newton_converged = false
                }
            }

          // Safety check: Check the current continuation parameter against user-provided min-allowable parameter value
          if (*continuation_parameter < min_continuation_parameter)
            {
              libMesh::out << "Continuation parameter fell below min-allowable value." << std::endl;
              break; // out of Newton iteration loop, newton_converged = false
            }

          // Safety check: Check the current continuation parameter against user-provided max-allowable parameter value
          if ( (max_continuation_parameter != 0.0) &&
               (*continuation_parameter > max_continuation_parameter) )
            {
              libMesh::out << "Current continuation parameter value: "
                           << *continuation_parameter
                           << " exceeded max-allowable value."
                           << std::endl;
              break; // out of Newton iteration loop, newton_converged = false
            }


          // Check the convergence of the parameter and the solution.  If they are small
          // enough, we can break out of the Newton iteration loop.
          const Real norm_delta_u = delta_u->l2_norm();
          const Real norm_u = solution->l2_norm();
          libMesh::out << "  delta_lambda                   = " << delta_lambda << std::endl;
          libMesh::out << "  newton_stepfactor*delta_lambda = " << newton_stepfactor*delta_lambda << std::endl;
          libMesh::out << "  lambda_current                 = " << *continuation_parameter << std::endl;
          libMesh::out << "  ||delta_u||                    = " << norm_delta_u << std::endl;
          libMesh::out << "  ||delta_u||/||u||              = " << norm_delta_u / norm_u << std::endl;


          // Evaluate the residual at the current Newton iterate.  We don't want to detect
          // convergence due to a small Newton step when the residual is still not small.
          rhs_mode = Residual;
          assembly(true,   // Residual
                   false); // Jacobian
          rhs->close();
          const Real norm_residual = rhs->l2_norm();
          libMesh::out << "  ||R||_{L2} = " << norm_residual << std::endl;
          libMesh::out << "  ||R||_{L2}/||u|| = " << norm_residual / norm_u << std::endl;


          // FIXME: The norm_delta_u tolerance (at least) should be relative.
          // It doesn't make sense to converge a solution whose size is ~ 10^5 to
          // a tolerance of 1.e-6.  Oh, and we should also probably check the
          // (relative) size of the residual as well, instead of just the step.
          if ((std::abs(delta_lambda) < continuation_parameter_tolerance) &&
              //(norm_delta_u       < solution_tolerance)               && // This is a *very* strict criterion we can probably skip
              (norm_residual      < solution_tolerance))
            {
              if (!quiet)
                libMesh::out << "Newton iterations converged!" << std::endl;

              newton_converged = true;
              break; // out of Newton iterations
            }
        } // end nonlinear loop

      if (!newton_converged)
        {
          libMesh::out << "Newton iterations of augmented system did not converge!" << std::endl;

          // Reduce ds_current, recompute the solution and parameter, and continue to next
          // arcstep, if there is one.
          ds_current *= 0.5;

          // Go back to previous solution and parameter value.
          *solution = *previous_u;
          *continuation_parameter = old_continuation_parameter;

          // Compute new predictor with smaller ds
          apply_predictor();
        }
      else
        {
          // Set step convergence and break out
          arcstep_converged=true;
          break; // out of arclength reduction loop
        }

    } // end loop over arclength reductions

  // Check for convergence of the whole arcstep.  If not converged at this
  // point, we have no choice but to quit.
  libmesh_error_msg_if(!arcstep_converged, "Arcstep failed to converge after max number of reductions! Exiting...");

  // Print converged solution control parameter and max value.
  libMesh::out << "lambda_current=" << *continuation_parameter << std::endl;
  //libMesh::out << "u_max=" << solution->max() << std::endl;

  // Reset old stream precision and flags.
  libMesh::out.precision(old_precision);
  libMesh::out.unsetf(std::ios_base::scientific);

  // Note: we don't want to go on to the next guess yet, since the user may
  // want to post-process this data.  It's up to the user to call advance_arcstep()
  // when they are ready to go on.
}

create_static_condensation()

void libMesh::ImplicitSystem::create_static_condensation ( )

overridevirtualinherited

Request that static condensation be performed for this system.

Reimplemented from libMesh::System.

Reimplemented in libMesh::NonlinearImplicitSystem, and libMesh::LinearImplicitSystem.

Definition at line 64 of file implicit_system.C.

References libMesh::System::create_static_condensation(), and libMesh::ImplicitSystem::create_static_condensation_system_matrix().

Referenced by libMesh::LinearImplicitSystem::create_static_condensation(), and libMesh::NonlinearImplicitSystem::create_static_condensation().

{
  Parent::create_static_condensation();
  this->create_static_condensation_system_matrix();
}

current_solution()

Number libMesh::System::current_solution ( const dof_id_type  global_dof_number ) const

inherited

Returns

The current solution for the specified global DOF.

Definition at line 165 of file system.C.

References libMesh::System::_dof_map, and libMesh::System::current_local_solution.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::HPCoarsenTest::add_projection(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::ExactErrorEstimator::estimate_error(), main(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::HPCoarsenTest::select_refinement(), SolidSystem::side_time_derivative(), libMesh::EnsightIO::write_scalar_ascii(), and libMesh::EnsightIO::write_vector_ascii().

{
  // Check the sizes
  libmesh_assert_less (global_dof_number, _dof_map->n_dofs());
  libmesh_assert_less (global_dof_number, current_local_solution->size());

  return (*current_local_solution)(global_dof_number);
}

damping_residual()

virtual bool libMesh::DifferentiablePhysics::damping_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Subtracts a damping vector contribution on elem from elem_residual.

This method is not used in first-order-in-time problems. For second-order-in-time problems, this is the \( C(u,\ddot{u})\ddot{u} \) term. This method is only called for UnsteadySolver-based TimeSolvers.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

If the problem has no damping, the default "do-nothing" is correct. Otherwise, this must be reimplemented.

Reimplemented in SecondOrderScalarSystemFirstOrderTimeSolverBase, and SecondOrderScalarSystemSecondOrderTimeSolverBase.

Definition at line 360 of file diff_physics.h.

Referenced by libMesh::EulerSolver::element_residual(), libMesh::Euler2Solver::element_residual(), and libMesh::NewmarkSolver::element_residual().

  {
    return request_jacobian;
  }

deactivate()

void libMesh::System::deactivate ( )

inlineinherited

Deactivates the system.

Only active systems are solved.

Definition at line 2406 of file system.h.

References libMesh::System::_active.

{
  _active = false;
}

disable_cache()

void libMesh::ImplicitSystem::disable_cache ( )

overridevirtualinherited

Avoids use of any cached data that might affect any solve result.

Should be overridden in derived systems.

Reimplemented from libMesh::System.

Definition at line 128 of file implicit_system.C.

References libMesh::System::assemble_before_solve, libMesh::ImplicitSystem::get_linear_solver(), and libMesh::LinearSolver< T >::reuse_preconditioner().

Referenced by libMesh::DifferentiableSystem::pop_physics(), libMesh::DifferentiableSystem::push_physics(), and libMesh::DifferentiableSystem::swap_physics().

                                    {
  this->assemble_before_solve = true;
  this->get_linear_solver()->reuse_preconditioner(false);
}

disable_print_counter_info()

void libMesh::ReferenceCounter::disable_print_counter_info ( )

staticinherited

Definition at line 100 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

{
  _enable_print_counter = false;
  return;
}

element_constraint()

virtual bool libMesh::DifferentiablePhysics::element_constraint ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds the constraint contribution on elem to elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Users may need to reimplement this for their particular PDE.

To implement the constraint 0 = G(u), the user should examine u = elem_solution and add (G(u), phi_i) to elem_residual in elem_constraint().

Reimplemented in CoupledSystem, and NavierSystem.

Definition at line 144 of file diff_physics.h.

Referenced by libMesh::EulerSolver::element_residual(), libMesh::SteadySolver::element_residual(), libMesh::Euler2Solver::element_residual(), libMesh::NewmarkSolver::element_residual(), and libMesh::EigenTimeSolver::element_residual().

  {
    return request_jacobian;
  }

element_postprocess()

virtual void libMesh::DifferentiableSystem::element_postprocess ( DiffContext &  )

inlinevirtualinherited

Does any work that needs to be done on elem in a postprocessing loop.

Reimplemented in LaplaceSystem, LaplaceSystem, and PoissonSystem.

Definition at line 301 of file diff_system.h.

{}

element_qoi()

virtual void libMesh::DifferentiableQoI::element_qoi ( DiffContext &  , const QoISet &    )

inlinevirtualinherited

Does any work that needs to be done on elem in a quantity of interest assembly loop, outputting to elem_qoi.

Only qois included in the supplied QoISet need to be assembled.

Reimplemented in HeatSystem, and LaplaceQoI.

Definition at line 124 of file diff_qoi.h.

  {}

element_qoi_derivative()

virtual void libMesh::DifferentiableQoI::element_qoi_derivative ( DiffContext &  , const QoISet &    )

inlinevirtualinherited

Does any work that needs to be done on elem in a quantity of interest derivative assembly loop, outputting to elem_qoi_derivative.

Only qois included in the supplied QoISet need their derivatives assembled.

Reimplemented in HeatSystem, LaplaceSystem, HeatSystem, LaplaceSystem, and LaplaceQoI.

Definition at line 136 of file diff_qoi.h.

  {}

element_time_derivative()

virtual bool libMesh::DifferentiablePhysics::element_time_derivative ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds the time derivative contribution on elem to elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Users need to reimplement this for their particular PDE.

To implement the physics model du/dt = F(u), the user should examine u = elem_solution and add (F(u), phi_i) to elem_residual in elem_time_derivative().

Reimplemented in SecondOrderScalarSystemFirstOrderTimeSolverBase, FirstOrderScalarSystemBase, HeatSystem, HilbertSystem, CoupledSystem, libMesh::VariationalSmootherSystem, ElasticitySystem, ElasticitySystem, HeatSystem, LaplaceSystem, CurlCurlSystem, LaplaceSystem, PoissonSystem, LaplaceSystem, LaplaceSystem, CurlCurlSystem, SolidSystem, NavierSystem, SigmaPhysics, and HeatSystem.

Definition at line 125 of file diff_physics.h.

Referenced by libMesh::DifferentiablePhysics::_eulerian_time_deriv(), libMesh::SteadySolver::element_residual(), and libMesh::EigenTimeSolver::element_residual().

  {
    return request_jacobian;
  }

enable_print_counter_info()

void libMesh::ReferenceCounter::enable_print_counter_info ( )

staticinherited

Methods to enable/disable the reference counter output from print_info()

Definition at line 94 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

{
  _enable_print_counter = true;
  return;
}

eulerian_residual() [1/2]

bool libMesh::FEMPhysics::eulerian_residual ( bool  request_jacobian, DiffContext &  context  )

overridevirtualinherited

Adds a pseudo-convection contribution on elem to elem_residual, if the nodes of elem are being translated by a moving mesh.

This function assumes that the user's time derivative equations (except for any equations involving unknown mesh xyz coordinates themselves) are expressed in an Eulerian frame of reference, and that the user is satisfied with an unstabilized convection term. Lagrangian equations will probably require overriding eulerian_residual() with a blank function; ALE or stabilized formulations will require reimplementing eulerian_residual() entirely.

Reimplemented from libMesh::DifferentiablePhysics.

Reimplemented in SolidSystem.

Definition at line 38 of file fem_physics.C.

References libMesh::DifferentiablePhysics::_mesh_sys, libMesh::DifferentiablePhysics::_mesh_x_var, libMesh::DifferentiablePhysics::_mesh_y_var, libMesh::DifferentiablePhysics::_mesh_z_var, libMesh::FEMContext::get_element_qrule(), libMesh::FEMContext::interior_gradient(), libMesh::invalid_uint, libMesh::DifferentiablePhysics::is_time_evolving(), libMesh::libmesh_assert(), libMesh::libmesh_real(), libMesh::make_range(), libMesh::DiffContext::n_vars(), and libMesh::UnsteadySolver::old_nonlinear_solution().

{
  // Only calculate a mesh movement residual if it's necessary
  if (!_mesh_sys)
    return request_jacobian;

  libmesh_not_implemented();

#if 0
  FEMContext & context = cast_ref<FEMContext &>(c);

  // This function only supports fully coupled mesh motion for now
  libmesh_assert_equal_to (_mesh_sys, this);

  unsigned int n_qpoints = (context.get_element_qrule())->n_points();

  const unsigned int n_x_dofs = (_mesh_x_var == libMesh::invalid_uint) ?
    0 : context.dof_indices_var[_mesh_x_var].size();
  const unsigned int n_y_dofs = (_mesh_y_var == libMesh::invalid_uint) ?
    0 : context.dof_indices_var[_mesh_y_var].size();
  const unsigned int n_z_dofs = (_mesh_z_var == libMesh::invalid_uint) ?
    0 : context.dof_indices_var[_mesh_z_var].size();

  const unsigned int mesh_xyz_var = n_x_dofs ? _mesh_x_var :
    (n_y_dofs ? _mesh_y_var :
     (n_z_dofs ? _mesh_z_var :
      libMesh::invalid_uint));

  // If we're our own _mesh_sys, we'd better be in charge of
  // at least one coordinate, and we'd better have the same
  // FE type for all coordinates we are in charge of
  libmesh_assert_not_equal_to (mesh_xyz_var, libMesh::invalid_uint);
  libmesh_assert(!n_x_dofs || context.element_fe_var[_mesh_x_var] ==
                 context.element_fe_var[mesh_xyz_var]);
  libmesh_assert(!n_y_dofs || context.element_fe_var[_mesh_y_var] ==
                 context.element_fe_var[mesh_xyz_var]);
  libmesh_assert(!n_z_dofs || context.element_fe_var[_mesh_z_var] ==
                 context.element_fe_var[mesh_xyz_var]);

  const std::vector<std::vector<Real>>     & psi =
    context.element_fe_var[mesh_xyz_var]->get_phi();

  for (auto var : make_range(context.n_vars()))
    {
      // Mesh motion only affects time-evolving variables
      if (this->is_time_evolving(var))
        continue;

      // The mesh coordinate variables themselves are Lagrangian,
      // not Eulerian, and no convective term is desired.
      if (/*_mesh_sys == this && */
          (var == _mesh_x_var ||
           var == _mesh_y_var ||
           var == _mesh_z_var))
        continue;

      // Some of this code currently relies on the assumption that
      // we can pull mesh coordinate data from our own system
      if (_mesh_sys != this)
        libmesh_not_implemented();

      // This residual should only be called by unsteady solvers:
      // if the mesh is steady, there's no mesh convection term!
      UnsteadySolver * unsteady;
      if (this->time_solver->is_steady())
        return request_jacobian;
      else
        unsteady = cast_ptr<UnsteadySolver*>(this->time_solver.get());

      const std::vector<Real> & JxW =
        context.element_fe_var[var]->get_JxW();

      const std::vector<std::vector<Real>> & phi =
        context.element_fe_var[var]->get_phi();

      const std::vector<std::vector<RealGradient>> & dphi =
        context.element_fe_var[var]->get_dphi();

      const unsigned int n_u_dofs = context.dof_indices_var[var].size();

      DenseSubVector<Number> & Fu = *context.elem_subresiduals[var];
      DenseSubMatrix<Number> & Kuu = *context.elem_subjacobians[var][var];

      DenseSubMatrix<Number> * Kux = n_x_dofs ?
        context.elem_subjacobians[var][_mesh_x_var] : nullptr;
      DenseSubMatrix<Number> * Kuy = n_y_dofs ?
        context.elem_subjacobians[var][_mesh_y_var] : nullptr;
      DenseSubMatrix<Number> * Kuz = n_z_dofs ?
        context.elem_subjacobians[var][_mesh_z_var] : nullptr;

      std::vector<Real> delta_x(n_x_dofs, 0.);
      std::vector<Real> delta_y(n_y_dofs, 0.);
      std::vector<Real> delta_z(n_z_dofs, 0.);

      for (unsigned int i = 0; i != n_x_dofs; ++i)
        {
          unsigned int j = context.dof_indices_var[_mesh_x_var][i];
          delta_x[i] = libmesh_real(this->current_solution(j)) -
            libmesh_real(unsteady->old_nonlinear_solution(j));
        }

      for (unsigned int i = 0; i != n_y_dofs; ++i)
        {
          unsigned int j = context.dof_indices_var[_mesh_y_var][i];
          delta_y[i] = libmesh_real(this->current_solution(j)) -
            libmesh_real(unsteady->old_nonlinear_solution(j));
        }

      for (unsigned int i = 0; i != n_z_dofs; ++i)
        {
          unsigned int j = context.dof_indices_var[_mesh_z_var][i];
          delta_z[i] = libmesh_real(this->current_solution(j)) -
            libmesh_real(unsteady->old_nonlinear_solution(j));
        }

      for (unsigned int qp = 0; qp != n_qpoints; ++qp)
        {
          Gradient grad_u = context.interior_gradient(var, qp);
          RealGradient convection(0.);

          for (unsigned int i = 0; i != n_x_dofs; ++i)
            convection(0) += delta_x[i] * psi[i][qp];
          for (unsigned int i = 0; i != n_y_dofs; ++i)
            convection(1) += delta_y[i] * psi[i][qp];
          for (unsigned int i = 0; i != n_z_dofs; ++i)
            convection(2) += delta_z[i] * psi[i][qp];

          for (unsigned int i = 0; i != n_u_dofs; ++i)
            {
              Number JxWxPhiI = JxW[qp] * phi[i][qp];
              Fu(i) += (convection * grad_u) * JxWxPhiI;
              if (request_jacobian)
                {
                  Number JxWxPhiI = JxW[qp] * phi[i][qp];
                  for (unsigned int j = 0; j != n_u_dofs; ++j)
                    Kuu(i,j) += JxWxPhiI * (convection * dphi[j][qp]);

                  Number JxWxPhiIoverDT = JxWxPhiI/this->deltat;

                  Number JxWxPhiIxDUDXoverDT = JxWxPhiIoverDT * grad_u(0);
                  for (unsigned int j = 0; j != n_x_dofs; ++j)
                    (*Kux)(i,j) += JxWxPhiIxDUDXoverDT * psi[j][qp];

                  Number JxWxPhiIxDUDYoverDT = JxWxPhiIoverDT * grad_u(1);
                  for (unsigned int j = 0; j != n_y_dofs; ++j)
                    (*Kuy)(i,j) += JxWxPhiIxDUDYoverDT * psi[j][qp];

                  Number JxWxPhiIxDUDZoverDT = JxWxPhiIoverDT * grad_u(2);
                  for (unsigned int j = 0; j != n_z_dofs; ++j)
                    (*Kuz)(i,j) += JxWxPhiIxDUDZoverDT * psi[j][qp];
                }
            }
        }
    }
#endif // 0

  return request_jacobian;
}

eulerian_residual() [2/2]

virtual bool libMesh::DifferentiablePhysics::eulerian_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds a pseudo-convection contribution on elem to elem_residual, if the nodes of elem are being translated by a moving mesh.

The library provides a basic implementation in FEMPhysics::eulerian_residual()

Reimplemented in libMesh::FEMPhysics, and SolidSystem.

Definition at line 277 of file diff_physics.h.

Referenced by libMesh::DifferentiablePhysics::_eulerian_time_deriv().

  {
    return request_jacobian;
  }

finalize_derivative()

void libMesh::DifferentiableQoI::finalize_derivative ( NumericVector< Number > &  derivatives, std::size_t  qoi_index  )

virtualinherited

Method to finalize qoi derivatives which require more than just a simple sum of element contributions.

Definition at line 53 of file diff_qoi.C.

Referenced by libMesh::FEMSystem::assemble_qoi_derivative().

{
  // by default, do nothing
}

forward_qoi_parameter_sensitivity()

void libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity ( const QoISet &  qoi_indices, const ParameterVector &  parameters, SensitivityData &  sensitivities  )

overridevirtualinherited

Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j].

Uses the forward sensitivity method.

Currently uses finite differenced derivatives (partial q / partial p) and (partial R / partial p).

Reimplemented from libMesh::System.

Definition at line 623 of file implicit_system.C.

References libMesh::SensitivityData::allocate_data(), libMesh::ExplicitSystem::assemble_qoi(), libMesh::ExplicitSystem::assemble_qoi_derivative(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::NumericVector< T >::dot(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_qoi_values(), libMesh::System::get_sensitivity_solution(), libMesh::QoISet::has_index(), libMesh::make_range(), libMesh::ImplicitSystem::matrix, libMesh::System::n_qois(), libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::ImplicitSystem::sensitivity_solve(), libMesh::ParameterVector::size(), and libMesh::TOLERANCE.

Referenced by main().

{
  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  const unsigned int Np = cast_int<unsigned int>
    (parameters_vec.size());
  const unsigned int Nq = this->n_qois();

  // An introduction to the problem:
  //
  // Residual R(u(p),p) = 0
  // partial R / partial u = J = system matrix
  //
  // This implies that:
  // d/dp(R) = 0
  // (partial R / partial p) +
  // (partial R / partial u) * (partial u / partial p) = 0

  // We first solve for (partial u / partial p) for each parameter:
  // J * (partial u / partial p) = - (partial R / partial p)

  this->sensitivity_solve(parameters_vec);

  // Get ready to fill in sensitivities:
  sensitivities.allocate_data(qoi_indices, *this, parameters_vec);

  // We use the identity:
  // dq/dp = (partial q / partial p) + (partial q / partial u) *
  //         (partial u / partial p)

  // We get (partial q / partial u) from the user
  this->assemble_qoi_derivative(qoi_indices,
                                /* include_liftfunc = */ true,
                                /* apply_constraints = */ false);

  // We don't need these to be closed() in this function, but libMesh
  // standard practice is to have them closed() by the time the
  // function exits
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      this->get_adjoint_rhs(i).close();

  for (unsigned int j=0; j != Np; ++j)
    {
      // We currently get partial derivatives via central differencing

      // (partial q / partial p) ~= (q(p+dp)-q(p-dp))/(2*dp)

      Number old_parameter = *parameters_vec[j];

      const Real delta_p =
        TOLERANCE * std::max(std::abs(old_parameter), 1e-3);

      *parameters_vec[j] = old_parameter - delta_p;
      this->assemble_qoi(qoi_indices);
      const std::vector<Number> qoi_minus = this->get_qoi_values();

      *parameters_vec[j] = old_parameter + delta_p;
      this->assemble_qoi(qoi_indices);
      const std::vector<Number> qoi_plus = this->get_qoi_values();

      std::vector<Number> partialq_partialp(Nq, 0);
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          partialq_partialp[i] = (qoi_plus[i] - qoi_minus[i]) / (2.*delta_p);

      // Don't leave the parameter changed
      *parameters_vec[j] = old_parameter;

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          sensitivities[i][j] = partialq_partialp[i] +
            this->get_adjoint_rhs(i).dot(this->get_sensitivity_solution(j));
    }

  // All parameters_vec have been reset.
  // We didn't cache the original rhs or matrix for memory reasons,
  // but we can restore them to a state consistent solution -
  // principle of least surprise.
  this->assembly(true, true);
  this->rhs->close();
  this->matrix->close();
  this->assemble_qoi(qoi_indices);
}

get_adjoint_rhs() [1/2]

NumericVector< Number > & libMesh::System::get_adjoint_rhs ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's adjoint rhs vectors, by default the one corresponding to the first qoi. This what the user's QoI derivative code should assemble when setting up an adjoint problem

Definition at line 1307 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::ImplicitSystem::adjoint_solve(), libMesh::FEMSystem::assemble_qoi_derivative(), libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), and libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve().

{
  std::ostringstream adjoint_rhs_name;
  adjoint_rhs_name << "adjoint_rhs" << i;

  return this->get_vector(adjoint_rhs_name.str());
}

get_adjoint_rhs() [2/2]

const NumericVector< Number > & libMesh::System::get_adjoint_rhs ( unsigned int  i = 0 ) const

inherited

Returns

A reference to one of the system's adjoint rhs vectors, by default the one corresponding to the first qoi.

Definition at line 1317 of file system.C.

References libMesh::System::get_vector().

{
  std::ostringstream adjoint_rhs_name;
  adjoint_rhs_name << "adjoint_rhs" << i;

  return this->get_vector(adjoint_rhs_name.str());
}

get_adjoint_solution() [1/2]

NumericVector< Number > & libMesh::System::get_adjoint_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's adjoint solution vectors, by default the one corresponding to the first qoi.

Definition at line 1245 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::ImplicitSystem::adjoint_solve(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), HeatSystem::init_context(), libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate(), main(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), libMesh::FileSolutionHistory::retrieve(), and libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve().

{
  std::ostringstream adjoint_name;
  adjoint_name << "adjoint_solution" << i;

  return this->get_vector(adjoint_name.str());
}

get_adjoint_solution() [2/2]

const NumericVector< Number > & libMesh::System::get_adjoint_solution ( unsigned int  i = 0 ) const

inherited

Returns

A reference to one of the system's adjoint solution vectors, by default the one corresponding to the first qoi.

Definition at line 1255 of file system.C.

References libMesh::System::get_vector().

{
  std::ostringstream adjoint_name;
  adjoint_name << "adjoint_solution" << i;

  return this->get_vector(adjoint_name.str());
}

get_all_variable_numbers()

void libMesh::System::get_all_variable_numbers ( std::vector< unsigned int > &  all_variable_numbers ) const

inherited

Fills all_variable_numbers with all the variable numbers for the variables that have been added to this system.

Definition at line 1617 of file system.C.

References libMesh::System::_variable_numbers, and libMesh::System::n_vars().

Referenced by MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), and SystemsTest::testProjectCubeWithMeshFunction().

{
  all_variable_numbers.resize(n_vars());

  unsigned int count = 0;
  for (auto vn : _variable_numbers)
    all_variable_numbers[count++] = vn.second;
}

get_constrain_in_solver()

virtual bool libMesh::DifferentiableSystem::get_constrain_in_solver ( )

inlinevirtualinherited

Definition at line 389 of file diff_system.h.

References libMesh::DifferentiableSystem::_constrain_in_solver.

  {
    return _constrain_in_solver;
  }

get_constraint_object()

System::Constraint & libMesh::System::get_constraint_object ( )

inherited

Return the user object for imposing constraints.

Definition at line 2226 of file system.C.

References libMesh::System::_constrain_system_object.

{
  libmesh_assert_msg(_constrain_system_object,"No constraint object available.");
  return *_constrain_system_object;
}

get_dof_map() [1/2]

const DofMap & libMesh::System::get_dof_map ( ) const

inlineinherited

Returns

A constant reference to this system's _dof_map.

Definition at line 2374 of file system.h.

References libMesh::System::_dof_map.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), libMesh::__libmesh_petsc_diff_solver_residual(), libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::DifferentiableSystem::add_dot_var_dirichlet_bcs(), libMesh::System::add_matrix(), libMesh::HPCoarsenTest::add_projection(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::ImplicitSystem::adjoint_solve(), libMesh::NewmarkSolver::advance_timestep(), libMesh::AdaptiveTimeSolver::advance_timestep(), libMesh::UnsteadySolver::advance_timestep(), libMesh::EquationSystems::allgather(), libMesh::TransientRBConstruction::allocate_data_structures(), libMesh::RBConstruction::allocate_data_structures(), alternative_fe_assembly(), assemble(), LinearElasticity::assemble(), assemble_1D(), AssembleOptimization::assemble_A_and_F(), libMesh::ClawSystem::assemble_advection_matrices(), assemble_and_solve(), libMesh::ClawSystem::assemble_avg_coupling_matrices(), assemble_biharmonic(), libMesh::ClawSystem::assemble_boundary_condition_matrices(), assemble_divgrad(), assemble_elasticity(), assemble_ellipticdg(), assemble_func(), assemble_graddiv(), assemble_helmholtz(), libMesh::ClawSystem::assemble_jump_coupling_matrix(), assemble_laplace(), assemble_mass(), libMesh::ClawSystem::assemble_mass_matrix(), assemble_matrices(), assemble_matrix_and_rhs(), assemble_poisson(), assemble_SchroedingerEquation(), assemble_shell(), assemble_stokes(), assemble_wave(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::PetscDMWrapper::build_sf(), libMesh::System::calculate_norm(), compute_jacobian(), compute_residual(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::Problem_Interface::computeF(), libMesh::Problem_Interface::computeJacobian(), libMesh::Problem_Interface::computePreconditioner(), MyConstraint::constrain(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), libMesh::CondensedEigenSystem::copy_sub_to_super(), libMesh::CondensedEigenSystem::copy_super_to_sub(), libMesh::System::create_static_condensation(), libMesh::ImplicitSystem::create_static_condensation_system_matrix(), create_wrapped_function(), DMCreateDomainDecomposition_libMesh(), DMCreateFieldDecomposition_libMesh(), DMlibMeshFunction(), DMlibMeshJacobian(), DMlibMeshSetSystem_libMesh(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), fe_assembly(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::find_dofs_to_send(), libMesh::VariationalSmootherConstraint::fix_node(), form_functionA(), form_functionB(), form_matrixA(), libMesh::CondensedEigenSystem::get_eigenpair(), libMesh::System::get_info(), libMesh::System::has_static_condensation(), libMesh::SystemSubsetBySubdomain::init(), libMesh::SecondOrderUnsteadySolver::init_data(), libMesh::UnsteadySolver::init_data(), HeatSystem::init_data(), SimpleRBConstruction::init_data(), libMesh::ClawSystem::init_data(), LaplaceSystem::init_dirichlet_bcs(), NonManifoldCouplingTestBase::init_es(), libMesh::FEMContext::init_internal_data(), libMesh::EigenSystem::init_matrices(), libMesh::System::init_matrices(), libMesh::PetscDMWrapper::init_petscdm(), libMesh::CondensedEigenSystem::initialize_condensed_dofs(), libMesh::OptimizationSystem::initialize_equality_constraints_storage(), libMesh::OptimizationSystem::initialize_inequality_constraints_storage(), LaplaceYoung::jacobian(), LargeDeformationElasticity::jacobian(), libMesh::System::late_matrix_init(), libMesh::libmesh_petsc_snes_fd_residual(), libMesh::libmesh_petsc_snes_jacobian(), libMesh::libmesh_petsc_snes_mffd_residual(), libMesh::libmesh_petsc_snes_residual(), libMesh::libmesh_petsc_snes_residual_helper(), libMesh::System::local_dof_indices(), AssembleOptimization::lower_and_upper_bounds(), main(), libMesh::DofMap::max_constraint_error(), LinearElasticityWithContact::move_mesh(), libMesh::DGFEMContext::neighbor_side_fe_reinit(), libMesh::UnsteadySolver::old_nonlinear_solution(), libMesh::SecondOrderUnsteadySolver::old_solution_accel(), libMesh::SecondOrderUnsteadySolver::old_solution_rate(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectSides::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectInteriors::operator()(), libMesh::RBSCMConstruction::perform_SCM_greedy(), periodic_bc_test_poisson(), libMesh::petsc_auto_fieldsplit(), libMesh::ErrorVector::plot_error(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::FEMContext::pre_fe_reinit(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::System::re_update(), libMesh::System::read_parallel_data(), libMesh::System::read_SCALAR_dofs(), libMesh::SecondOrderUnsteadySolver::reinit(), libMesh::UnsteadySolver::reinit(), libMesh::System::reinit(), libMesh::System::reinit_constraints(), libMesh::EquationSystems::reinit_solutions(), LaplaceYoung::residual(), LargeDeformationElasticity::residual(), LinearElasticityWithContact::residual_and_jacobian(), libMesh::UnsteadySolver::retrieve_timestep(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), libMesh::HPCoarsenTest::select_refinement(), libMesh::ImplicitSystem::sensitivity_solve(), libMesh::RBConstruction::set_context_solution_vec(), libMesh::PetscDMWrapper::set_point_range_in_section(), set_system_parameters(), SlitMeshRefinedSystemTest::setUp(), FETestBase< order, family, elem_type, 1 >::setUp(), SolidSystem::side_time_derivative(), libMesh::NewtonSolver::solve(), libMesh::PetscDiffSolver::solve(), libMesh::EigenSystem::solve(), libMesh::RBConstruction::solve_for_matrix_and_rhs(), SystemsTest::test100KVariables(), ConstraintOperatorTest::test1DCoarseningNewNodes(), ConstraintOperatorTest::test1DCoarseningOperator(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), MeshFunctionTest::test_subdomain_id_sets(), SystemsTest::testBlockRestrictedVarNDofs(), DofMapTest::testConstraintLoopDetection(), DefaultCouplingTest::testCoupling(), PointNeighborCouplingTest::testCoupling(), EquationSystemsTest::testDisableDefaultGhosting(), SystemsTest::testDofCouplingWithVarGroups(), DofMapTest::testDofOwner(), MeshInputTest::testDynaReadPatch(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), MeshAssignTest::testMeshMoveAssign(), PeriodicBCTest::testPeriodicBC(), SystemsTest::testPostInitAddVectorTypeChange(), SystemsTest::testProjectCubeWithMeshFunction(), SystemsTest::testProjectMatrix1D(), SystemsTest::testProjectMatrix2D(), SystemsTest::testProjectMatrix3D(), InfFERadialTest::testRefinement(), EquationSystemsTest::testSelectivePRefine(), BoundaryInfoTest::testShellFaceConstraints(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::BoundaryVolumeSolutionTransfer::transfer_boundary_volume(), libMesh::UnsteadySolver::update(), update_current_local_solution(), NonManifoldGhostingFunctorTest::verify_send_list_entries_helper(), libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve(), libMesh::ImplicitSystem::weighted_sensitivity_solve(), libMesh::Nemesis_IO_Helper::write_nodal_solution(), libMesh::System::write_parallel_data(), libMesh::EnsightIO::write_scalar_ascii(), libMesh::System::write_SCALAR_dofs(), libMesh::EnsightIO::write_vector_ascii(), and libMesh::RBConstruction::zero_constrained_dofs_on_vector().

{
  return *_dof_map;
}

get_dof_map() [2/2]

DofMap & libMesh::System::get_dof_map ( )

inlineinherited

Returns

A writable reference to this system's _dof_map.

Definition at line 2382 of file system.h.

References libMesh::System::_dof_map.

{
  return *_dof_map;
}

get_equation_systems() [1/2]

const EquationSystems& libMesh::System::get_equation_systems ( ) const

inlineinherited

Returns

A constant reference to this system's parent EquationSystems object.

Definition at line 721 of file system.h.

References libMesh::System::_equation_systems.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::RBSCMConstruction::add_scaled_symm_Aq(), libMesh::NewmarkSystem::clear(), libMesh::FrequencySystem::clear_all(), compute_jacobian(), compute_residual(), LinearElasticityWithContact::compute_stresses(), SolidSystem::element_time_derivative(), libMesh::RBConstruction::enrich_basis_from_rhs_terms(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::ImplicitSystem::get_linear_solve_parameters(), SolidSystem::init_data(), HeatSystem::init_data(), libMesh::FrequencySystem::init_data(), LaplaceYoung::jacobian(), libMesh::RBSCMConstruction::load_matrix_B(), LinearElasticityWithContact::move_mesh(), libMesh::FrequencySystem::n_frequencies(), libMesh::RBSCMConstruction::perform_SCM_greedy(), libMesh::System::point_gradient(), libMesh::System::point_value(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::StaticCondensationDofMap::reinit(), LaplaceYoung::residual(), LinearElasticityWithContact::residual_and_jacobian(), libMesh::FileHistoryData::retrieve_adjoint_solution(), libMesh::FileHistoryData::retrieve_primal_solution(), libMesh::FileHistoryData::rewrite_stored_solution(), SolidSystem::save_initial_mesh(), libMesh::FrequencySystem::set_current_frequency(), libMesh::FrequencySystem::set_frequencies(), libMesh::FrequencySystem::set_frequencies_by_range(), libMesh::FrequencySystem::set_frequencies_by_steps(), libMesh::NewmarkSystem::set_newmark_parameters(), libMesh::NonlinearImplicitSystem::set_solver_parameters(), SolidSystem::side_time_derivative(), libMesh::EigenSystem::solve(), libMesh::CondensedEigenSystem::solve(), libMesh::FrequencySystem::solve(), libMesh::ClawSystem::solve_conservation_law(), libMesh::RBConstruction::solve_for_matrix_and_rhs(), libMesh::EigenSystem::solve_helper(), libMesh::FileHistoryData::store_adjoint_solution(), libMesh::FileHistoryData::store_initial_solution(), libMesh::FileHistoryData::store_primal_solution(), MeshFunctionTest::test_p_level(), MeshFunctionTest::test_subdomain_id_sets(), MeshAssignTest::testMeshMoveAssign(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::DirectSolutionTransfer::transfer(), libMesh::MeshfreeSolutionTransfer::transfer(), libMesh::DTKSolutionTransfer::transfer(), libMesh::TransientRBConstruction::truth_solve(), libMesh::RBConstruction::truth_solve(), and libMesh::WrappedFunction< Output >::WrappedFunction().

{ return _equation_systems; }

get_equation_systems() [2/2]

EquationSystems& libMesh::System::get_equation_systems ( )

inlineinherited

Returns

A reference to this system's parent EquationSystems object.

Definition at line 726 of file system.h.

References libMesh::System::_equation_systems.

{ return _equation_systems; }

get_first_order_vars()

const std::set<unsigned int>& libMesh::DifferentiablePhysics::get_first_order_vars ( ) const

inlineinherited

Returns

The set of first order in time variable indices. May be empty.

Definition at line 506 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_first_order_vars.

Referenced by libMesh::DifferentiableSystem::have_first_order_scalar_vars().

  { return _first_order_vars; }

get_info() [1/2]

std::string libMesh::ReferenceCounter::get_info ( )

staticinherited

Gets a string containing the reference information.

Definition at line 47 of file reference_counter.C.

References libMesh::ReferenceCounter::_counts, and libMesh::Quality::name().

Referenced by libMesh::ReferenceCounter::print_info().

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)

  std::ostringstream oss;

  oss << '\n'
      << " ---------------------------------------------------------------------------- \n"
      << "| Reference count information                                                |\n"
      << " ---------------------------------------------------------------------------- \n";

  for (const auto & [name, cd] : _counts)
    oss << "| " << name << " reference count information:\n"
        << "|  Creations:    " << cd.first    << '\n'
        << "|  Destructions: " << cd.second << '\n';

  oss << " ---------------------------------------------------------------------------- \n";

  return oss.str();

#else

  return "";

#endif
}

get_info() [2/2]

std::string libMesh::System::get_info ( ) const

inherited

Returns

A string containing information about the system.

Definition at line 2040 of file system.C.

References libMesh::ParallelObject::comm(), libMesh::FEType::family, libMesh::System::get_dof_map(), libMesh::DofMap::get_info(), libMesh::FEType::inf_map, libMesh::make_range(), TIMPI::Communicator::max(), libMesh::System::n_constrained_dofs(), libMesh::System::n_dofs(), libMesh::System::n_local_constrained_dofs(), libMesh::System::n_local_dofs(), libMesh::System::n_matrices(), libMesh::System::n_variable_groups(), libMesh::VariableGroup::n_variables(), libMesh::System::n_vectors(), libMesh::VariableGroup::name(), libMesh::System::name(), libMesh::System::number(), libMesh::FEType::order, libMesh::FEType::radial_family, libMesh::FEType::radial_order, libMesh::System::system_type(), libMesh::Variable::type(), libMesh::DofMap::variable_group(), and libMesh::System::variable_group().

{
  std::ostringstream oss;


  const std::string & sys_name = this->name();

  oss << "   System #"  << this->number() << ", \"" << sys_name << "\"\n"
      << "    Type \""  << this->system_type() << "\"\n"
      << "    Variables=";

  for (auto vg : make_range(this->n_variable_groups()))
    {
      const VariableGroup & vg_description (this->variable_group(vg));

      if (vg_description.n_variables() > 1) oss << "{ ";
      for (auto vn : make_range(vg_description.n_variables()))
        oss << "\"" << vg_description.name(vn) << "\" ";
      if (vg_description.n_variables() > 1) oss << "} ";
    }

  oss << '\n';

  oss << "    Finite Element Types=";
#ifndef LIBMESH_ENABLE_INFINITE_ELEMENTS
  for (auto vg : make_range(this->n_variable_groups()))
    oss << "\""
        << Utility::enum_to_string<FEFamily>(this->get_dof_map().variable_group(vg).type().family)
        << "\" ";
#else
  for (auto vg : make_range(this->n_variable_groups()))
    {
      oss << "\""
          << Utility::enum_to_string<FEFamily>(this->get_dof_map().variable_group(vg).type().family)
          << "\", \""
          << Utility::enum_to_string<FEFamily>(this->get_dof_map().variable_group(vg).type().radial_family)
          << "\" ";
    }

  oss << '\n' << "    Infinite Element Mapping=";
  for (auto vg : make_range(this->n_variable_groups()))
    oss << "\""
        << Utility::enum_to_string<InfMapType>(this->get_dof_map().variable_group(vg).type().inf_map)
        << "\" ";
#endif

  oss << '\n';

  oss << "    Approximation Orders=";
  for (auto vg : make_range(this->n_variable_groups()))
    {
#ifndef LIBMESH_ENABLE_INFINITE_ELEMENTS
      oss << "\""
          << Utility::enum_to_string<Order>(this->get_dof_map().variable_group(vg).type().order)
          << "\" ";
#else
      oss << "\""
          << Utility::enum_to_string<Order>(this->get_dof_map().variable_group(vg).type().order)
          << "\", \""
          << Utility::enum_to_string<Order>(this->get_dof_map().variable_group(vg).type().radial_order)
          << "\" ";
#endif
    }

  oss << '\n';

  oss << "    n_dofs()="             << this->n_dofs()             << '\n';
  dof_id_type local_dofs = this->n_local_dofs();
  oss << "    n_local_dofs()="       << local_dofs                 << '\n';
  this->comm().max(local_dofs);
  oss << "    max(n_local_dofs())="       << local_dofs                 << '\n';
#ifdef LIBMESH_ENABLE_CONSTRAINTS
  oss << "    n_constrained_dofs()=" << this->n_constrained_dofs() << '\n';
  oss << "    n_local_constrained_dofs()=" << this->n_local_constrained_dofs() << '\n';
  dof_id_type local_unconstrained_dofs = this->n_local_dofs() - this->n_local_constrained_dofs();
  this->comm().max(local_unconstrained_dofs);
  oss << "    max(local unconstrained dofs)=" << local_unconstrained_dofs << '\n';
#endif

  oss << "    " << "n_vectors()="  << this->n_vectors()  << '\n';
  oss << "    " << "n_matrices()="  << this->n_matrices()  << '\n';
  //   oss << "    " << "n_additional_matrices()=" << this->n_additional_matrices() << '\n';

  oss << this->get_dof_map().get_info();

  return oss.str();
}

get_linear_solve_parameters()

std::pair< unsigned int, Real > libMesh::DifferentiableSystem::get_linear_solve_parameters ( ) const

overridevirtualinherited

Returns

An integer corresponding to the upper iteration count limit and a Real corresponding to the convergence tolerance to be used in linear adjoint and/or sensitivity solves

Reimplemented from libMesh::ImplicitSystem.

Definition at line 172 of file diff_system.C.

References libMesh::libmesh_assert(), and libMesh::DifferentiableSystem::time_solver.

{
  libmesh_assert(time_solver.get());
  libmesh_assert_equal_to (&(time_solver->system()), this);
  return std::make_pair(this->time_solver->diff_solver()->max_linear_iterations,
                        this->time_solver->diff_solver()->relative_residual_tolerance);
}

get_linear_solver()

LinearSolver< Number > * libMesh::DifferentiableSystem::get_linear_solver ( ) const

overridevirtualinherited

Returns

A pointer to a linear solver appropriate for use in adjoint and/or sensitivity solves

Reimplemented from libMesh::ImplicitSystem.

Definition at line 163 of file diff_system.C.

References libMesh::libmesh_assert(), and libMesh::DifferentiableSystem::time_solver.

Referenced by adjust_linear_solvers(), and main().

{
  libmesh_assert(time_solver.get());
  libmesh_assert_equal_to (&(time_solver->system()), this);
  return this->time_solver->linear_solver().get();
}

get_matrix() [1/2]

const SparseMatrix< Number > & libMesh::System::get_matrix ( std::string_view  mat_name ) const

inherited

Returns

A const reference to this system's matrix named mat_name.

Definition at line 1124 of file system.C.

References libMesh::System::_matrices.

Referenced by add_M_C_K_helmholtz(), assemble(), assemble_helmholtz(), assemble_poisson(), libMesh::NewmarkSystem::compute_matrix(), libMesh::ImplicitSystem::get_system_matrix(), main(), libMesh::EigenTimeSolver::solve(), and libMesh::NewmarkSystem::update_rhs().

{
  return *libmesh_map_find(_matrices, mat_name);
}

get_matrix() [2/2]

SparseMatrix< Number > & libMesh::System::get_matrix ( std::string_view  mat_name )

inherited

Returns

A writable reference to this system's matrix named mat_name.

Definition at line 1131 of file system.C.

References libMesh::System::_matrices.

{
  return *libmesh_map_find(_matrices, mat_name);
}

get_mesh() [1/2]

const MeshBase & libMesh::System::get_mesh ( ) const

inlineinherited

Returns

A constant reference to this systems's _mesh.

Definition at line 2358 of file system.h.

References libMesh::System::_mesh.

Referenced by libMesh::ExactSolution::_compute_error(), LinearElasticityWithContact::add_contact_edge_elements(), libMesh::PetscDMWrapper::add_dofs_to_section(), libMesh::System::add_matrix(), libMesh::HPCoarsenTest::add_projection(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), AssembleOptimization::assemble_A_and_F(), libMesh::ClawSystem::assemble_advection_matrices(), libMesh::ClawSystem::assemble_avg_coupling_matrices(), libMesh::ClawSystem::assemble_boundary_condition_matrices(), libMesh::ClawSystem::assemble_jump_coupling_matrix(), libMesh::ClawSystem::assemble_mass_matrix(), libMesh::FEMSystem::assemble_qoi(), libMesh::FEMSystem::assemble_qoi_derivative(), libMesh::VariationalSmootherSystem::assembly(), libMesh::FEMSystem::assembly(), AssemblyA0::boundary_assembly(), AssemblyA1::boundary_assembly(), AssemblyF0::boundary_assembly(), AssemblyF1::boundary_assembly(), AssemblyA2::boundary_assembly(), AssemblyF2::boundary_assembly(), libMesh::System::calculate_norm(), libMesh::VariationalSmootherSystem::compute_element_reference_volume(), compute_jacobian(), compute_residual(), LinearElasticityWithContact::compute_stresses(), libMesh::VariationalSmootherConstraint::constrain(), libMesh::System::create_static_condensation(), libMesh::ImplicitSystem::create_static_condensation_system_matrix(), libMesh::RBEIMEvaluation::distribute_bfs(), DMCreateDomainDecomposition_libMesh(), DMCreateFieldDecomposition_libMesh(), DMlibMeshSetSystem_libMesh(), SolidSystem::element_time_derivative(), HeatSystem::element_time_derivative(), libMesh::RBConstruction::enrich_basis_from_rhs_terms(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_interiors(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_sides(), libMesh::PatchRecoveryErrorEstimator::estimate_error(), libMesh::WeightedPatchRecoveryErrorEstimator::estimate_error(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::find_dofs_to_send(), libMesh::VariationalSmootherConstraint::fix_node(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::GenericProjector(), LinearElasticityWithContact::get_least_and_max_gap_function(), libMesh::SystemSubsetBySubdomain::init(), libMesh::RBEIMConstruction::init_context(), SolidSystem::init_data(), libMesh::VariationalSmootherSystem::init_data(), libMesh::System::init_data(), libMesh::System::init_matrices(), libMesh::PetscDMWrapper::init_petscdm(), LinearElasticityWithContact::initialize_contact_load_paths(), libMesh::RBEIMConstruction::initialize_qp_data(), libMesh::System::local_dof_indices(), libMesh::DofMap::max_constraint_error(), libMesh::FEMSystem::mesh_position_get(), libMesh::FEMSystem::mesh_position_set(), LinearElasticityWithContact::move_mesh(), libMesh::System::n_components(), libMesh::RBEIMEvaluation::node_distribute_bfs(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectVertices::operator()(), libMesh::petsc_auto_fieldsplit(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::FEMSystem::postprocess(), libMesh::RBParametrizedFunction::preevaluate_parametrized_function_on_mesh(), libMesh::RBParametrizedFunction::preevaluate_parametrized_function_on_mesh_sides(), libMesh::System::read_header(), libMesh::RBEvaluation::read_in_vectors_from_multiple_files(), libMesh::System::read_legacy_data(), libMesh::System::read_parallel_data(), libMesh::System::read_serialized_vector(), libMesh::System::read_serialized_vectors(), libMesh::System::reinit(), LinearElasticityWithContact::residual_and_jacobian(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), SolidSystem::save_initial_mesh(), libMesh::HPSingularity::select_refinement(), libMesh::HPCoarsenTest::select_refinement(), libMesh::PetscDMWrapper::set_point_range_in_section(), libMesh::RBEIMEvaluation::side_distribute_bfs(), SolidSystem::side_time_derivative(), libMesh::PetscDiffSolver::solve(), libMesh::ClawSystem::solve_conservation_law(), MeshAssignTest::testMeshMoveAssign(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::BoundaryVolumeSolutionTransfer::transfer(), libMesh::BoundaryVolumeSolutionTransfer::transfer_boundary_volume(), libMesh::BoundaryVolumeSolutionTransfer::transfer_volume_boundary(), libMesh::TransientRBConstruction::truth_solve(), libMesh::RBConstruction::truth_solve(), libMesh::System::write_header(), libMesh::RBEvaluation::write_out_vectors(), libMesh::System::write_parallel_data(), libMesh::System::write_serialized_vector(), libMesh::System::write_serialized_vectors(), and libMesh::System::zero_variable().

{
  return _mesh;
}

get_mesh() [2/2]

MeshBase & libMesh::System::get_mesh ( )

inlineinherited

Returns

A reference to this systems's _mesh.

Definition at line 2366 of file system.h.

References libMesh::System::_mesh.

{
  return _mesh;
}

get_mesh_system() [1/2]

const System * libMesh::DifferentiablePhysics::get_mesh_system ( ) const

inlineinherited

Returns

A const reference to the system with variables corresponding to mesh nodal coordinates, or nullptr if the mesh is fixed. Useful for ALE calculations.

Definition at line 613 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_sys.

Referenced by libMesh::FEMSystem::build_context().

{
  return _mesh_sys;
}

get_mesh_system() [2/2]

System * libMesh::DifferentiablePhysics::get_mesh_system ( )

inlineinherited

Returns

A reference to the system with variables corresponding to mesh nodal coordinates, or nullptr if the mesh is fixed.

Definition at line 619 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_sys.

{
  return _mesh_sys;
}

get_mesh_x_var()

unsigned int libMesh::DifferentiablePhysics::get_mesh_x_var ( ) const

inlineinherited

Returns

The variable number corresponding to the mesh x coordinate. Useful for ALE calculations.

Definition at line 625 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_x_var.

Referenced by libMesh::FEMSystem::build_context().

{
  return _mesh_x_var;
}

get_mesh_y_var()

unsigned int libMesh::DifferentiablePhysics::get_mesh_y_var ( ) const

inlineinherited

Returns

The variable number corresponding to the mesh y coordinate. Useful for ALE calculations.

Definition at line 631 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_y_var.

Referenced by libMesh::FEMSystem::build_context().

{
  return _mesh_y_var;
}

get_mesh_z_var()

unsigned int libMesh::DifferentiablePhysics::get_mesh_z_var ( ) const

inlineinherited

Returns

The variable number corresponding to the mesh z coordinate. Useful for ALE calculations.

Definition at line 637 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_z_var.

Referenced by libMesh::FEMSystem::build_context().

{
  return _mesh_z_var;
}

get_physics() [1/2]

const DifferentiablePhysics* libMesh::DifferentiableSystem::get_physics ( ) const

inlineinherited

Returns

A const reference to a DifferentiablePhysics object.

Note

If no external Physics objects have been attached, the default is this.

Definition at line 181 of file diff_system.h.

References libMesh::DifferentiableSystem::_diff_physics.

Referenced by libMesh::EulerSolver::_general_residual(), libMesh::Euler2Solver::_general_residual(), libMesh::SteadySolver::_general_residual(), libMesh::NewmarkSolver::_general_residual(), libMesh::FEMSystem::build_context(), libMesh::EulerSolver::element_residual(), libMesh::Euler2Solver::element_residual(), libMesh::EigenTimeSolver::element_residual(), libMesh::FEMSystem::init_context(), libMesh::EigenTimeSolver::nonlocal_residual(), and libMesh::EigenTimeSolver::side_residual().

  { if (this->_diff_physics.empty())
      return this;
    return this->_diff_physics.top().get(); }

get_physics() [2/2]

DifferentiablePhysics* libMesh::DifferentiableSystem::get_physics ( )

inlineinherited

Returns

A reference to a DifferentiablePhysics object.

Note

If no external Physics object is attached, the default is this.

Definition at line 192 of file diff_system.h.

References libMesh::DifferentiableSystem::_diff_physics.

  { if (this->_diff_physics.empty())
      return this;
    return this->_diff_physics.top().get(); }

get_project_with_constraints()

bool libMesh::System::get_project_with_constraints ( )

inlineinherited

Setter and getter functions for project_with_constraints boolean.

Definition at line 1795 of file system.h.

References libMesh::System::project_with_constraints.

Referenced by libMesh::AdjointRefinementEstimator::estimate_error().

  {
    return project_with_constraints;
  }

get_qoi() [1/2]

const DifferentiableQoI* libMesh::DifferentiableSystem::get_qoi ( ) const

inlineinherited

Returns

A const reference to a DifferentiableQoI object.

Note

If no external QoI object is attached, the default is this.

Definition at line 229 of file diff_system.h.

References libMesh::DifferentiableSystem::_diff_qoi.

Referenced by libMesh::FEMSystem::assemble_qoi(), and libMesh::FEMSystem::assemble_qoi_derivative().

  { if (this->_diff_qoi.empty())
      return this;
    return this->_diff_qoi.top().get(); }

get_qoi() [2/2]

DifferentiableQoI* libMesh::DifferentiableSystem::get_qoi ( )

inlineinherited

Returns

A reference to a DifferentiableQoI object.

Note

If no external QoI object is attached, the default is this.

Definition at line 239 of file diff_system.h.

References libMesh::DifferentiableSystem::_diff_qoi.

  { if (this->_diff_qoi.empty())
      return this;
    return this->_diff_qoi.top().get(); }

get_qoi_error_estimate_value()

Number libMesh::System::get_qoi_error_estimate_value ( unsigned int  qoi_index ) const

inherited

Definition at line 2413 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::qoi_error_estimates.

Referenced by libMesh::TwostepTimeSolver::integrate_adjoint_refinement_error_estimate(), and main().

{
  libmesh_assert(qoi_index < qoi_error_estimates.size());
  return qoi_error_estimates[qoi_index];
}

get_qoi_value()

Number libMesh::System::get_qoi_value ( unsigned int  qoi_index ) const

inherited

Definition at line 2386 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::qoi.

Referenced by libMesh::Euler2Solver::integrate_qoi_timestep(), libMesh::TwostepTimeSolver::integrate_qoi_timestep(), libMesh::EulerSolver::integrate_qoi_timestep(), main(), libMesh::ImplicitSystem::qoi_parameter_hessian(), and libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product().

{
  libmesh_assert(qoi_index < qoi.size());
  return qoi[qoi_index];
}

get_qoi_values()

std::vector< Number > libMesh::System::get_qoi_values ( ) const

inherited

Returns a copy of qoi, not a reference.

Definition at line 2393 of file system.C.

References libMesh::System::qoi.

Referenced by libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity(), libMesh::FEMSystem::assemble_qoi(), libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::ImplicitSystem::qoi_parameter_hessian(), and libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product().

{
  return this->qoi;
}

get_second_order_dot_var()

unsigned int libMesh::DifferentiableSystem::get_second_order_dot_var ( unsigned int  var ) const

inherited

For a given second order (in time) variable var, this method will return the index to the corresponding "dot" variable.

For FirstOrderUnsteadySolver classes, the "dot" variable would automatically be added and the returned index will correspond to that variable. For SecondOrderUnsteadySolver classes, this method will return var as there this is no "dot" variable per se, but having this function allows one to use the interface to treat both FirstOrderUnsteadySolver and SecondOrderUnsteadySolver simultaneously.

Definition at line 306 of file diff_system.C.

References libMesh::DifferentiablePhysics::_second_order_dot_vars, libMesh::UnsteadySolver::time_order(), and libMesh::DifferentiableSystem::time_solver.

Referenced by libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns().

{
  // For SteadySolver or SecondOrderUnsteadySolvers, we just give back var
  unsigned int dot_var = var;

  if (!time_solver->is_steady())
    {
      const UnsteadySolver & unsteady_solver =
        cast_ref<const UnsteadySolver &>(*(time_solver.get()));

      if (unsteady_solver.time_order() == 1)
        dot_var = this->_second_order_dot_vars.find(var)->second;
    }

  return dot_var;
}

get_second_order_vars()

const std::set<unsigned int>& libMesh::DifferentiablePhysics::get_second_order_vars ( ) const

inlineinherited

Returns

The set of second order in time variable indices. May be empty.

Definition at line 519 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_second_order_vars.

Referenced by libMesh::DifferentiableSystem::add_second_order_dot_vars(), libMesh::DiffContext::DiffContext(), libMesh::Euler2Solver::element_residual(), libMesh::DifferentiableSystem::have_second_order_scalar_vars(), and libMesh::FEMContext::pre_fe_reinit().

  { return _second_order_vars; }

get_sensitivity_rhs() [1/2]

NumericVector< Number > & libMesh::System::get_sensitivity_rhs ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's sensitivity rhs vectors, by default the one corresponding to the first parameter. By default these vectors are built by the library, using finite differences, when assemble_residual_derivatives() is called.

When assembled, this vector should hold -(partial R / partial p_i)

Definition at line 1337 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity(), and libMesh::ImplicitSystem::sensitivity_solve().

{
  std::ostringstream sensitivity_rhs_name;
  sensitivity_rhs_name << "sensitivity_rhs" << i;

  return this->get_vector(sensitivity_rhs_name.str());
}

get_sensitivity_rhs() [2/2]

const NumericVector< Number > & libMesh::System::get_sensitivity_rhs ( unsigned int  i = 0 ) const

inherited

Returns

A reference to one of the system's sensitivity rhs vectors, by default the one corresponding to the first parameter.

Definition at line 1347 of file system.C.

References libMesh::System::get_vector().

{
  std::ostringstream sensitivity_rhs_name;
  sensitivity_rhs_name << "sensitivity_rhs" << i;

  return this->get_vector(sensitivity_rhs_name.str());
}

get_sensitivity_solution() [1/2]

NumericVector< Number > & libMesh::System::get_sensitivity_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's solution sensitivity vectors, by default the one corresponding to the first parameter.

Definition at line 1192 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::ImplicitSystem::qoi_parameter_hessian(), and libMesh::ImplicitSystem::sensitivity_solve().

{
  std::ostringstream sensitivity_name;
  sensitivity_name << "sensitivity_solution" << i;

  return this->get_vector(sensitivity_name.str());
}

get_sensitivity_solution() [2/2]

const NumericVector< Number > & libMesh::System::get_sensitivity_solution ( unsigned int  i = 0 ) const

inherited

Returns

A reference to one of the system's solution sensitivity vectors, by default the one corresponding to the first parameter.

Definition at line 1202 of file system.C.

References libMesh::System::get_vector().

{
  std::ostringstream sensitivity_name;
  sensitivity_name << "sensitivity_solution" << i;

  return this->get_vector(sensitivity_name.str());
}

get_static_condensation()

StaticCondensation & libMesh::ImplicitSystem::get_static_condensation ( )

inlineinherited

Returns

The static condensation system matrix

Definition at line 373 of file implicit_system.h.

References libMesh::ImplicitSystem::_sc_system_matrix, and libMesh::libmesh_assert().

Referenced by assemble_poisson().

{
  libmesh_assert(_sc_system_matrix);
  return *_sc_system_matrix;
}

get_system_matrix() [1/2]

const SparseMatrix< Number > & libMesh::ImplicitSystem::get_system_matrix ( ) const

inherited

Returns

A const reference to the system's primary matrix.

Definition at line 1261 of file implicit_system.C.

References libMesh::System::get_matrix(), libMesh::libmesh_assert(), and libMesh::ImplicitSystem::matrix.

Referenced by libMesh::HDGProblem::add_matrix(), assemble(), LinearElasticity::assemble(), assemble_1D(), assemble_biharmonic(), assemble_divgrad(), assemble_elasticity(), assemble_ellipticdg(), assemble_graddiv(), assemble_helmholtz(), assemble_laplace(), assemble_matrix_and_rhs(), assemble_poisson(), assemble_shell(), assemble_stokes(), assemble_wave(), assembly_with_dg_fem_context(), libMesh::HDGProblem::jacobian(), libMesh::libmesh_petsc_snes_residual(), main(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), and libMesh::EigenTimeSolver::solve().

{
  libmesh_assert(matrix);
  libmesh_assert_equal_to(&get_matrix("System Matrix"), matrix);
  return *matrix;
}

get_system_matrix() [2/2]

SparseMatrix< Number > & libMesh::ImplicitSystem::get_system_matrix ( )

inherited

Returns

A reference to the system's primary matrix.

Definition at line 1270 of file implicit_system.C.

References libMesh::System::get_matrix(), libMesh::libmesh_assert(), and libMesh::ImplicitSystem::matrix.

{
  libmesh_assert(matrix);
  libmesh_assert_equal_to(&get_matrix("System Matrix"), matrix);
  return *matrix;
}

get_time_solver() [1/2]

TimeSolver & libMesh::DifferentiableSystem::get_time_solver ( )

inlineinherited

Returns

A pointer to the time solver attached to the calling system

Definition at line 456 of file diff_system.h.

References libMesh::libmesh_assert(), and libMesh::DifferentiableSystem::time_solver.

Referenced by libMesh::DifferentiableSystem::adjoint_solve(), adjust_linear_solvers(), libMesh::FEMSystem::build_context(), libMesh::DiffContext::DiffContext(), libMesh::FEMSystem::postprocess(), libMesh::FEMContext::pre_fe_reinit(), and libMesh::DifferentiableSystem::solve().

{
  libmesh_assert(time_solver.get());
  libmesh_assert_equal_to (&(time_solver->system()), this);
  return *time_solver;
}

get_time_solver() [2/2]

const TimeSolver & libMesh::DifferentiableSystem::get_time_solver ( ) const

inlineinherited

Non-const version of the above.

Definition at line 464 of file diff_system.h.

References libMesh::libmesh_assert(), and libMesh::DifferentiableSystem::time_solver.

{
  libmesh_assert(time_solver.get());
  libmesh_assert_equal_to (&(time_solver->system()), this);
  return *time_solver;
}

get_vector() [1/4]

const NumericVector< Number > & libMesh::System::get_vector ( std::string_view  vec_name ) const

inherited

Returns

A const reference to this system's additional vector named vec_name. Access is only granted when the vector is already properly initialized.

Definition at line 943 of file system.C.

References libMesh::System::_vectors.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), add_M_C_K_helmholtz(), libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::NewmarkSolver::advance_timestep(), libMesh::AdaptiveTimeSolver::advance_timestep(), libMesh::UnsteadySolver::advance_timestep(), apply_initial(), assemble(), libMesh::System::compare(), libMesh::NewmarkSolver::compute_initial_accel(), libMesh::UnsteadySolver::du(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_adjoint_solution(), libMesh::System::get_sensitivity_rhs(), libMesh::System::get_sensitivity_solution(), libMesh::System::get_weighted_sensitivity_adjoint_solution(), libMesh::System::get_weighted_sensitivity_solution(), libMesh::NewmarkSystem::initial_conditions(), AssembleOptimization::lower_and_upper_bounds(), main(), libMesh::NewmarkSolver::project_initial_accel(), libMesh::SecondOrderUnsteadySolver::project_initial_rate(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::SecondOrderUnsteadySolver::reinit(), libMesh::UnsteadySolver::reinit(), libMesh::FileSolutionHistory::retrieve(), libMesh::UnsteadySolver::retrieve_timestep(), libMesh::MemoryHistoryData::retrieve_vectors(), libMesh::TwostepTimeSolver::solve(), libMesh::FrequencySystem::solve(), libMesh::UnsteadySolver::update(), libMesh::NewmarkSystem::update_rhs(), and libMesh::NewmarkSystem::update_u_v_a().

{
  return *(libmesh_map_find(_vectors, vec_name));
}

get_vector() [2/4]

NumericVector< Number > & libMesh::System::get_vector ( std::string_view  vec_name )

inherited

Returns

A writable reference to this system's additional vector named vec_name. Access is only granted when the vector is already properly initialized.

Definition at line 950 of file system.C.

References libMesh::System::_vectors.

{
  return *(libmesh_map_find(_vectors, vec_name));
}

get_vector() [3/4]

const NumericVector< Number > & libMesh::System::get_vector ( const unsigned int  vec_num ) const

inherited

Returns

A const reference to this system's additional vector number vec_num (where the vectors are counted starting with 0).

Definition at line 957 of file system.C.

References libMesh::System::_vectors, and libMesh::System::vectors_begin().

{
  // If we don't have that many vectors, throw an error
  libmesh_assert_less(vec_num, _vectors.size());

  // Otherwise return a reference to the vec_num'th vector
  auto it = vectors_begin();
  std::advance(it, vec_num);
  return *(it->second);
}

get_vector() [4/4]

NumericVector< Number > & libMesh::System::get_vector ( const unsigned int  vec_num )

inherited

Returns

A writable reference to this system's additional vector number vec_num (where the vectors are counted starting with 0).

Definition at line 970 of file system.C.

References libMesh::System::_vectors, and libMesh::System::vectors_begin().

{
  // If we don't have that many vectors, throw an error
  libmesh_assert_less(vec_num, _vectors.size());

  // Otherwise return a reference to the vec_num'th vector
  auto it = vectors_begin();
  std::advance(it, vec_num);
  return *(it->second);
}

get_weighted_sensitivity_adjoint_solution() [1/2]

NumericVector< Number > & libMesh::System::get_weighted_sensitivity_adjoint_solution ( unsigned int  i = 0 )

inherited

Returns

A reference to one of the system's weighted sensitivity adjoint solution vectors, by default the one corresponding to the first qoi.

Definition at line 1277 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), and libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve().

{
  std::ostringstream adjoint_name;
  adjoint_name << "weighted_sensitivity_adjoint_solution" << i;

  return this->get_vector(adjoint_name.str());
}

get_weighted_sensitivity_adjoint_solution() [2/2]

const NumericVector< Number > & libMesh::System::get_weighted_sensitivity_adjoint_solution ( unsigned int  i = 0 ) const

inherited

Returns

A reference to one of the system's weighted sensitivity adjoint solution vectors, by default the one corresponding to the first qoi.

Definition at line 1287 of file system.C.

References libMesh::System::get_vector().

{
  std::ostringstream adjoint_name;
  adjoint_name << "weighted_sensitivity_adjoint_solution" << i;

  return this->get_vector(adjoint_name.str());
}

get_weighted_sensitivity_solution() [1/2]

NumericVector< Number > & libMesh::System::get_weighted_sensitivity_solution ( )

inherited

Returns

A reference to the solution of the last weighted sensitivity solve

Definition at line 1219 of file system.C.

References libMesh::System::get_vector().

Referenced by libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), and libMesh::ImplicitSystem::weighted_sensitivity_solve().

{
  return this->get_vector("weighted_sensitivity_solution");
}

get_weighted_sensitivity_solution() [2/2]

const NumericVector< Number > & libMesh::System::get_weighted_sensitivity_solution ( ) const

inherited

Returns

A reference to the solution of the last weighted sensitivity solve

Definition at line 1226 of file system.C.

References libMesh::System::get_vector().

{
  return this->get_vector("weighted_sensitivity_solution");
}

has_constraint_object()

bool libMesh::System::has_constraint_object ( ) const

inherited

Returns

true if there is a user-defined constraint object attached to this object, false otherwise. Calling System:: get_constraint_object() when there is no user-defined constraint object attached leads to either undefined behavior (dereferencing a nullptr) or an assert (in dbg mode) so you should call this function first unless you are sure there is a user-defined constraint object attached.

Definition at line 2221 of file system.C.

References libMesh::System::_constrain_system_object.

{
  return _constrain_system_object != nullptr;
}

has_static_condensation()

bool libMesh::System::has_static_condensation ( ) const

inherited

Returns

Whether this system will be statically condensed

Definition at line 2871 of file system.C.

References libMesh::System::get_dof_map(), and libMesh::DofMap::has_static_condensation().

Referenced by libMesh::System::add_matrix(), assemble_poisson(), libMesh::ImplicitSystem::ImplicitSystem(), libMesh::LinearImplicitSystem::LinearImplicitSystem(), and libMesh::NonlinearImplicitSystem::NonlinearImplicitSystem().

{
  return this->get_dof_map().has_static_condensation();
}

has_variable()

bool libMesh::System::has_variable ( std::string_view  var ) const

inherited

Returns

true if a variable named var exists in this System

Definition at line 1602 of file system.C.

References libMesh::System::_variable_numbers.

Referenced by libMesh::GMVIO::copy_nodal_solution(), and main().

{
  return _variable_numbers.count(var);
}

have_first_order_scalar_vars()

bool libMesh::DifferentiableSystem::have_first_order_scalar_vars ( ) const

inherited

Check for any first order vars that are also belong to FEFamily::SCALAR.

Definition at line 323 of file diff_system.C.

References libMesh::DifferentiablePhysics::get_first_order_vars(), libMesh::DifferentiablePhysics::have_first_order_vars(), libMesh::SCALAR, and libMesh::System::variable().

{
  bool have_first_order_scalar_vars = false;

  if (this->have_first_order_vars())
    for (const auto & var : this->get_first_order_vars())
      if (this->variable(var).type().family == SCALAR)
        have_first_order_scalar_vars = true;

  return have_first_order_scalar_vars;
}

have_first_order_vars()

bool libMesh::DifferentiablePhysics::have_first_order_vars ( ) const

inlineinherited

Definition at line 500 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_first_order_vars.

Referenced by libMesh::DifferentiableSystem::have_first_order_scalar_vars().

  { return !_first_order_vars.empty(); }

have_matrix()

bool libMesh::System::have_matrix ( std::string_view  mat_name ) const

inlineinherited

Returns

true if this System has a matrix associated with the given name, false otherwise.

Definition at line 1891 of file system.h.

References libMesh::System::_matrices.

Referenced by libMesh::EigenTimeSolver::init().

{ return _matrices.count(mat_name); }

have_second_order_scalar_vars()

bool libMesh::DifferentiableSystem::have_second_order_scalar_vars ( ) const

inherited

Check for any second order vars that are also belong to FEFamily::SCALAR.

Definition at line 335 of file diff_system.C.

References libMesh::DifferentiablePhysics::get_second_order_vars(), libMesh::DifferentiablePhysics::have_second_order_vars(), libMesh::SCALAR, and libMesh::System::variable().

Referenced by libMesh::EulerSolver::nonlocal_residual(), and libMesh::Euler2Solver::nonlocal_residual().

{
  bool have_second_order_scalar_vars = false;

  if (this->have_second_order_vars())
    for (const auto & var : this->get_second_order_vars())
      if (this->variable(var).type().family == SCALAR)
        have_second_order_scalar_vars = true;

  return have_second_order_scalar_vars;
}

have_second_order_vars()

bool libMesh::DifferentiablePhysics::have_second_order_vars ( ) const

inlineinherited

Definition at line 513 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_second_order_vars.

Referenced by libMesh::EulerSolver::element_residual(), and libMesh::DifferentiableSystem::have_second_order_scalar_vars().

  { return !_second_order_vars.empty(); }

have_vector()

bool libMesh::System::have_vector ( std::string_view  vec_name ) const

inlineinherited

Returns

true if this System has a vector associated with the given name, false otherwise.

Definition at line 2550 of file system.h.

References libMesh::System::_vectors.

{
  return (_vectors.count(vec_name));
}

hide_output()

bool& libMesh::System::hide_output ( )

inlineinherited

Returns

A writable reference to a boolean that determines if this system can be written to file or not. If set to true, then EquationSystems::write will ignore this system.

Definition at line 1810 of file system.h.

References libMesh::System::_hide_output.

{ return _hide_output; }

identify_variable_groups() [1/2]

bool libMesh::System::identify_variable_groups ( ) const

inlineinherited

Returns

true when VariableGroup structures should be automatically identified, false otherwise.

Definition at line 2526 of file system.h.

References libMesh::System::_identify_variable_groups.

Referenced by libMesh::System::add_variable(), and libMesh::System::add_variables().

{
  return _identify_variable_groups;
}

identify_variable_groups() [2/2]

void libMesh::System::identify_variable_groups ( const bool  ivg )

inlineinherited

Toggle automatic VariableGroup identification.

Definition at line 2534 of file system.h.

References libMesh::System::_identify_variable_groups.

{
  _identify_variable_groups = ivg;
}

increment_constructor_count()

void libMesh::ReferenceCounter::increment_constructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the construction counter.

Should be called in the constructor of any derived class that will be reference counted.

Definition at line 183 of file reference_counter.h.

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::ReferenceCountedObject().

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.first++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_constructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

increment_destructor_count()

void libMesh::ReferenceCounter::increment_destructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the destruction counter.

Should be called in the destructor of any derived class that will be reference counted.

Definition at line 207 of file reference_counter.h.

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::~ReferenceCountedObject().

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.second++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_destructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

init()

void libMesh::System::init ( )

inherited

Initializes degrees of freedom on the current mesh.

Sets the

Definition at line 197 of file system.C.

References libMesh::System::is_initialized(), libMesh::libmesh_assert(), and libMesh::System::reinit_mesh().

Referenced by libMesh::StaticCondensationDofMap::reinit().

{
  // Calling init() twice on the same system currently works evil
  // magic, whether done directly or via EquationSystems::read()
  libmesh_assert(!this->is_initialized());

  this->reinit_mesh();
}

init_context()

void FEMSystem::init_context ( DiffContext &  c )

overridevirtualinherited

Reimplemented from libMesh::DifferentiablePhysics.

Reimplemented in HeatSystem, HilbertSystem, CoupledSystem, libMesh::VariationalSmootherSystem, ElasticitySystem, ElasticitySystem, HeatSystem, LaplaceSystem, CurlCurlSystem, LaplaceSystem, PoissonSystem, LaplaceSystem, LaplaceSystem, CurlCurlSystem, SolidSystem, NavierSystem, and HeatSystem.

Definition at line 1370 of file fem_system.C.

References libMesh::DifferentiableSystem::deltat, dim, libMesh::FEMContext::elem_dimensions(), libMesh::FEInterface::field_type(), libMesh::FEMContext::get_element_fe(), libMesh::FEAbstract::get_JxW(), libMesh::FEGenericBase< OutputType >::get_phi(), libMesh::DifferentiableSystem::get_physics(), libMesh::DifferentiablePhysics::is_time_evolving(), libMesh::make_range(), libMesh::System::n_vars(), libMesh::DiffContext::set_deltat_pointer(), libMesh::TYPE_SCALAR, libMesh::TYPE_VECTOR, and libMesh::System::variable_type().

Referenced by libMesh::FEMSystem::assembly(), libMesh::VariationalSmootherSystem::init_context(), HilbertSystem::init_context(), HeatSystem::init_context(), libMesh::FEMSystem::mesh_position_get(), and libMesh::FEMSystem::mesh_position_set().

{
  // Parent::init_context(c);  // may be a good idea in derived classes

  // Although we do this in DiffSystem::build_context() and
  // FEMSystem::build_context() as well, we do it here just to be
  // extra sure that the deltat pointer gets set.  Since the
  // intended behavior is for classes derived from FEMSystem to
  // call Parent::init_context() in their own init_context()
  // overloads, we can ensure that those classes get the correct
  // deltat pointers even if they have different build_context()
  // overloads.
  c.set_deltat_pointer ( &deltat );

  FEMContext & context = cast_ref<FEMContext &>(c);

  // Make sure we're prepared to do mass integration
  for (auto var : make_range(this->n_vars()))
    if (this->get_physics()->is_time_evolving(var))
      {
        // Request shape functions based on FEType
        switch( FEInterface::field_type( this->variable_type(var) ) )
          {
          case( TYPE_SCALAR ):
            {
              FEBase * elem_fe = nullptr;
              for (auto dim : context.elem_dimensions())
                {
                  context.get_element_fe(var, elem_fe, dim);
                  elem_fe->get_JxW();
                  elem_fe->get_phi();
                }
            }
            break;
          case( TYPE_VECTOR ):
            {
              FEGenericBase<RealGradient> * elem_fe = nullptr;
              for (auto dim : context.elem_dimensions())
                {
                  context.get_element_fe(var, elem_fe, dim);
                  elem_fe->get_JxW();
                  elem_fe->get_phi();
                }
            }
            break;
          default:
            libmesh_error_msg("Unrecognized field type!");
          }
      }
}

init_data()

void libMesh::ContinuationSystem::init_data ( )

overrideprotectedvirtual

Initializes the member data fields associated with the system, so that, e.g., assemble() may be used.

Reimplemented from libMesh::FEMSystem.

Definition at line 91 of file continuation_system.C.

References libMesh::System::add_vector(), delta_u, du_ds, libMesh::FEMSystem::init_data(), previous_du_ds, previous_u, y, y_old, and z.

{
  // Add a vector which stores the tangent "du/ds" to the system and save its pointer.
  du_ds = &(add_vector("du_ds"));

  // Add a vector which stores the tangent "du/ds" to the system and save its pointer.
  previous_du_ds = &(add_vector("previous_du_ds"));

  // Add a vector to keep track of the previous nonlinear solution
  // at the old value of lambda.
  previous_u = &(add_vector("previous_u"));

  // Add a vector to keep track of the temporary solution "y" of Ay=G_{\lambda}.
  y = &(add_vector("y"));

  // Add a vector to keep track of the "old value" of "y" which is the solution of Ay=G_{\lambda}.
  y_old = &(add_vector("y_old"));

  // Add a vector to keep track of the temporary solution "z" of Az=-G.
  z = &(add_vector("z"));

  // Add a vector to keep track of the Newton update during the constrained PDE solves.
  delta_u = &(add_vector("delta_u"));

  // Call the Parent's initialization routine.
  Parent::init_data();
}

init_matrices()

void libMesh::System::init_matrices ( )

protectedvirtualinherited

Initializes the matrices associated with this system.

Reimplemented in libMesh::EigenSystem.

Definition at line 323 of file system.C.

References libMesh::System::_matrices, libMesh::System::_matrices_initialized, libMesh::System::_matrix_types, libMesh::System::_prefer_hash_table_matrix_assembly, libMesh::System::_require_sparsity_pattern, libMesh::DofMap::attach_matrix(), libMesh::DofMap::compute_sparsity(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::SparseMatrix< T >::initialized(), libMesh::DofMap::is_attached(), libMesh::libmesh_assert(), and libMesh::System::name().

Referenced by libMesh::System::init_data(), and libMesh::EigenSystem::init_matrices().

{
  parallel_object_only();

  // No matrices to init
  if (_matrices.empty())
    {
      // any future matrices to be added will need their own
      // initialization
      _matrices_initialized = true;

      return;
    }

  // Check for quick return in case the first matrix
  // (and by extension all the matrices) has already
  // been initialized
  if (_matrices.begin()->second->initialized())
    {
      libmesh_assert(_matrices_initialized);
      return;
    }

  _matrices_initialized = true;

  // Tell the matrices about the dof map, and vice versa
  for (auto & pr : _matrices)
    {
      SparseMatrix<Number> & m = *(pr.second);
      libmesh_assert (!m.initialized());

      // We want to allow repeated init() on systems, but we don't
      // want to attach the same matrix to the DofMap twice
      if (!this->get_dof_map().is_attached(m))
        this->get_dof_map().attach_matrix(m);

      // If the user has already explicitly requested that this matrix use a hash table, then we
      // always honor that
      const bool use_hash =
          pr.second->use_hash_table() ||
          (this->_prefer_hash_table_matrix_assembly && pr.second->supports_hash_table());
      pr.second->use_hash_table(use_hash);
      // Make this call after we've determined whether the matrix is using a hash table
      if (pr.second->require_sparsity_pattern())
        this->_require_sparsity_pattern = true;
    }

  // Compute the sparsity pattern for the current
  // mesh and DOF distribution.  This also updates
  // additional matrices, \p DofMap now knows them
  if (this->_require_sparsity_pattern)
    this->get_dof_map().compute_sparsity(this->get_mesh());

  // Initialize matrices and set to zero
  for (auto & [name, mat] : _matrices)
    {
      mat->init(_matrix_types[name]);
      mat->zero();
    }
}

init_physics()

void libMesh::DifferentiablePhysics::init_physics ( const System &  sys )

virtualinherited

Initialize any data structures associated with the physics.

Definition at line 35 of file diff_physics.C.

References libMesh::DifferentiablePhysics::_time_evolving, and libMesh::System::n_vars().

Referenced by libMesh::DifferentiableSystem::init_data().

{
  // give us flags for every variable that might be time evolving
  _time_evolving.resize(sys.n_vars(), false);
}

init_qoi() [1/2]

virtual void libMesh::DifferentiableQoI::init_qoi ( std::vector< Number > &  )

inlinevirtualinherited

Initialize system qoi.

This version of the function required direct vector access, and is now deprecated.

Definition at line 72 of file diff_qoi.h.

{}

init_qoi() [2/2]

void libMesh::DifferentiableQoI::init_qoi ( std::vector< Number > &  )

inlineinherited

Non-virtual, to try to help deprecated user code catch this change at compile time (if they specified override)

Definition at line 78 of file diff_qoi.h.

{}

init_qoi_count()

virtual void libMesh::DifferentiableQoI::init_qoi_count ( System &  )

inlinevirtualinherited

Initialize system qoi.

Often this will just call sys.init_qois(some_desired_number_of_qois)

Reimplemented in LaplaceQoI, and CoupledSystemQoI.

Definition at line 85 of file diff_qoi.h.

{}

init_qois()

void libMesh::System::init_qois ( unsigned int  n_qois )

inherited

Accessors for qoi and qoi_error_estimates vectors.

Definition at line 2371 of file system.C.

References libMesh::System::n_qois(), libMesh::System::qoi, and libMesh::System::qoi_error_estimates.

Referenced by CoupledSystemQoI::init_qoi_count(), LaplaceQoI::init_qoi_count(), and main().

{
  qoi.resize(n_qois);
  qoi_error_estimates.resize(n_qois);
}

initialize_tangent()

void libMesh::ContinuationSystem::initialize_tangent ( )

private

Before starting arclength continuation, we need at least 2 prior solutions (both solution and u_previous should be filled with meaningful values) And we need to initialize the tangent vector.

This only needs to be called once.

Definition at line 132 of file continuation_system.C.

References libMesh::NumericVector< T >::add(), libMesh::NumericVector< T >::close(), continuation_parameter, dlambda_ds, ds_current, du_ds, libMesh::NumericVector< T >::l2_norm(), libMesh::libmesh_assert(), old_continuation_parameter, libMesh::out, previous_u, quiet, libMesh::Real, libMesh::NumericVector< T >::scale(), set_Theta(), libMesh::System::solution, solve_tangent(), tangent_initialized, Theta, Theta_LOCA, update_solution(), and y.

Referenced by continuation_solve().

{
  // Be sure the tangent was not already initialized.
  libmesh_assert (!tangent_initialized);

  // Compute delta_s_zero, the initial arclength traveled during the
  // first step.  Here we assume that previous_u and lambda_old store
  // the previous solution and control parameter.  You may need to
  // read in an old solution (or solve the non-continuation system)
  // first and call save_current_solution() before getting here.

  // 1.) Compute delta_s_zero as ||u|| - ||u_old|| + ...
  // Compute norms of the current and previous solutions
  //   Real norm_u          = solution->l2_norm();
  //   Real norm_previous_u = previous_u->l2_norm();

  //   if (!quiet)
  //     {
  //       libMesh::out << "norm_u=" << norm_u << std::endl;
  //       libMesh::out << "norm_previous_u=" << norm_previous_u << std::endl;
  //     }

  //   if (norm_u == norm_previous_u)
  //     {
  //       libMesh::err << "Warning, it appears u and previous_u are the "
  //   << "same, are you sure this is correct?"
  //   << "It's possible you forgot to set one or the other..."
  //   << std::endl;
  //     }

  //   Real delta_s_zero = std::sqrt(
  //   (norm_u - norm_previous_u)*(norm_u - norm_previous_u) +
  //   (*continuation_parameter-old_continuation_parameter)*
  //   (*continuation_parameter-old_continuation_parameter)
  //   );

  //   // 2.) Compute delta_s_zero as ||u -u_old|| + ...
  //   *delta_u = *solution;
  //   delta_u->add(-1., *previous_u);
  //   delta_u->close();
  //   Real norm_delta_u = delta_u->l2_norm();
  //   Real norm_u          = solution->l2_norm();
  //   Real norm_previous_u = previous_u->l2_norm();

  //   // Scale norm_delta_u by the bigger of either norm_u or norm_previous_u
  //   norm_delta_u /= std::max(norm_u, norm_previous_u);

  //   if (!quiet)
  //     {
  //       libMesh::out << "norm_u=" << norm_u << std::endl;
  //       libMesh::out << "norm_previous_u=" << norm_previous_u << std::endl;
  //       //libMesh::out << "norm_delta_u=" << norm_delta_u << std::endl;
  //       libMesh::out << "norm_delta_u/max(|u|,|u_old|)=" << norm_delta_u << std::endl;
  //       libMesh::out << "|norm_u-norm_previous_u|=" << std::abs(norm_u - norm_previous_u) << std::endl;
  //     }

  //   const Real dlambda = *continuation_parameter-old_continuation_parameter;

  //   if (!quiet)
  //     libMesh::out << "dlambda=" << dlambda << std::endl;

  //   Real delta_s_zero = std::sqrt(
  //   (norm_delta_u*norm_delta_u) +
  //   (dlambda*dlambda)
  //   );

  //   if (!quiet)
  //     libMesh::out << "delta_s_zero=" << delta_s_zero << std::endl;

  // 1.) + 2.)
  //   // Now approximate the initial tangent d(lambda)/ds
  //   this->dlambda_ds = (*continuation_parameter-old_continuation_parameter) / delta_s_zero;


  //   // We can also approximate the deriv. wrt s by finite differences:
  //   // du/ds = (u1 - u0) / delta_s_zero.
  //   // FIXME: Use delta_u from above if we decide to keep that method.
  //   *du_ds = *solution;
  //   du_ds->add(-1., *previous_u);
  //   du_ds->scale(1./delta_s_zero);
  //   du_ds->close();


  // 3.) Treating (u-previous_u)/(lambda - lambda_old) as an approximation to du/d(lambda),
  // we follow the same technique as Carnes and Shadid.
  //   const Real dlambda = *continuation_parameter-old_continuation_parameter;
  //   libmesh_assert_greater (dlambda, 0.);

  //   // Use delta_u for temporary calculation of du/d(lambda)
  //   *delta_u = *solution;
  //   delta_u->add(-1., *previous_u);
  //   delta_u->scale(1. / dlambda);
  //   delta_u->close();

  //   // Determine initial normalization parameter
  //   const Real solution_size = std::max(solution->l2_norm(), previous_u->l2_norm());
  //   if (solution_size > 1.)
  //     {
  //       Theta = 1./solution_size;

  //       if (!quiet)
  // libMesh::out << "Setting Normalization Parameter Theta=" << Theta << std::endl;
  //     }

  //   // Compute d(lambda)/ds
  //   // The correct sign of d(lambda)/ds should be positive, since we assume that (lambda > lambda_old)
  //   // but we could always double-check that as well.
  //   Real norm_delta_u = delta_u->l2_norm();
  //   this->dlambda_ds = 1. / std::sqrt(1. + Theta*Theta*norm_delta_u*norm_delta_u);

  //   // Finally, compute du/ds = d(lambda)/ds * du/d(lambda)
  //   *du_ds = *delta_u;
  //   du_ds->scale(dlambda_ds);
  //   du_ds->close();


  // 4.) Use normalized arclength formula to estimate delta_s_zero
  //   // Determine initial normalization parameter
  //   set_Theta();

  //   // Compute (normalized) delta_s_zero
  //   *delta_u = *solution;
  //   delta_u->add(-1., *previous_u);
  //   delta_u->close();
  //   Real norm_delta_u = delta_u->l2_norm();

  //   const Real dlambda = *continuation_parameter-old_continuation_parameter;

  //   if (!quiet)
  //     libMesh::out << "dlambda=" << dlambda << std::endl;

  //   Real delta_s_zero = std::sqrt(
  //   (Theta_LOCA*Theta_LOCA*Theta*norm_delta_u*norm_delta_u) +
  //   (dlambda*dlambda)
  //   );
  //   *du_ds = *delta_u;
  //   du_ds->scale(1./delta_s_zero);
  //   dlambda_ds = dlambda / delta_s_zero;

  //   if (!quiet)
  //     {
  //       libMesh::out << "delta_s_zero=" << delta_s_zero << std::endl;
  //       libMesh::out << "initial d(lambda)/ds|_0 = " << dlambda_ds << std::endl;
  //       libMesh::out << "initial ||du_ds||_0 = " << du_ds->l2_norm() << std::endl;
  //     }

  //   // FIXME: Also store the initial finite-differenced approximation to -du/dlambda as y.
  //   // We stick to the convention of storing negative y, since that is what we typically
  //   // solve for anyway.
  //   *y = *delta_u;
  //   y->scale(-1./dlambda);
  //   y->close();



  // 5.) Assume dlambda/ds_0 ~ 1/sqrt(2) and determine the value of Theta_LOCA which
  // will satisfy this criterion

  // Initial change in parameter
  const Real dlambda = *continuation_parameter-old_continuation_parameter;
  libmesh_assert_not_equal_to (dlambda, 0.0);

  // Ideal initial value of dlambda_ds
  dlambda_ds = 1. / std::sqrt(2.);
  if (dlambda < 0.)
    dlambda_ds *= -1.;

  // This also implies the initial value of ds
  ds_current = dlambda / dlambda_ds;

  if (!quiet)
    libMesh::out << "Setting ds_current|_0=" << ds_current << std::endl;

  // Set y = -du/dlambda using finite difference approximation
  *y = *solution;
  y->add(-1., *previous_u);
  y->scale(-1./dlambda);
  y->close();
  const Real ynorm=y->l2_norm();

  // Finally, set the value of du_ds to be used in the upcoming
  // tangent calculation. du/ds = du/dlambda * dlambda/ds
  *du_ds = *y;
  du_ds->scale(-dlambda_ds);
  du_ds->close();

  // Determine additional solution normalization parameter
  // (Since we just set du/ds, it will be:  ||du||*||du/ds||)
  set_Theta();

  // The value of Theta_LOCA which makes dlambda_ds = 1/sqrt(2),
  // assuming our Theta = ||du||^2.
  // Theta_LOCA = std::abs(dlambda);

  // Assuming general Theta
  Theta_LOCA = std::sqrt(1./Theta/ynorm/ynorm);


  if (!quiet)
    {
      libMesh::out << "Setting initial Theta_LOCA = " << Theta_LOCA << std::endl;
      libMesh::out << "Theta_LOCA^2*Theta         = " << Theta_LOCA*Theta_LOCA*Theta << std::endl;
      libMesh::out << "initial d(lambda)/ds|_0    = " << dlambda_ds << std::endl;
      libMesh::out << "initial ||du_ds||_0        = " << du_ds->l2_norm() << std::endl;
    }



  // OK, we estimated the tangent at point u0.
  // Now, to estimate the tangent at point u1, we call the solve_tangent routine.

  // Set the flag which tells us the method has been initialized.
  tangent_initialized = true;

  solve_tangent();

  // Advance the solution and the parameter to the next value.
  update_solution();
}

is_adjoint_already_solved()

bool libMesh::System::is_adjoint_already_solved ( ) const

inlineinherited

Accessor for the adjoint_already_solved boolean.

Definition at line 409 of file system.h.

References libMesh::System::adjoint_already_solved.

Referenced by libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::ImplicitSystem::qoi_parameter_hessian(), and libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product().

  { return adjoint_already_solved;}

is_first_order_var()

bool libMesh::DifferentiablePhysics::is_first_order_var ( unsigned int  var ) const

inlineinherited

Definition at line 509 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_first_order_vars.

  { return _first_order_vars.find(var) != _first_order_vars.end(); }

is_initialized()

bool libMesh::System::is_initialized ( ) const

inlineinherited

Returns

true iff this system has been initialized.

Definition at line 2414 of file system.h.

References libMesh::System::_is_initialized.

Referenced by libMesh::System::add_variable(), libMesh::System::add_variables(), libMesh::System::init(), and libMesh::StaticCondensationDofMap::reinit().

{
  return _is_initialized;
}

is_second_order_var()

bool libMesh::DifferentiablePhysics::is_second_order_var ( unsigned int  var ) const

inlineinherited

Definition at line 522 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_second_order_vars.

Referenced by libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns().

  { return _second_order_vars.find(var) != _second_order_vars.end(); }

is_time_evolving()

bool libMesh::DifferentiablePhysics::is_time_evolving ( unsigned int  var ) const

inlineinherited

Returns

true iff variable var is evolving with respect to time. In general, the user's init() function should have set time_evolving() for any variables which behave like du/dt = F(u), and should not call time_evolving() for any variables which behave like 0 = G(u).

Definition at line 260 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_time_evolving, and libMesh::libmesh_assert().

Referenced by libMesh::FEMPhysics::eulerian_residual(), libMesh::FEMSystem::init_context(), libMesh::FEMPhysics::mass_residual(), and libMesh::DifferentiablePhysics::nonlocal_mass_residual().

  {
    libmesh_assert_less(var,_time_evolving.size());
    libmesh_assert( _time_evolving[var] == 0 ||
                    _time_evolving[var] == 1 ||
                    _time_evolving[var] == 2 );
    return _time_evolving[var];
  }

local_dof_indices()

void libMesh::System::local_dof_indices ( const unsigned int  var, std::set< dof_id_type > &  var_indices  ) const

inherited

Fills the std::set with the degrees of freedom on the local processor corresponding the the variable number passed in.

Definition at line 1627 of file system.C.

References libMesh::DofMap::dof_indices(), libMesh::DofMapBase::end_dof(), libMesh::DofMapBase::first_dof(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), and libMesh::libmesh_assert().

Referenced by libMesh::System::discrete_var_norm(), SystemsTest::testBlockRestrictedVarNDofs(), and libMesh::DirectSolutionTransfer::transfer().

{
  // Make sure the set is clear
  var_indices.clear();

  std::vector<dof_id_type> dof_indices;

  const dof_id_type
    first_local = this->get_dof_map().first_dof(),
    end_local   = this->get_dof_map().end_dof();

  // Begin the loop over the elements
  for (const auto & elem : this->get_mesh().active_local_element_ptr_range())
    {
      this->get_dof_map().dof_indices (elem, dof_indices, var);

      for (dof_id_type dof : dof_indices)
        //If the dof is owned by the local processor
        if (first_local <= dof && dof < end_local)
          var_indices.insert(dof);
    }

  // we may have missed assigning DOFs to nodes that we own
  // but to which we have no connected elements matching our
  // variable restriction criterion.  this will happen, for example,
  // if variable V is restricted to subdomain S.  We may not own
  // any elements which live in S, but we may own nodes which are
  // *connected* to elements which do.
  for (const auto & node : this->get_mesh().local_node_ptr_range())
    {
      libmesh_assert(node);
      this->get_dof_map().dof_indices (node, dof_indices, var);
      for (auto dof : dof_indices)
        if (first_local <= dof && dof < end_local)
          var_indices.insert(dof);
    }
}

mass_residual() [1/2]

bool libMesh::FEMPhysics::mass_residual ( bool  request_jacobian, DiffContext &  c  )

overridevirtualinherited

Subtracts a mass vector contribution on elem from elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Many problems can use the reimplementation in FEMPhysics::mass_residual which subtracts (du/dt,v) for each transient variable u; users with more complicated transient problems will need to reimplement this themselves.

Reimplemented from libMesh::DifferentiablePhysics.

Reimplemented in SecondOrderScalarSystemFirstOrderTimeSolverBase, SecondOrderScalarSystemSecondOrderTimeSolverBase, FirstOrderScalarSystemBase, ElasticitySystem, ElasticitySystem, and NavierSystem.

Definition at line 200 of file fem_physics.C.

References libMesh::DiffContext::elem_solution_rate_derivative, libMesh::DiffContext::get_dof_indices(), libMesh::DiffContext::get_elem_jacobian(), libMesh::DiffContext::get_elem_residual(), libMesh::FEMContext::get_element_fe(), libMesh::FEMContext::get_element_qrule(), libMesh::FEAbstract::get_JxW(), libMesh::FEGenericBase< OutputType >::get_phi(), libMesh::FEMContext::interior_rate(), libMesh::DifferentiablePhysics::is_time_evolving(), libMesh::make_range(), libMesh::QBase::n_points(), and libMesh::DiffContext::n_vars().

{
  FEMContext & context = cast_ref<FEMContext &>(c);

  unsigned int n_qpoints = context.get_element_qrule().n_points();

  for (auto var : make_range(context.n_vars()))
    {
      if (!this->is_time_evolving(var))
        continue;

      FEBase * elem_fe = nullptr;
      context.get_element_fe( var, elem_fe );

      const std::vector<Real> & JxW = elem_fe->get_JxW();

      const std::vector<std::vector<Real>> & phi = elem_fe->get_phi();

      const unsigned int n_dofs = cast_int<unsigned int>
        (context.get_dof_indices(var).size());

      DenseSubVector<Number> & Fu = context.get_elem_residual(var);
      DenseSubMatrix<Number> & Kuu = context.get_elem_jacobian( var, var );

      for (unsigned int qp = 0; qp != n_qpoints; ++qp)
        {
          Number uprime;
          context.interior_rate(var, qp, uprime);
          const Number JxWxU = JxW[qp] * uprime;
          for (unsigned int i = 0; i != n_dofs; ++i)
            {
              Fu(i) -= JxWxU * phi[i][qp];
              if (request_jacobian && context.elem_solution_rate_derivative)
                {
                  const Number JxWxPhiIxDeriv = JxW[qp] * phi[i][qp] *
                    context.elem_solution_rate_derivative;
                  Kuu(i,i) -= JxWxPhiIxDeriv * phi[i][qp];
                  for (unsigned int j = i+1; j < n_dofs; ++j)
                    {
                      const Number Kij = JxWxPhiIxDeriv * phi[j][qp];
                      Kuu(i,j) -= Kij;
                      Kuu(j,i) -= Kij;
                    }
                }
            }
        }
    }

  return request_jacobian;
}

mass_residual() [2/2]

virtual bool libMesh::DifferentiablePhysics::mass_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Subtracts a mass vector contribution on elem from elem_residual.

For first-order-in-time problems, this is the \( M(u,\dot{u})\dot{u} \) term. For second-order-in-time problems, this is the \( M(u,\ddot{u})\ddot{u} \) term. This method is only called for UnsteadySolver-based TimeSolvers.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Many first-order-in-time problems can use the reimplementation in FEMPhysics::mass_residual which subtracts (du/dt,v) for each transient variable u; users with more complicated transient problems or second-order-in-time problems will need to reimplement this themselves.

Reimplemented in SecondOrderScalarSystemFirstOrderTimeSolverBase, SecondOrderScalarSystemSecondOrderTimeSolverBase, FirstOrderScalarSystemBase, libMesh::FEMPhysics, ElasticitySystem, ElasticitySystem, and NavierSystem.

Definition at line 302 of file diff_physics.h.

Referenced by libMesh::EulerSolver::element_residual(), libMesh::Euler2Solver::element_residual(), libMesh::NewmarkSolver::element_residual(), and libMesh::EigenTimeSolver::element_residual().

  {
    return request_jacobian;
  }

matrices_begin() [1/2]

System::matrices_iterator libMesh::System::matrices_begin ( )

inlineinherited

Beginning of matrices container.

Definition at line 2588 of file system.h.

References libMesh::System::_matrices.

{
  return _matrices.begin();
}

matrices_begin() [2/2]

System::const_matrices_iterator libMesh::System::matrices_begin ( ) const

inlineinherited

Beginning of matrices container.

Definition at line 2594 of file system.h.

References libMesh::System::_matrices.

{
  return _matrices.begin();
}

matrices_end() [1/2]

System::matrices_iterator libMesh::System::matrices_end ( )

inlineinherited

End of matrices container.

Definition at line 2600 of file system.h.

References libMesh::System::_matrices.

{
  return _matrices.end();
}

matrices_end() [2/2]

System::const_matrices_iterator libMesh::System::matrices_end ( ) const

inlineinherited

End of matrices container.

Definition at line 2606 of file system.h.

References libMesh::System::_matrices.

{
  return _matrices.end();
}

mesh_position_get()

void FEMSystem::mesh_position_get ( )

inherited

Tells the FEMSystem to set the degree of freedom coefficients which should correspond to mesh nodal coordinates.

Definition at line 1423 of file fem_system.C.

References libMesh::DifferentiablePhysics::_mesh_sys, libMesh::DifferentiablePhysics::_mesh_x_var, libMesh::DifferentiablePhysics::_mesh_y_var, libMesh::DifferentiablePhysics::_mesh_z_var, libMesh::FEMSystem::build_context(), libMesh::FEMContext::elem_position_get(), libMesh::DiffContext::get_dof_indices(), libMesh::DiffContext::get_elem_solution(), libMesh::System::get_mesh(), libMesh::FEMSystem::init_context(), libMesh::invalid_uint, mesh, libMesh::FEMContext::pre_fe_reinit(), libMesh::System::solution, and libMesh::System::update().

Referenced by SolidSystem::init_data().

{
  // This function makes no sense unless we've already picked out some
  // variable(s) to reflect mesh position coordinates
  libmesh_error_msg_if(!_mesh_sys, "_mesh_sys was nullptr!");

  // We currently assume mesh variables are in our own system
  if (_mesh_sys != this)
    libmesh_not_implemented();

  // Loop over every active mesh element on this processor
  const MeshBase & mesh = this->get_mesh();

  std::unique_ptr<DiffContext> con = this->build_context();
  FEMContext & _femcontext = cast_ref<FEMContext &>(*con);
  this->init_context(_femcontext);

  // Get the solution's mesh variables from every element
  for (const auto & elem : mesh.active_local_element_ptr_range())
    {
      _femcontext.pre_fe_reinit(*this, elem);

      _femcontext.elem_position_get();

      if (_mesh_x_var != libMesh::invalid_uint)
        this->solution->insert(_femcontext.get_elem_solution(_mesh_x_var),
                               _femcontext.get_dof_indices(_mesh_x_var) );
      if (_mesh_y_var != libMesh::invalid_uint)
        this->solution->insert(_femcontext.get_elem_solution(_mesh_y_var),
                               _femcontext.get_dof_indices(_mesh_y_var));
      if (_mesh_z_var != libMesh::invalid_uint)
        this->solution->insert(_femcontext.get_elem_solution(_mesh_z_var),
                               _femcontext.get_dof_indices(_mesh_z_var));
    }

  this->solution->close();

  // And make sure the current_local_solution is up to date too
  this->System::update();
}

mesh_position_set()

void FEMSystem::mesh_position_set ( )

inherited

Tells the FEMSystem to set the mesh nodal coordinates which should correspond to degree of freedom coefficients.

Definition at line 1087 of file fem_system.C.

References libMesh::DifferentiablePhysics::_mesh_sys, libMesh::FEMSystem::build_context(), libMesh::ParallelObject::comm(), libMesh::FEMContext::elem_fe_reinit(), libMesh::FEMContext::elem_position_set(), libMesh::FEMContext::get_elem(), libMesh::System::get_mesh(), libMesh::Elem::has_children(), libMesh::FEMSystem::init_context(), libMesh::libmesh_assert(), mesh, libMesh::FEMContext::pre_fe_reinit(), and libMesh::Parallel::sync_dofobject_data_by_id().

Referenced by libMesh::FEMSystem::solve(), and SolidSystem::update().

{
  // If we don't need to move the mesh, we're done
  if (_mesh_sys != this)
    return;

  MeshBase & mesh = this->get_mesh();

  std::unique_ptr<DiffContext> con = this->build_context();
  FEMContext & _femcontext = cast_ref<FEMContext &>(*con);
  this->init_context(_femcontext);

  // Move every mesh element we can
  for (const auto & elem : mesh.active_local_element_ptr_range())
    {
      // We need the algebraic data
      _femcontext.pre_fe_reinit(*this, elem);
      // And when asserts are on, we also need the FE so
      // we can assert that the mesh data is of the right type.
#ifndef NDEBUG
      _femcontext.elem_fe_reinit();
#endif

      // This code won't handle moving subactive elements
      libmesh_assert(!_femcontext.get_elem().has_children());

      _femcontext.elem_position_set(1.);
    }

  // We've now got positions set on all local nodes (and some
  // semilocal nodes); let's request positions for non-local nodes
  // from their processors.

  SyncNodalPositions sync_object(mesh);
  Parallel::sync_dofobject_data_by_id
    (this->comm(), mesh.nodes_begin(), mesh.nodes_end(), sync_object);
}

n_active_dofs()

dof_id_type libMesh::System::n_active_dofs ( ) const

inlineinherited

Returns

The number of active degrees of freedom for this System.

Definition at line 2542 of file system.h.

References libMesh::System::n_constrained_dofs(), and libMesh::System::n_dofs().

{
  return this->n_dofs() - this->n_constrained_dofs();
}

n_components()

unsigned int libMesh::System::n_components ( ) const

inlineinherited

Returns

The total number of scalar components in the system's variables. This will equal n_vars() in the case of all scalar-valued variables.

Definition at line 2446 of file system.h.

References libMesh::System::_variables, libMesh::Variable::first_scalar_number(), libMesh::System::get_mesh(), and libMesh::Variable::n_components().

Referenced by libMesh::System::add_variables().

{
  if (_variables.empty())
    return 0;

  const Variable & last = _variables.back();
  return last.first_scalar_number() + last.n_components(this->get_mesh());
}

n_constrained_dofs()

dof_id_type libMesh::System::n_constrained_dofs ( ) const

inherited

Returns

The total number of constrained degrees of freedom in the system.

Definition at line 128 of file system.C.

References libMesh::System::_dof_map.

Referenced by form_functionA(), form_functionB(), form_matrixA(), libMesh::System::get_info(), libMesh::System::n_active_dofs(), libMesh::EigenSystem::solve(), and BoundaryInfoTest::testShellFaceConstraints().

{
#ifdef LIBMESH_ENABLE_CONSTRAINTS

  return _dof_map->n_constrained_dofs();

#else

  return 0;

#endif
}

n_dofs()

dof_id_type libMesh::System::n_dofs ( ) const

inherited

Returns

The number of degrees of freedom in the system

Definition at line 121 of file system.C.

References libMesh::System::_dof_map.

Referenced by libMesh::TransientRBConstruction::add_IC_to_RB_space(), libMesh::System::add_vector(), libMesh::TransientRBConstruction::allocate_data_structures(), libMesh::RBConstruction::allocate_data_structures(), libMesh::TransientRBConstruction::assemble_affine_expansion(), libMesh::ClawSystem::assemble_avg_coupling_matrices(), libMesh::ClawSystem::assemble_boundary_condition_matrices(), libMesh::AdvectionSystem::assemble_claw_rhs(), libMesh::ClawSystem::assemble_jump_coupling_matrix(), libMesh::RBConstruction::compute_Fq_representor_innerprods(), libMesh::RBConstruction::compute_output_dual_innerprods(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), libMesh::TransientRBConstruction::enrich_RB_space(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::System::get_info(), libMesh::SecondOrderUnsteadySolver::init_data(), libMesh::AdvectionSystem::init_data(), libMesh::UnsteadySolver::init_data(), libMesh::System::init_data(), libMesh::OptimizationSystem::initialize_equality_constraints_storage(), libMesh::OptimizationSystem::initialize_inequality_constraints_storage(), main(), libMesh::TransientRBConstruction::mass_matrix_scaled_matvec(), libMesh::System::n_active_dofs(), libMesh::CondensedEigenSystem::n_global_non_condensed_dofs(), libMesh::FEMSystem::numerical_jacobian(), libMesh::RBSCMConstruction::perform_SCM_greedy(), libMesh::RBEvaluation::read_in_vectors_from_multiple_files(), libMesh::System::read_legacy_data(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), libMesh::RBConstruction::read_riesz_representors_from_files(), libMesh::SecondOrderUnsteadySolver::reinit(), libMesh::UnsteadySolver::reinit(), libMesh::System::restrict_vectors(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), libMesh::TransientRBConstruction::set_error_temporal_data(), libMesh::ClawSystem::solve_conservation_law(), SystemsTest::test100KVariables(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), SystemsTest::testPostInitAddVector(), SystemsTest::testPostInitAddVectorTypeChange(), SystemsTest::testProjectCubeWithMeshFunction(), SystemsTest::testProjectMatrix1D(), SystemsTest::testProjectMatrix2D(), SystemsTest::testProjectMatrix3D(), libMesh::RBConstruction::train_reduced_basis_with_POD(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::RBConstruction::truth_assembly(), libMesh::TransientRBConstruction::update_RB_initial_condition_all_N(), libMesh::TransientRBConstruction::update_RB_system_matrices(), libMesh::RBConstruction::update_RB_system_matrices(), libMesh::TransientRBConstruction::update_residual_terms(), and libMesh::RBConstruction::update_residual_terms().

{
  return _dof_map->n_dofs();
}

n_local_constrained_dofs()

dof_id_type libMesh::System::n_local_constrained_dofs ( ) const

inherited

Returns

The number of constrained degrees of freedom on this processor.

Definition at line 143 of file system.C.

References libMesh::System::_dof_map.

Referenced by libMesh::System::get_info().

{
#ifdef LIBMESH_ENABLE_CONSTRAINTS

  return _dof_map->n_local_constrained_dofs();

#else

  return 0;

#endif
}

n_local_dofs()

dof_id_type libMesh::System::n_local_dofs ( ) const

inherited

Returns

The number of degrees of freedom local to this processor

Definition at line 158 of file system.C.

References libMesh::System::_dof_map.

Referenced by libMesh::TransientRBConstruction::add_IC_to_RB_space(), libMesh::System::add_vector(), libMesh::TransientRBConstruction::allocate_data_structures(), libMesh::RBConstruction::allocate_data_structures(), libMesh::TransientRBConstruction::assemble_affine_expansion(), libMesh::AdvectionSystem::assemble_claw_rhs(), libMesh::PetscDMWrapper::build_section(), libMesh::RBConstruction::compute_Fq_representor_innerprods(), libMesh::RBConstruction::compute_output_dual_innerprods(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), libMesh::TransientRBConstruction::enrich_RB_space(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::System::get_info(), libMesh::SecondOrderUnsteadySolver::init_data(), libMesh::AdvectionSystem::init_data(), libMesh::UnsteadySolver::init_data(), libMesh::System::init_data(), libMesh::OptimizationSystem::initialize_equality_constraints_storage(), libMesh::OptimizationSystem::initialize_inequality_constraints_storage(), main(), libMesh::TransientRBConstruction::mass_matrix_scaled_matvec(), libMesh::RBEvaluation::read_in_vectors_from_multiple_files(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), libMesh::RBConstruction::read_riesz_representors_from_files(), libMesh::SecondOrderUnsteadySolver::reinit(), libMesh::UnsteadySolver::reinit(), libMesh::System::restrict_vectors(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), libMesh::TransientRBConstruction::set_error_temporal_data(), libMesh::ClawSystem::solve_conservation_law(), MeshFunctionTest::test_p_level(), libMesh::RBConstruction::train_reduced_basis_with_POD(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::RBConstruction::truth_assembly(), libMesh::TransientRBConstruction::update_RB_initial_condition_all_N(), libMesh::TransientRBConstruction::update_RB_system_matrices(), libMesh::RBConstruction::update_RB_system_matrices(), libMesh::TransientRBConstruction::update_residual_terms(), and libMesh::RBConstruction::update_residual_terms().

{
  return _dof_map->n_local_dofs();
}

n_matrices()

unsigned int libMesh::System::n_matrices ( ) const

inlineinherited

Returns

The number of matrices handled by this system. This is the size of the _matrices map

Definition at line 2699 of file system.h.

References libMesh::System::_matrices.

Referenced by libMesh::ImplicitSystem::add_matrices(), and libMesh::System::get_info().

{
  return cast_int<unsigned int>(_matrices.size());
}

n_objects()

static unsigned int libMesh::ReferenceCounter::n_objects ( )

inlinestaticinherited

Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 85 of file reference_counter.h.

References libMesh::ReferenceCounter::_n_objects.

Referenced by libMesh::LibMeshInit::~LibMeshInit().

  { return _n_objects; }

n_processors()

processor_id_type libMesh::ParallelObject::n_processors ( ) const

inlineinherited

Returns

The number of processors in the group.

Definition at line 103 of file parallel_object.h.

References libMesh::ParallelObject::_communicator, libMesh::libmesh_assert(), and TIMPI::Communicator::size().

Referenced by libMesh::Partitioner::_find_global_index_by_pid_map(), libMesh::BoundaryInfo::_find_id_maps(), libMesh::DofMap::add_constraints_to_send_list(), libMesh::PetscDMWrapper::add_dofs_to_section(), libMesh::DistributedMesh::add_elem(), libMesh::DofMap::add_neighbors_to_send_list(), libMesh::DistributedMesh::add_node(), libMesh::System::add_vector(), libMesh::LaplaceMeshSmoother::allgather_graph(), libMesh::DofMap::allgather_recursive_constraints(), libMesh::FEMSystem::assembly(), libMesh::Nemesis_IO::assert_symmetric_cmaps(), libMesh::Partitioner::assign_partitioning(), libMesh::AztecLinearSolver< T >::AztecLinearSolver(), libMesh::Partitioner::build_graph(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::DistributedMesh::clear(), libMesh::DistributedMesh::clear_elems(), libMesh::Nemesis_IO_Helper::compute_border_node_ids(), libMesh::Nemesis_IO_Helper::construct_nemesis_filename(), libMesh::UnstructuredMesh::copy_nodes_and_elements(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), libMesh::UnstructuredMesh::create_pid_mesh(), libMesh::MeshTools::create_processor_bounding_box(), libMesh::DofMap::distribute_dofs(), libMesh::DofMap::distribute_scalar_dofs(), libMesh::DistributedMesh::DistributedMesh(), libMesh::EnsightIO::EnsightIO(), libMesh::RBEIMEvaluation::gather_bfs(), libMesh::MeshBase::get_info(), libMesh::StaticCondensation::init(), libMesh::SystemSubsetBySubdomain::init(), libMesh::PetscDMWrapper::init_petscdm(), libMesh::Nemesis_IO_Helper::initialize(), libMesh::ExodusII_IO_Helper::initialize(), libMesh::DistributedMesh::insert_elem(), libMesh::MeshTools::libmesh_assert_contiguous_dof_ids(), libMesh::MeshTools::libmesh_assert_parallel_consistent_new_node_procids(), libMesh::MeshTools::libmesh_assert_parallel_consistent_procids< Elem >(), libMesh::MeshTools::libmesh_assert_parallel_consistent_procids< Node >(), libMesh::MeshTools::libmesh_assert_topology_consistent_procids< Node >(), libMesh::MeshTools::libmesh_assert_valid_boundary_ids(), libMesh::MeshTools::libmesh_assert_valid_dof_ids(), libMesh::MeshTools::libmesh_assert_valid_neighbors(), libMesh::MeshTools::libmesh_assert_valid_refinement_flags(), libMesh::DofMap::local_variable_indices(), libMesh::MeshRefinement::make_coarsening_compatible(), libMesh::MeshBase::n_active_elem_on_proc(), libMesh::DofMap::n_dofs_per_processor(), libMesh::MeshBase::n_elem_on_proc(), libMesh::MeshBase::n_nodes_on_proc(), libMesh::RBEIMEvaluation::node_gather_bfs(), libMesh::Partitioner::partition(), libMesh::MeshBase::partition(), libMesh::Partitioner::partition_unpartitioned_elements(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::DofMap::prepare_send_list(), libMesh::MeshBase::print_constraint_rows(), libMesh::DofMap::print_dof_constraints(), libMesh::NameBasedIO::read(), libMesh::Nemesis_IO::read(), libMesh::CheckpointIO::read(), libMesh::CheckpointIO::read_connectivity(), libMesh::XdrIO::read_header(), libMesh::CheckpointIO::read_nodes(), libMesh::System::read_parallel_data(), libMesh::System::read_SCALAR_dofs(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::System::read_serialized_vector(), libMesh::DistributedMesh::renumber_dof_objects(), libMesh::Partitioner::repartition(), OverlappingFunctorTest::run_partitioner_test(), libMesh::DofMap::scatter_constraints(), libMesh::DistributedMesh::set_next_unique_id(), libMesh::DofMap::set_nonlocal_dof_objects(), libMesh::PetscDMWrapper::set_point_range_in_section(), WriteVecAndScalar::setupTests(), libMesh::RBEIMEvaluation::side_gather_bfs(), DistributedMeshTest::testRemoteElemError(), CheckpointIOTest::testSplitter(), libMesh::MeshRefinement::uniformly_coarsen(), libMesh::DistributedMesh::update_parallel_id_counts(), libMesh::GMVIO::write_binary(), libMesh::GMVIO::write_discontinuous_gmv(), libMesh::ExodusII_IO_Helper::write_nodal_coordinates(), libMesh::VTKIO::write_nodal_data(), libMesh::ExodusII_IO::write_nodal_data(), libMesh::System::write_parallel_data(), libMesh::System::write_SCALAR_dofs(), libMesh::XdrIO::write_serialized_bcs_helper(), libMesh::System::write_serialized_blocked_dof_objects(), libMesh::XdrIO::write_serialized_connectivity(), libMesh::XdrIO::write_serialized_nodes(), and libMesh::XdrIO::write_serialized_nodesets().

  {
    processor_id_type returnval =
      cast_int<processor_id_type>(_communicator.size());
    libmesh_assert(returnval); // We never have an empty comm
    return returnval;
  }

n_qois()

unsigned int libMesh::System::n_qois ( ) const

inlineinherited

Number of currently active quantities of interest.

Definition at line 2621 of file system.h.

References libMesh::System::qoi, and libMesh::System::qoi_error_estimates.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::ImplicitSystem::adjoint_qoi_parameter_sensitivity(), libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::ImplicitSystem::adjoint_solve(), libMesh::SensitivityData::allocate_data(), libMesh::SensitivityData::allocate_hessian_data(), libMesh::ExplicitSystem::assemble_qoi(), libMesh::FEMSystem::assemble_qoi(), libMesh::ExplicitSystem::assemble_qoi_derivative(), libMesh::FEMSystem::assemble_qoi_derivative(), libMesh::DiffContext::DiffContext(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::FileSolutionHistory::FileSolutionHistory(), libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::UnsteadySolver::init_adjoints(), libMesh::TimeSolver::init_adjoints(), libMesh::System::init_qois(), libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::TwostepTimeSolver::integrate_adjoint_refinement_error_estimate(), libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate(), libMesh::Euler2Solver::integrate_qoi_timestep(), libMesh::TwostepTimeSolver::integrate_qoi_timestep(), libMesh::EulerSolver::integrate_qoi_timestep(), main(), libMesh::FEMContext::pre_fe_reinit(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), libMesh::FileSolutionHistory::retrieve(), libMesh::QoISet::size(), libMesh::UnsteadySolver::UnsteadySolver(), and libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve().

{
#ifndef LIBMESH_ENABLE_DEPRECATED
  libmesh_assert_equal_to(this->qoi.size(), this->qoi_error_estimates.size());
#endif

  return cast_int<unsigned int>(this->qoi.size());
}

n_variable_groups()

unsigned int libMesh::System::n_variable_groups ( ) const

inlineinherited

Returns

The number of VariableGroup variable groups in the system

Definition at line 2438 of file system.h.

References libMesh::System::_variable_groups.

Referenced by libMesh::System::add_variable(), libMesh::System::add_variables(), libMesh::FEMSystem::assembly(), libMesh::System::get_info(), and libMesh::System::init_data().

{
  return cast_int<unsigned int>(_variable_groups.size());
}

n_vars()

unsigned int libMesh::System::n_vars ( ) const

inlineinherited

Returns

The number of variables in the system

Definition at line 2430 of file system.h.

References libMesh::System::_variables.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::PetscDMWrapper::add_dofs_helper(), libMesh::DiffContext::add_localized_vector(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::System::add_variable(), libMesh::System::add_variables(), libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::FEMContext::attach_quadrature_rules(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::PetscDMWrapper::build_section(), libMesh::System::calculate_norm(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::DGFEMContext::DGFEMContext(), libMesh::DiffContext::DiffContext(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::ErrorEstimator::estimate_errors(), libMesh::ExactSolution::ExactSolution(), libMesh::FEMContext::find_hardest_fe_type(), libMesh::EquationSystems::find_variable_numbers(), libMesh::System::get_all_variable_numbers(), libMesh::FEMSystem::init_context(), libMesh::RBEIMConstruction::init_context(), libMesh::FEMContext::init_internal_data(), libMesh::PetscDMWrapper::init_petscdm(), libMesh::DifferentiablePhysics::init_physics(), AssemblyA0::interior_assembly(), AssemblyA1::interior_assembly(), AssemblyA2::interior_assembly(), InnerProductAssembly::interior_assembly(), main(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), output_norms(), libMesh::petsc_auto_fieldsplit(), libMesh::FEMContext::pre_fe_reinit(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::System::re_update(), libMesh::System::read_legacy_data(), libMesh::System::read_parallel_data(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::System::read_serialized_vector(), libMesh::System::read_serialized_vectors(), libMesh::System::reinit_mesh(), libMesh::HPCoarsenTest::select_refinement(), libMesh::PetscDMWrapper::set_point_range_in_section(), libMesh::SystemSubsetBySubdomain::set_var_nums(), OverlappingTestBase::setup_coupling_matrix(), SystemsTest::testDofCouplingWithVarGroups(), SlitMeshRefinedSystemTest::testRestart(), SlitMeshRefinedSystemTest::testSystem(), libMesh::System::write_header(), libMesh::System::write_parallel_data(), libMesh::System::write_serialized_blocked_dof_objects(), libMesh::System::write_serialized_vector(), libMesh::System::write_serialized_vectors(), and libMesh::System::zero_variable().

{
  return cast_int<unsigned int>(_variables.size());
}

n_vectors()

unsigned int libMesh::System::n_vectors ( ) const

inlineinherited

Returns

The number of vectors (in addition to the solution) handled by this system This is the size of the _vectors map

Definition at line 2558 of file system.h.

References libMesh::System::_vectors.

Referenced by libMesh::ExplicitSystem::add_system_rhs(), libMesh::System::compare(), libMesh::System::get_info(), main(), libMesh::InterMeshProjection::project_system_vectors(), and libMesh::System::write_header().

{
  return cast_int<unsigned int>(_vectors.size());
}

name()

const std::string & libMesh::System::name ( ) const

inlineinherited

Returns

The system name.

Definition at line 2342 of file system.h.

References libMesh::System::_sys_name.

Referenced by libMesh::System::compare(), compute_jacobian(), compute_residual(), DMlibMeshSetUpName_Private(), libMesh::RBConstruction::enrich_basis_from_rhs_terms(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::ExactSolution::ExactSolution(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::System::get_info(), libMesh::NewtonSolver::init(), libMesh::StaticCondensation::init(), libMesh::TimeSolver::init_data(), libMesh::System::init_matrices(), main(), output_norms(), libMesh::petsc_auto_fieldsplit(), libMesh::System::prefix(), libMesh::RBSCMConstruction::print_info(), libMesh::ClawSystem::print_info(), libMesh::RBEIMConstruction::print_info(), libMesh::RBConstruction::print_info(), libMesh::TimeSolver::reinit(), libMesh::PetscDiffSolver::setup_petsc_data(), libMesh::FrequencySystem::solve(), libMesh::RBConstruction::truth_solve(), libMesh::System::user_assembly(), libMesh::System::user_constrain(), libMesh::System::user_initialization(), libMesh::System::user_QOI(), libMesh::System::user_QOI_derivative(), libMesh::System::variable_number(), libMesh::System::write_header(), libMesh::System::write_parallel_data(), and libMesh::System::write_serialized_data().

{
  return _sys_name;
}

nonlocal_constraint()

virtual bool libMesh::DifferentiablePhysics::nonlocal_constraint ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds any nonlocal constraint contributions (e.g.

some components of constraints in scalar variable equations) to elem_residual

If this method receives request_jacobian = true, then it should also modify elem_jacobian and return true if possible. If the Jacobian changes have not been computed then the method should return false.

Users may need to reimplement this for PDEs on systems to which SCALAR variables with non-transient equations have been added.

Definition at line 233 of file diff_physics.h.

Referenced by libMesh::EulerSolver::nonlocal_residual(), libMesh::SteadySolver::nonlocal_residual(), libMesh::Euler2Solver::nonlocal_residual(), libMesh::EigenTimeSolver::nonlocal_residual(), and libMesh::NewmarkSolver::nonlocal_residual().

  {
    return request_jacobian;
  }

nonlocal_damping_residual()

virtual bool libMesh::DifferentiablePhysics::nonlocal_damping_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Subtracts any nonlocal damping vector contributions (e.g.

any first time derivative coefficients in scalar variable equations) from elem_residual

If this method receives request_jacobian = true, then it should also modify elem_jacobian and return true if possible. If the Jacobian changes have not been computed then the method should return false.

Definition at line 394 of file diff_physics.h.

Referenced by libMesh::EulerSolver::nonlocal_residual(), libMesh::Euler2Solver::nonlocal_residual(), and libMesh::NewmarkSolver::nonlocal_residual().

  {
    return request_jacobian;
  }

nonlocal_mass_residual()

bool libMesh::DifferentiablePhysics::nonlocal_mass_residual ( bool  request_jacobian, DiffContext &  c  )

virtualinherited

Subtracts any nonlocal mass vector contributions (e.g.

any time derivative coefficients in scalar variable equations) from elem_residual

If this method receives request_jacobian = true, then it should also modify elem_jacobian and return true if possible. If the Jacobian changes have not been computed then the method should return false.

Many problems can use the reimplementation in FEMPhysics::mass_residual which subtracts (du/dt,v) for each transient scalar variable u; users with more complicated transient scalar variable equations will need to reimplement this themselves.

Definition at line 57 of file diff_physics.C.

References libMesh::DiffContext::elem_solution_rate_derivative, libMesh::FEType::family, libMesh::DiffContext::get_dof_indices(), libMesh::DiffContext::get_elem_jacobian(), libMesh::DiffContext::get_elem_residual(), libMesh::DiffContext::get_elem_solution(), libMesh::DiffContext::get_system(), libMesh::DifferentiablePhysics::is_time_evolving(), libMesh::make_range(), libMesh::DiffContext::n_vars(), libMesh::SCALAR, libMesh::Variable::type(), and libMesh::System::variable().

Referenced by libMesh::EulerSolver::nonlocal_residual(), libMesh::Euler2Solver::nonlocal_residual(), libMesh::EigenTimeSolver::nonlocal_residual(), and libMesh::NewmarkSolver::nonlocal_residual().

{
  FEMContext & context = cast_ref<FEMContext &>(c);

  for (auto var : make_range(context.n_vars()))
    {
      if (!this->is_time_evolving(var))
        continue;

      if (c.get_system().variable(var).type().family != SCALAR)
        continue;

      const std::vector<dof_id_type> & dof_indices =
        context.get_dof_indices(var);

      const unsigned int n_dofs = cast_int<unsigned int>
        (dof_indices.size());

      DenseSubVector<Number> & Fs = context.get_elem_residual(var);
      DenseSubMatrix<Number> & Kss = context.get_elem_jacobian( var, var );

      const libMesh::DenseSubVector<libMesh::Number> & Us =
        context.get_elem_solution(var);

      for (unsigned int i=0; i != n_dofs; ++i)
        {
          Fs(i) -= Us(i);

          if (request_jacobian)
            Kss(i,i) -= context.elem_solution_rate_derivative;
        }
    }

  return request_jacobian;
}

nonlocal_time_derivative()

virtual bool libMesh::DifferentiablePhysics::nonlocal_time_derivative ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds any nonlocal time derivative contributions (e.g.

some components of time derivatives in scalar variable equations) to elem_residual

If this method receives request_jacobian = true, then it should also modify elem_jacobian and return true if possible. If the Jacobian changes have not been computed then the method should return false.

Users may need to reimplement this for PDEs on systems to which SCALAR variables have been added.

Definition at line 214 of file diff_physics.h.

Referenced by libMesh::EulerSolver::nonlocal_residual(), libMesh::SteadySolver::nonlocal_residual(), libMesh::Euler2Solver::nonlocal_residual(), libMesh::EigenTimeSolver::nonlocal_residual(), and libMesh::NewmarkSolver::nonlocal_residual().

  {
    return request_jacobian;
  }

number()

unsigned int libMesh::System::number ( ) const

inlineinherited

Returns

The system number.

Definition at line 2350 of file system.h.

References libMesh::System::_sys_number.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::PetscDMWrapper::add_dofs_helper(), assemble_matrix_and_rhs(), assemble_shell(), libMesh::VariationalSmootherSystem::assembly(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::Nemesis_IO::copy_nodal_solution(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::EquationSystems::find_variable_numbers(), libMesh::VariationalSmootherConstraint::fix_node(), libMesh::System::get_info(), libMesh::VariationalSmootherSystem::init_data(), main(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SortAndCopy::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectVertices::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectEdges::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectSides::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectInteriors::operator()(), libMesh::System::read_legacy_data(), libMesh::System::read_parallel_data(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::StaticCondensationDofMap::reinit(), LinearElasticityWithContact::residual_and_jacobian(), SolidSystem::save_initial_mesh(), libMesh::HPCoarsenTest::select_refinement(), libMesh::PetscDMWrapper::set_point_range_in_section(), MeshInputTest::testCopyElementVectorImpl(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::MeshfreeSolutionTransfer::transfer(), libMesh::BoundaryVolumeSolutionTransfer::transfer_boundary_volume(), libMesh::BoundaryVolumeSolutionTransfer::transfer_volume_boundary(), libMesh::DTKAdapter::update_variable_values(), libMesh::System::write_parallel_data(), libMesh::System::write_serialized_blocked_dof_objects(), and libMesh::System::zero_variable().

{
  return _sys_number;
}

numerical_elem_jacobian()

void FEMSystem::numerical_elem_jacobian ( FEMContext &  context ) const

inherited

Uses the results of multiple element_residual() calls to numerically differentiate the corresponding jacobian on an element.

Definition at line 1322 of file fem_system.C.

References libMesh::TimeSolver::element_residual(), and libMesh::FEMSystem::numerical_jacobian().

{
  LOG_SCOPE("numerical_elem_jacobian()", "FEMSystem");
  this->numerical_jacobian(&TimeSolver::element_residual, context);
}

numerical_jacobian()

void FEMSystem::numerical_jacobian ( TimeSolverResPtr  res, FEMContext &  context  ) const

inherited

Uses the results of multiple res calls to numerically differentiate the corresponding jacobian.

Definition at line 1210 of file fem_system.C.

References libMesh::DifferentiablePhysics::_mesh_sys, libMesh::DifferentiablePhysics::_mesh_x_var, libMesh::DifferentiablePhysics::_mesh_y_var, libMesh::DifferentiablePhysics::_mesh_z_var, libMesh::DiffContext::get_dof_indices(), libMesh::FEMContext::get_elem(), libMesh::DiffContext::get_elem_jacobian(), libMesh::DiffContext::get_elem_residual(), libMesh::DiffContext::get_elem_solution(), libMesh::Elem::hmin(), libMesh::invalid_uint, libMesh::libmesh_real(), libMesh::make_range(), libMesh::System::n_dofs(), libMesh::DiffContext::n_vars(), libMesh::FEMSystem::numerical_jacobian_h, libMesh::FEMSystem::numerical_jacobian_h_for_var(), libMesh::Elem::point(), libMesh::Real, and libMesh::DenseVector< T >::zero().

Referenced by libMesh::FEMSystem::numerical_elem_jacobian(), libMesh::FEMSystem::numerical_nonlocal_jacobian(), and libMesh::FEMSystem::numerical_side_jacobian().

{
  // Logging is done by numerical_elem_jacobian
  // or numerical_side_jacobian

  DenseVector<Number> original_residual(context.get_elem_residual());
  DenseVector<Number> backwards_residual(context.get_elem_residual());
  DenseMatrix<Number> numeric_jacobian(context.get_elem_jacobian());
#ifdef DEBUG
  DenseMatrix<Number> old_jacobian(context.get_elem_jacobian());
#endif

  Real numerical_point_h = 0.;
  if (_mesh_sys == this)
    numerical_point_h = numerical_jacobian_h * context.get_elem().hmin();

  const unsigned int n_dofs =
    cast_int<unsigned int>(context.get_dof_indices().size());

  for (auto v : make_range(context.n_vars()))
    {
      const Real my_h = this->numerical_jacobian_h_for_var(v);

      unsigned int j_offset = libMesh::invalid_uint;

      if (!context.get_dof_indices(v).empty())
        {
          for (auto i : make_range(n_dofs))
            if (context.get_dof_indices()[i] ==
                context.get_dof_indices(v)[0])
              j_offset = i;

          libmesh_assert_not_equal_to(j_offset, libMesh::invalid_uint);
        }

      for (auto j : make_range(context.get_dof_indices(v).size()))
        {
          const unsigned int total_j = j + j_offset;

          // Take the "minus" side of a central differenced first derivative
          Number original_solution = context.get_elem_solution(v)(j);
          context.get_elem_solution(v)(j) -= my_h;

          // Make sure to catch any moving mesh terms
          Real * coord = nullptr;
          if (_mesh_sys == this)
            {
              if (_mesh_x_var == v)
                coord = &(context.get_elem().point(j)(0));
              else if (_mesh_y_var == v)
                coord = &(context.get_elem().point(j)(1));
              else if (_mesh_z_var == v)
                coord = &(context.get_elem().point(j)(2));
            }
          if (coord)
            {
              // We have enough information to scale the perturbations
              // here appropriately
              context.get_elem_solution(v)(j) = original_solution - numerical_point_h;
              *coord = libmesh_real(context.get_elem_solution(v)(j));
            }

          context.get_elem_residual().zero();
          ((*time_solver).*(res))(false, context);
#ifdef DEBUG
          libmesh_assert_equal_to (old_jacobian, context.get_elem_jacobian());
#endif
          backwards_residual = context.get_elem_residual();

          // Take the "plus" side of a central differenced first derivative
          context.get_elem_solution(v)(j) = original_solution + my_h;
          if (coord)
            {
              context.get_elem_solution()(j) = original_solution + numerical_point_h;
              *coord = libmesh_real(context.get_elem_solution(v)(j));
            }
          context.get_elem_residual().zero();
          ((*time_solver).*(res))(false, context);
#ifdef DEBUG
          libmesh_assert_equal_to (old_jacobian, context.get_elem_jacobian());
#endif

          context.get_elem_solution(v)(j) = original_solution;
          if (coord)
            {
              *coord = libmesh_real(context.get_elem_solution(v)(j));
              for (auto i : make_range(n_dofs))
                {
                  numeric_jacobian(i,total_j) =
                    (context.get_elem_residual()(i) - backwards_residual(i)) /
                    2. / numerical_point_h;
                }
            }
          else
            {
              for (auto i : make_range(n_dofs))
                {
                  numeric_jacobian(i,total_j) =
                    (context.get_elem_residual()(i) - backwards_residual(i)) /
                    2. / my_h;
                }
            }
        }
    }

  context.get_elem_residual() = original_residual;
  context.get_elem_jacobian() = numeric_jacobian;
}

numerical_jacobian_h_for_var()

Real FEMSystem::numerical_jacobian_h_for_var ( unsigned int  var_num ) const

inlineinherited

If numerical_jacobian_h_for_var(var_num) is changed from its default value (numerical_jacobian_h), the FEMSystem will perturb solution vector entries for variable var_num by that amount when calculating finite differences with respect to that variable.

This is useful in multiphysics problems which have not been normalized.

Definition at line 265 of file fem_system.h.

References libMesh::FEMSystem::_numerical_jacobian_h_for_var, libMesh::FEMSystem::numerical_jacobian_h, and libMesh::Real.

Referenced by libMesh::FEMSystem::numerical_jacobian().

{
  if ((var_num >= _numerical_jacobian_h_for_var.size()) ||
      _numerical_jacobian_h_for_var[var_num] == Real(0))
    return numerical_jacobian_h;

  return _numerical_jacobian_h_for_var[var_num];
}

numerical_nonlocal_jacobian()

void FEMSystem::numerical_nonlocal_jacobian ( FEMContext &  context ) const

inherited

Uses the results of multiple side_residual() calls to numerically differentiate the corresponding jacobian on nonlocal DoFs.

Definition at line 1338 of file fem_system.C.

References libMesh::TimeSolver::nonlocal_residual(), and libMesh::FEMSystem::numerical_jacobian().

Referenced by libMesh::FEMSystem::assembly().

{
  LOG_SCOPE("numerical_nonlocal_jacobian()", "FEMSystem");
  this->numerical_jacobian(&TimeSolver::nonlocal_residual, context);
}

numerical_side_jacobian()

void FEMSystem::numerical_side_jacobian ( FEMContext &  context ) const

inherited

Uses the results of multiple side_residual() calls to numerically differentiate the corresponding jacobian on an element's side.

Definition at line 1330 of file fem_system.C.

References libMesh::FEMSystem::numerical_jacobian(), and libMesh::TimeSolver::side_residual().

{
  LOG_SCOPE("numerical_side_jacobian()", "FEMSystem");
  this->numerical_jacobian(&TimeSolver::side_residual, context);
}

operator=() [1/2]

ContinuationSystem& libMesh::ContinuationSystem::operator= ( const ContinuationSystem &  )

delete

operator=() [2/2]

ContinuationSystem& libMesh::ContinuationSystem::operator= ( ContinuationSystem &&  )

delete

parallel_op()

void libMesh::DifferentiableQoI::parallel_op ( const Parallel::Communicator &  communicator, std::vector< Number > &  sys_qoi, std::vector< Number > &  local_qoi, const QoISet &  qoi_indices  )

virtualinherited

Method to populate system qoi data structure with process-local qoi.

By default, simply sums process qois into system qoi.

Definition at line 41 of file diff_qoi.C.

References communicator.

Referenced by libMesh::FEMSystem::assemble_qoi().

{
  // Sum everything into local_qoi
  communicator.sum(local_qoi);

  // Now put into system qoi
  sys_qoi = local_qoi;
}

point_gradient() [1/4]

Gradient libMesh::System::point_gradient ( unsigned int  var, const Point &  p, const bool  insist_on_success = true, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The gradient of the solution variable var at the physical point p in the mesh, similarly to point_value.

Definition at line 2550 of file system.C.

References libMesh::Variable::active_subdomains(), TIMPI::Communicator::broadcast(), libMesh::ParallelObject::comm(), libMesh::PointLocatorBase::enable_out_of_mesh_mode(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::libmesh_assert(), mesh, TIMPI::Communicator::min(), libMesh::ParallelObject::n_processors(), libMesh::ParallelObject::processor_id(), libMesh::DofObject::processor_id(), and libMesh::System::variable().

Referenced by line_print(), and libMesh::System::point_gradient().

{
  // This function must be called on every processor; there's no
  // telling where in the partition p falls.
  parallel_object_only();

  // And every processor had better agree about which point we're
  // looking for
#ifndef NDEBUG
  libmesh_assert(this->comm().verify(p(0)));
#if LIBMESH_DIM > 1
  libmesh_assert(this->comm().verify(p(1)));
#endif
#if LIBMESH_DIM > 2
  libmesh_assert(this->comm().verify(p(2)));
#endif
#endif // NDEBUG

  // Get a reference to the mesh object associated with the system object that calls this function
  const MeshBase & mesh = this->get_mesh();

  // Use an existing PointLocator or create a new one
  std::unique_ptr<PointLocatorBase> locator_ptr = mesh.sub_point_locator();
  PointLocatorBase & locator = *locator_ptr;

  if (!insist_on_success || !mesh.is_serial())
    locator.enable_out_of_mesh_mode();

  // Get a pointer to an element that contains p and allows us to
  // evaluate var
  const std::set<subdomain_id_type> & raw_subdomains =
    this->variable(var).active_subdomains();
  const std::set<subdomain_id_type> * implicit_subdomains =
    raw_subdomains.empty() ? nullptr : &raw_subdomains;
  const Elem * e = locator(p, implicit_subdomains);

  Gradient grad_u;

  if (e && this->get_dof_map().is_evaluable(*e, var))
    grad_u = point_gradient(var, p, *e, sol);

  // If I have an element containing p, then let's let everyone know
  processor_id_type lowest_owner =
    (e && (e->processor_id() == this->processor_id())) ?
    this->processor_id() : this->n_processors();
  this->comm().min(lowest_owner);

  // Everybody should get their value from a processor that was able
  // to compute it.
  // If nobody admits owning the point, we may have a problem.
  if (lowest_owner != this->n_processors())
    this->comm().broadcast(grad_u, lowest_owner);
  else
    libmesh_assert(!insist_on_success);

  return grad_u;
}

point_gradient() [2/4]

Gradient libMesh::System::point_gradient ( unsigned int  var, const Point &  p, const Elem &  e, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The gradient of the solution variable var at the physical point p in local Elem e in the mesh, similarly to point_value.

Definition at line 2612 of file system.C.

References libMesh::FEInterface::compute_data(), libMesh::Elem::contains_point(), libMesh::System::current_local_solution, dim, libMesh::Elem::dim(), libMesh::DofMap::dof_indices(), libMesh::FEComputeData::dshape, libMesh::FEComputeData::enable_derivative(), libMesh::System::get_dof_map(), libMesh::System::get_equation_systems(), libMesh::FEMap::inverse_map(), libMesh::DofMap::is_evaluable(), libMesh::libmesh_assert(), libMesh::FEComputeData::local_transform, and libMesh::DofMap::variable_type().

{
  // Ensuring that the given point is really in the element is an
  // expensive assert, but as long as debugging is turned on we might
  // as well try to catch a particularly nasty potential error
  libmesh_assert (e.contains_point(p));

  if (!sol)
    sol = this->current_local_solution.get();

  // Get the dof map to get the proper indices for our computation
  const DofMap & dof_map = this->get_dof_map();

  // write the element dimension into a separate variable.
  const unsigned int dim = e.dim();

  // Make sure we can evaluate on this element.
  libmesh_assert (dof_map.is_evaluable(e, var));

  // Need dof_indices for phi[i][j]
  std::vector<dof_id_type> dof_indices;

  // Fill in the dof_indices for our element
  dof_map.dof_indices (&e, dof_indices, var);

  // Get the no of dofs associated with this point
  const unsigned int num_dofs = cast_int<unsigned int>
    (dof_indices.size());

  FEType fe_type = dof_map.variable_type(var);

  // Map the physical co-ordinates to the master co-ordinates
  Point coor = FEMap::inverse_map(dim, &e, p);

  // get the shape function value via the FEInterface to also handle the case
  // of infinite elements correctly, the shape function is not fe->phi().
  FEComputeData fe_data(this->get_equation_systems(), coor);
  fe_data.enable_derivative();
  FEInterface::compute_data(dim, fe_type, &e, fe_data);

  // Get ready to accumulate a gradient
  Gradient grad_u;

  for (unsigned int l=0; l<num_dofs; l++)
    {
      // Chartesian coordinates have always LIBMESH_DIM entries,
      // local coordinates have as many coordinates as the element has.
      for (std::size_t v=0; v<dim; v++)
        for (std::size_t xyz=0; xyz<LIBMESH_DIM; xyz++)
          {
            // FIXME: this needs better syntax: It is matrix-vector multiplication.
            grad_u(xyz) += fe_data.local_transform[v][xyz]
              * fe_data.dshape[l](v)
              * (*sol)(dof_indices[l]);
          }
    }

  return grad_u;
}

point_gradient() [3/4]

Gradient libMesh::System::point_gradient ( unsigned int  var, const Point &  p, const Elem *  e  ) const

inherited

Calls the version of point_gradient() which takes a reference.

This function exists only to prevent people from calling the version of point_gradient() that has a boolean third argument, which would result in unnecessary PointLocator calls.

Definition at line 2677 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::point_gradient().

{
  libmesh_assert(e);
  return this->point_gradient(var, p, *e);
}

point_gradient() [4/4]

Gradient libMesh::System::point_gradient ( unsigned int  var, const Point &  p, const NumericVector< Number > *  sol  ) const

inherited

Calls the parallel version of point_gradient().

This function exists only to prevent people from accidentally calling the version of point_gradient() that has a boolean third argument, which would result in incorrect output.

Definition at line 2685 of file system.C.

References libMesh::System::point_gradient().

{
  return this->point_gradient(var, p, true, sol);
}

point_hessian() [1/4]

Tensor libMesh::System::point_hessian ( unsigned int  var, const Point &  p, const bool  insist_on_success = true, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The second derivative tensor of the solution variable var at the physical point p in the mesh, similarly to point_value.

Definition at line 2694 of file system.C.

References libMesh::Variable::active_subdomains(), TIMPI::Communicator::broadcast(), libMesh::ParallelObject::comm(), libMesh::PointLocatorBase::enable_out_of_mesh_mode(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::libmesh_assert(), mesh, TIMPI::Communicator::min(), libMesh::ParallelObject::n_processors(), libMesh::ParallelObject::processor_id(), libMesh::DofObject::processor_id(), and libMesh::System::variable().

Referenced by libMesh::System::point_hessian().

{
  // This function must be called on every processor; there's no
  // telling where in the partition p falls.
  parallel_object_only();

  // And every processor had better agree about which point we're
  // looking for
#ifndef NDEBUG
  libmesh_assert(this->comm().verify(p(0)));
#if LIBMESH_DIM > 1
  libmesh_assert(this->comm().verify(p(1)));
#endif
#if LIBMESH_DIM > 2
  libmesh_assert(this->comm().verify(p(2)));
#endif
#endif // NDEBUG

  // Get a reference to the mesh object associated with the system object that calls this function
  const MeshBase & mesh = this->get_mesh();

  // Use an existing PointLocator or create a new one
  std::unique_ptr<PointLocatorBase> locator_ptr = mesh.sub_point_locator();
  PointLocatorBase & locator = *locator_ptr;

  if (!insist_on_success || !mesh.is_serial())
    locator.enable_out_of_mesh_mode();

  // Get a pointer to an element that contains p and allows us to
  // evaluate var
  const std::set<subdomain_id_type> & raw_subdomains =
    this->variable(var).active_subdomains();
  const std::set<subdomain_id_type> * implicit_subdomains =
    raw_subdomains.empty() ? nullptr : &raw_subdomains;
  const Elem * e = locator(p, implicit_subdomains);

  Tensor hess_u;

  if (e && this->get_dof_map().is_evaluable(*e, var))
    hess_u = point_hessian(var, p, *e, sol);

  // If I have an element containing p, then let's let everyone know
  processor_id_type lowest_owner =
    (e && (e->processor_id() == this->processor_id())) ?
    this->processor_id() : this->n_processors();
  this->comm().min(lowest_owner);

  // Everybody should get their value from a processor that was able
  // to compute it.
  // If nobody admits owning the point, we may have a problem.
  if (lowest_owner != this->n_processors())
    this->comm().broadcast(hess_u, lowest_owner);
  else
    libmesh_assert(!insist_on_success);

  return hess_u;
}

point_hessian() [2/4]

Tensor libMesh::System::point_hessian ( unsigned int  var, const Point &  p, const Elem &  e, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The second derivative tensor of the solution variable var at the physical point p in local Elem e in the mesh, similarly to point_value.

Definition at line 2755 of file system.C.

References libMesh::TypeTensor< T >::add_scaled(), libMesh::FEGenericBase< OutputType >::build(), libMesh::Elem::contains_point(), libMesh::System::current_local_solution, libMesh::Elem::dim(), libMesh::DofMap::dof_indices(), libMesh::System::get_dof_map(), libMesh::Elem::infinite(), libMesh::FEMap::inverse_map(), libMesh::DofMap::is_evaluable(), libMesh::libmesh_assert(), and libMesh::DofMap::variable_type().

{
  // Ensuring that the given point is really in the element is an
  // expensive assert, but as long as debugging is turned on we might
  // as well try to catch a particularly nasty potential error
  libmesh_assert (e.contains_point(p));

  if (!sol)
    sol = this->current_local_solution.get();

  if (e.infinite())
    libmesh_not_implemented();

  // Get the dof map to get the proper indices for our computation
  const DofMap & dof_map = this->get_dof_map();

  // Make sure we can evaluate on this element.
  libmesh_assert (dof_map.is_evaluable(e, var));

  // Need dof_indices for phi[i][j]
  std::vector<dof_id_type> dof_indices;

  // Fill in the dof_indices for our element
  dof_map.dof_indices (&e, dof_indices, var);

  // Get the no of dofs associated with this point
  const unsigned int num_dofs = cast_int<unsigned int>
    (dof_indices.size());

  FEType fe_type = dof_map.variable_type(var);

  // Build a FE again so we can calculate u(p)
  std::unique_ptr<FEBase> fe (FEBase::build(e.dim(), fe_type));

  // Map the physical co-ordinates to the master co-ordinates
  // Build a vector of point co-ordinates to send to reinit
  std::vector<Point> coor(1, FEMap::inverse_map(e.dim(), &e, p));

  // Get the values of the shape function derivatives
  const std::vector<std::vector<RealTensor>> &  d2phi = fe->get_d2phi();

  // Reinitialize the element and compute the shape function values at coor
  fe->reinit (&e, &coor);

  // Get ready to accumulate a hessian
  Tensor hess_u;

  for (unsigned int l=0; l<num_dofs; l++)
    {
      hess_u.add_scaled (d2phi[l][0], (*sol)(dof_indices[l]));
    }

  return hess_u;
}

point_hessian() [3/4]

Tensor libMesh::System::point_hessian ( unsigned int  var, const Point &  p, const Elem *  e  ) const

inherited

Calls the version of point_hessian() which takes a reference.

This function exists only to prevent people from calling the version of point_hessian() that has a boolean third argument, which would result in unnecessary PointLocator calls.

Definition at line 2815 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::point_hessian().

{
  libmesh_assert(e);
  return this->point_hessian(var, p, *e);
}

point_hessian() [4/4]

Tensor libMesh::System::point_hessian ( unsigned int  var, const Point &  p, const NumericVector< Number > *  sol  ) const

inherited

Calls the parallel version of point_hessian().

This function exists only to prevent people from accidentally calling the version of point_hessian() that has a boolean third argument, which would result in incorrect output.

Definition at line 2823 of file system.C.

References libMesh::System::point_hessian().

{
  return this->point_hessian(var, p, true, sol);
}

point_value() [1/4]

Number libMesh::System::point_value ( unsigned int  var, const Point &  p, const bool  insist_on_success = true, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The value of the solution variable var at the physical point p in the mesh, without knowing a priori which element contains p, using the degree of freedom coefficients in sol (or in current_local_solution if sol is left null).

Note

This function uses MeshBase::sub_point_locator(); users may or may not want to call MeshBase::clear_point_locator() afterward. Also, point_locator() is expensive (N log N for initial construction, log N for evaluations). Avoid using this function in any context where you are already looping over elements.

Because the element containing p may lie on any processor, this function is parallel-only.

By default this method expects the point to reside inside the domain and will abort if no element can be found which contains p. The optional parameter insist_on_success can be set to false to allow the method to return 0 when the point is not located.

Definition at line 2421 of file system.C.

References libMesh::Variable::active_subdomains(), TIMPI::Communicator::broadcast(), libMesh::ParallelObject::comm(), libMesh::PointLocatorBase::enable_out_of_mesh_mode(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::libmesh_assert(), mesh, TIMPI::Communicator::min(), libMesh::ParallelObject::n_processors(), libMesh::ParallelObject::processor_id(), libMesh::DofObject::processor_id(), and libMesh::System::variable().

Referenced by line_print(), main(), libMesh::System::point_value(), MeshInputTest::testCopyElementSolutionImpl(), MeshInputTest::testCopyElementVectorImpl(), MeshInputTest::testCopyNodalSolutionImpl(), DefaultCouplingTest::testCoupling(), PointNeighborCouplingTest::testCoupling(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), PeriodicBCTest::testPeriodicBC(), SystemsTest::testProjectCubeWithMeshFunction(), and EquationSystemsTest::testRepartitionThenReinit().

{
  // This function must be called on every processor; there's no
  // telling where in the partition p falls.
  parallel_object_only();

  // And every processor had better agree about which point we're
  // looking for
#ifndef NDEBUG
  libmesh_assert(this->comm().verify(p(0)));
#if LIBMESH_DIM > 1
  libmesh_assert(this->comm().verify(p(1)));
#endif
#if LIBMESH_DIM > 2
  libmesh_assert(this->comm().verify(p(2)));
#endif
#endif // NDEBUG

  // Get a reference to the mesh object associated with the system object that calls this function
  const MeshBase & mesh = this->get_mesh();

  // Use an existing PointLocator or create a new one
  std::unique_ptr<PointLocatorBase> locator_ptr = mesh.sub_point_locator();
  PointLocatorBase & locator = *locator_ptr;

  if (!insist_on_success || !mesh.is_serial())
    locator.enable_out_of_mesh_mode();

  // Get a pointer to an element that contains p and allows us to
  // evaluate var
  const std::set<subdomain_id_type> & raw_subdomains =
    this->variable(var).active_subdomains();
  const std::set<subdomain_id_type> * implicit_subdomains =
    raw_subdomains.empty() ? nullptr : &raw_subdomains;
  const Elem * e = locator(p, implicit_subdomains);

  Number u = 0;

  if (e && this->get_dof_map().is_evaluable(*e, var))
    u = point_value(var, p, *e, sol);

  // If I have an element containing p, then let's let everyone know
  processor_id_type lowest_owner =
    (e && (e->processor_id() == this->processor_id())) ?
    this->processor_id() : this->n_processors();
  this->comm().min(lowest_owner);

  // Everybody should get their value from a processor that was able
  // to compute it.
  // If nobody admits owning the point, we have a problem.
  if (lowest_owner != this->n_processors())
    this->comm().broadcast(u, lowest_owner);
  else
    libmesh_assert(!insist_on_success);

  return u;
}

point_value() [2/4]

Number libMesh::System::point_value ( unsigned int  var, const Point &  p, const Elem &  e, const NumericVector< Number > *  sol = nullptr  ) const

inherited

Returns

The value of the solution variable var at the physical point p contained in local Elem e, using the degree of freedom coefficients in sol (or in current_local_solution if sol is left null).

This version of point_value can be run in serial, but assumes e is in the local mesh partition or is algebraically ghosted.

Definition at line 2482 of file system.C.

References libMesh::FEInterface::compute_data(), libMesh::Elem::contains_point(), libMesh::System::current_local_solution, libMesh::Elem::dim(), libMesh::DofMap::dof_indices(), libMesh::System::get_dof_map(), libMesh::System::get_equation_systems(), libMesh::FEMap::inverse_map(), libMesh::DofMap::is_evaluable(), libMesh::libmesh_assert(), and libMesh::DofMap::variable_type().

{
  // Ensuring that the given point is really in the element is an
  // expensive assert, but as long as debugging is turned on we might
  // as well try to catch a particularly nasty potential error
  libmesh_assert (e.contains_point(p));

  if (!sol)
    sol = this->current_local_solution.get();

  // Get the dof map to get the proper indices for our computation
  const DofMap & dof_map = this->get_dof_map();

  // Make sure we can evaluate on this element.
  libmesh_assert (dof_map.is_evaluable(e, var));

  // Need dof_indices for phi[i][j]
  std::vector<dof_id_type> dof_indices;

  // Fill in the dof_indices for our element
  dof_map.dof_indices (&e, dof_indices, var);

  // Get the no of dofs associated with this point
  const unsigned int num_dofs = cast_int<unsigned int>
    (dof_indices.size());

  FEType fe_type = dof_map.variable_type(var);

  // Map the physical co-ordinates to the master co-ordinates
  Point coor = FEMap::inverse_map(e.dim(), &e, p);

  // get the shape function value via the FEInterface to also handle the case
  // of infinite elements correctly, the shape function is not fe->phi().
  FEComputeData fe_data(this->get_equation_systems(), coor);
  FEInterface::compute_data(e.dim(), fe_type, &e, fe_data);

  // Get ready to accumulate a value
  Number u = 0;

  for (unsigned int l=0; l<num_dofs; l++)
    {
      u += fe_data.shape[l] * (*sol)(dof_indices[l]);
    }

  return u;
}

point_value() [3/4]

Number libMesh::System::point_value ( unsigned int  var, const Point &  p, const Elem *  e  ) const

inherited

Calls the version of point_value() which takes a reference.

This function exists only to prevent people from calling the version of point_value() that has a boolean third argument, which would result in unnecessary PointLocator calls.

Definition at line 2534 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::point_value().

{
  libmesh_assert(e);
  return this->point_value(var, p, *e);
}

point_value() [4/4]

Number libMesh::System::point_value ( unsigned int  var, const Point &  p, const NumericVector< Number > *  sol  ) const

inherited

Calls the parallel version of point_value().

This function exists only to prevent people from accidentally calling the version of point_value() that has a boolean third argument, which would result in incorrect output.

Definition at line 2542 of file system.C.

References libMesh::System::point_value().

{
  return this->point_value(var, p, true, sol);
}

pop_physics()

void libMesh::DifferentiableSystem::pop_physics ( )

inherited

Pop a physics object off of our stack.

Definition at line 411 of file diff_system.C.

References libMesh::DifferentiableSystem::_diff_physics, libMesh::ImplicitSystem::disable_cache(), and libMesh::libmesh_assert().

Referenced by main().

{
  libmesh_assert(!this->_diff_physics.empty());

  this->_diff_physics.pop();

  // If the physics has been changed, we will reassemble
  // the matrix from scratch before doing an adjoint solve
  // rather than just transposing
  this->disable_cache();
}

postprocess()

void FEMSystem::postprocess ( void  )

overridevirtualinherited

Runs a postprocessing loop over all elements, and if postprocess_sides is true over all sides.

Reimplemented from libMesh::DifferentiableSystem.

Reimplemented in CoupledSystem, NavierSystem, LaplaceSystem, LaplaceSystem, and PoissonSystem.

Definition at line 1127 of file fem_system.C.

References libMesh::System::get_mesh(), libMesh::DifferentiableSystem::get_time_solver(), mesh, libMesh::Threads::parallel_for(), libMesh::StoredRange< iterator_type, object_type >::reset(), libMesh::TimeSolver::set_is_adjoint(), and libMesh::System::update().

Referenced by main(), PoissonSystem::postprocess(), and LaplaceSystem::postprocess().

{
  LOG_SCOPE("postprocess()", "FEMSystem");

  const MeshBase & mesh = this->get_mesh();

  this->update();

  // Get the time solver object associated with the system, and tell it that
  // we are not solving the adjoint problem
  this->get_time_solver().set_is_adjoint(false);

  // Loop over every active mesh element on this processor
  Threads::parallel_for (elem_range.reset(mesh.active_local_elements_begin(),
                                          mesh.active_local_elements_end()),
                         PostprocessContributions(*this));
}

prefer_hash_table_matrix_assembly()

void libMesh::System::prefer_hash_table_matrix_assembly ( bool  preference )

inlineinherited

Sets whether to use hash table matrix assembly if the matrix sub-classes support it.

Definition at line 2728 of file system.h.

References libMesh::System::_matrices_initialized, and libMesh::System::_prefer_hash_table_matrix_assembly.

Referenced by main().

{
  libmesh_error_msg_if(
      _matrices_initialized,
      "System::prefer_hash_table_matrix_assembly() should be called before matrices are initialized");
  _prefer_hash_table_matrix_assembly = preference;
}

prefix()

std::string libMesh::System::prefix ( ) const

inlineinherited

Returns

A prefix that may be applied to solver options. Note that this prefix is only used if prefix_with_name()

Definition at line 1938 of file system.h.

References libMesh::System::name().

Referenced by libMesh::ImplicitSystem::get_linear_solver(), libMesh::LinearImplicitSystem::solve(), and libMesh::NonlinearImplicitSystem::solve().

{ return this->name() + "_"; }

prefix_with_name() [1/2]

void libMesh::System::prefix_with_name ( bool  value )

inlineinherited

Instructs this system to prefix solve options with its name for solvers that leverage prefixes.

Definition at line 1927 of file system.h.

References libMesh::System::_prefix_with_name, and value.

{ _prefix_with_name = value; }

prefix_with_name() [2/2]

bool libMesh::System::prefix_with_name ( ) const

inlineinherited

Returns

Whether we are name prefixing

Definition at line 1932 of file system.h.

References libMesh::System::_prefix_with_name.

Referenced by ContinuationSystem(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::LinearImplicitSystem::solve(), libMesh::NonlinearImplicitSystem::solve(), and libMesh::System::System().

{ return _prefix_with_name; }

print_info()

void libMesh::ReferenceCounter::print_info ( std::ostream &  out_stream = libMesh::out )

staticinherited

Prints the reference information, by default to libMesh::out.

Definition at line 81 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter, and libMesh::ReferenceCounter::get_info().

Referenced by libMesh::LibMeshInit::~LibMeshInit().

{
  if (_enable_print_counter)
    out_stream << ReferenceCounter::get_info();
}

processor_id()

processor_id_type libMesh::ParallelObject::processor_id ( ) const

inlineinherited

Returns

The rank of this processor in the group.

Definition at line 114 of file parallel_object.h.

References libMesh::ParallelObject::_communicator, and TIMPI::Communicator::rank().

Referenced by libMesh::BoundaryInfo::_find_id_maps(), libMesh::PetscDMWrapper::add_dofs_to_section(), libMesh::DistributedMesh::add_elem(), libMesh::BoundaryInfo::add_elements(), libMesh::DofMap::add_neighbors_to_send_list(), libMesh::DistributedMesh::add_node(), libMesh::MeshTools::Modification::all_tri(), libMesh::DofMap::allgather_recursive_constraints(), libMesh::FEMSystem::assembly(), libMesh::Nemesis_IO::assert_symmetric_cmaps(), libMesh::Partitioner::assign_partitioning(), libMesh::Nemesis_IO_Helper::build_element_and_node_maps(), libMesh::Partitioner::build_graph(), libMesh::InfElemBuilder::build_inf_elem(), libMesh::BoundaryInfo::build_node_list_from_side_list(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::MeshFunction::check_found_elem(), libMesh::DistributedMesh::clear(), libMesh::DistributedMesh::clear_elems(), libMesh::ExodusII_IO_Helper::close(), libMesh::Nemesis_IO_Helper::compute_border_node_ids(), libMesh::Nemesis_IO_Helper::compute_communication_map_parameters(), libMesh::Nemesis_IO_Helper::compute_internal_and_border_elems_and_internal_nodes(), libMesh::RBConstruction::compute_max_error_bound(), libMesh::Nemesis_IO_Helper::compute_node_communication_maps(), libMesh::Nemesis_IO_Helper::compute_num_global_elem_blocks(), libMesh::Nemesis_IO_Helper::compute_num_global_nodesets(), libMesh::Nemesis_IO_Helper::compute_num_global_sidesets(), libMesh::Nemesis_IO_Helper::construct_nemesis_filename(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), libMesh::MeshTools::correct_node_proc_ids(), libMesh::ExodusII_IO_Helper::create(), libMesh::DistributedMesh::delete_elem(), libMesh::MeshCommunication::delete_remote_elements(), libMesh::DofMap::distribute_dofs(), libMesh::DofMap::distribute_scalar_dofs(), libMesh::DistributedMesh::DistributedMesh(), libMesh::DofMapBase::end_dof(), libMesh::DofMapBase::end_old_dof(), libMesh::EnsightIO::EnsightIO(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::find_dofs_to_send(), libMesh::UnstructuredMesh::find_neighbors(), libMesh::DofMapBase::first_dof(), libMesh::DofMapBase::first_old_dof(), libMesh::RBEIMEvaluation::gather_bfs(), libMesh::Nemesis_IO_Helper::get_cmap_params(), libMesh::Nemesis_IO_Helper::get_eb_info_global(), libMesh::Nemesis_IO_Helper::get_elem_cmap(), libMesh::Nemesis_IO_Helper::get_elem_map(), libMesh::MeshBase::get_info(), libMesh::DofMap::get_info(), libMesh::Nemesis_IO_Helper::get_init_global(), libMesh::Nemesis_IO_Helper::get_init_info(), libMesh::RBEIMEvaluation::get_interior_basis_functions_as_vecs(), libMesh::Nemesis_IO_Helper::get_loadbal_param(), libMesh::DofMap::get_local_constraints(), libMesh::MeshBase::get_local_constraints(), libMesh::Nemesis_IO_Helper::get_node_cmap(), libMesh::Nemesis_IO_Helper::get_node_map(), libMesh::Nemesis_IO_Helper::get_ns_param_global(), libMesh::Nemesis_IO_Helper::get_ss_param_global(), libMesh::SparsityPattern::Build::handle_vi_vj(), libMesh::LaplaceMeshSmoother::init(), libMesh::SystemSubsetBySubdomain::init(), HeatSystem::init_data(), libMesh::ExodusII_IO_Helper::initialize(), libMesh::ExodusII_IO_Helper::initialize_element_variables(), libMesh::ExodusII_IO_Helper::initialize_global_variables(), libMesh::ExodusII_IO_Helper::initialize_nodal_variables(), libMesh::DistributedMesh::insert_elem(), libMesh::DofMap::is_evaluable(), libMesh::SparsityPattern::Build::join(), libMesh::TransientRBEvaluation::legacy_write_offline_data_to_files(), libMesh::RBSCMEvaluation::legacy_write_offline_data_to_files(), libMesh::RBEvaluation::legacy_write_offline_data_to_files(), libMesh::MeshTools::libmesh_assert_consistent_distributed(), libMesh::MeshTools::libmesh_assert_consistent_distributed_nodes(), libMesh::MeshTools::libmesh_assert_contiguous_dof_ids(), libMesh::MeshTools::libmesh_assert_parallel_consistent_procids< Elem >(), libMesh::MeshTools::libmesh_assert_valid_neighbors(), libMesh::DistributedMesh::libmesh_assert_valid_parallel_object_ids(), libMesh::DofMap::local_variable_indices(), main(), libMesh::MeshRefinement::make_coarsening_compatible(), AugmentSparsityOnInterface::mesh_reinit(), libMesh::TriangulatorInterface::MeshedHole::MeshedHole(), libMesh::MeshBase::n_active_local_elem(), libMesh::BoundaryInfo::n_boundary_conds(), libMesh::MeshTools::n_connected_components(), libMesh::MeshBase::n_constraint_rows(), libMesh::BoundaryInfo::n_edge_conds(), libMesh::DofMapBase::n_local_dofs(), libMesh::MeshBase::n_local_elem(), libMesh::MeshBase::n_local_nodes(), libMesh::BoundaryInfo::n_nodeset_conds(), libMesh::BoundaryInfo::n_shellface_conds(), libMesh::RBEIMEvaluation::node_gather_bfs(), libMesh::DistributedMesh::own_node(), libMesh::BoundaryInfo::parallel_sync_node_ids(), libMesh::BoundaryInfo::parallel_sync_side_ids(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::MeshBase::print_constraint_rows(), libMesh::DofMap::print_dof_constraints(), libMesh::DofMap::process_mesh_constraint_rows(), libMesh::Nemesis_IO_Helper::put_cmap_params(), libMesh::Nemesis_IO_Helper::put_elem_cmap(), libMesh::Nemesis_IO_Helper::put_elem_map(), libMesh::Nemesis_IO_Helper::put_loadbal_param(), libMesh::Nemesis_IO_Helper::put_node_cmap(), libMesh::Nemesis_IO_Helper::put_node_map(), libMesh::NameBasedIO::read(), libMesh::Nemesis_IO::read(), libMesh::XdrIO::read(), libMesh::CheckpointIO::read(), libMesh::EquationSystems::read(), libMesh::ExodusII_IO_Helper::read_elem_num_map(), libMesh::ExodusII_IO_Helper::read_global_values(), libMesh::ExodusII_IO::read_header(), libMesh::CheckpointIO::read_header(), libMesh::XdrIO::read_header(), libMesh::System::read_header(), libMesh::System::read_legacy_data(), libMesh::DynaIO::read_mesh(), libMesh::ExodusII_IO_Helper::read_node_num_map(), libMesh::System::read_parallel_data(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), libMesh::RBConstruction::read_riesz_representors_from_files(), libMesh::System::read_SCALAR_dofs(), libMesh::XdrIO::read_serialized_bc_names(), libMesh::XdrIO::read_serialized_bcs_helper(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::XdrIO::read_serialized_connectivity(), libMesh::System::read_serialized_data(), libMesh::XdrIO::read_serialized_nodes(), libMesh::XdrIO::read_serialized_nodesets(), libMesh::XdrIO::read_serialized_subdomain_names(), libMesh::System::read_serialized_vector(), libMesh::System::read_serialized_vectors(), libMesh::Nemesis_IO_Helper::read_var_names_impl(), libMesh::SimplexRefiner::refine_via_edges(), libMesh::StaticCondensationDofMap::reinit(), libMesh::DistributedMesh::renumber_dof_objects(), libMesh::DistributedMesh::renumber_nodes_and_elements(), libMesh::DofMap::scatter_constraints(), libMesh::CheckpointIO::select_split_config(), libMesh::DistributedMesh::set_next_unique_id(), libMesh::DofMap::set_nonlocal_dof_objects(), libMesh::PetscDMWrapper::set_point_range_in_section(), libMesh::RBEIMEvaluation::side_gather_bfs(), ExodusTest< elem_type >::test_read_gold(), ExodusTest< elem_type >::test_write(), MeshInputTest::testAbaqusRead(), MeshInputTest::testBadGmsh(), MeshInputTest::testCopyElementSolutionImpl(), MeshInputTest::testCopyElementVectorImpl(), MeshInputTest::testCopyNodalSolutionImpl(), DefaultCouplingTest::testCoupling(), PointNeighborCouplingTest::testCoupling(), MeshInputTest::testDynaFileMappings(), MeshInputTest::testDynaNoSplines(), MeshInputTest::testDynaReadElem(), MeshInputTest::testDynaReadPatch(), MeshInputTest::testExodusFileMappings(), MeshInputTest::testExodusIGASidesets(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), MeshInputTest::testGmshBCIDOverlap(), MeshInputTest::testGoodGmsh(), MeshInputTest::testGoodSTL(), MeshInputTest::testGoodSTLBinary(), MeshInputTest::testLowOrderEdgeBlocks(), SystemsTest::testProjectMatrix3D(), BoundaryInfoTest::testShellFaceConstraints(), MeshInputTest::testSingleElementImpl(), WriteVecAndScalar::testSolution(), CheckpointIOTest::testSplitter(), MeshInputTest::testTetgenIO(), libMesh::MeshTools::total_weight(), libMesh::NetGenMeshInterface::triangulate(), libMesh::MeshRefinement::uniformly_coarsen(), libMesh::DistributedMesh::update_parallel_id_counts(), libMesh::DTKAdapter::update_variable_values(), libMesh::MeshTools::volume(), libMesh::STLIO::write(), libMesh::NameBasedIO::write(), libMesh::XdrIO::write(), libMesh::CheckpointIO::write(), libMesh::EquationSystems::write(), libMesh::GMVIO::write_discontinuous_gmv(), libMesh::ExodusII_IO::write_element_data(), libMesh::ExodusII_IO_Helper::write_element_values(), libMesh::ExodusII_IO_Helper::write_element_values_element_major(), libMesh::ExodusII_IO_Helper::write_elements(), libMesh::ExodusII_IO_Helper::write_elemset_data(), libMesh::ExodusII_IO_Helper::write_elemsets(), libMesh::ExodusII_IO::write_global_data(), libMesh::ExodusII_IO_Helper::write_global_values(), libMesh::System::write_header(), libMesh::ExodusII_IO::write_information_records(), libMesh::ExodusII_IO_Helper::write_information_records(), libMesh::ExodusII_IO_Helper::write_nodal_coordinates(), libMesh::UCDIO::write_nodal_data(), libMesh::VTKIO::write_nodal_data(), libMesh::ExodusII_IO::write_nodal_data(), libMesh::ExodusII_IO::write_nodal_data_common(), libMesh::ExodusII_IO::write_nodal_data_discontinuous(), libMesh::ExodusII_IO_Helper::write_nodal_values(), libMesh::ExodusII_IO_Helper::write_nodeset_data(), libMesh::Nemesis_IO_Helper::write_nodesets(), libMesh::ExodusII_IO_Helper::write_nodesets(), libMesh::RBEIMEvaluation::write_out_interior_basis_functions(), libMesh::RBEIMEvaluation::write_out_node_basis_functions(), libMesh::RBEIMEvaluation::write_out_side_basis_functions(), write_output_solvedata(), libMesh::System::write_parallel_data(), libMesh::RBConstruction::write_riesz_representors_to_files(), libMesh::System::write_SCALAR_dofs(), libMesh::XdrIO::write_serialized_bc_names(), libMesh::XdrIO::write_serialized_bcs_helper(), libMesh::System::write_serialized_blocked_dof_objects(), libMesh::XdrIO::write_serialized_connectivity(), libMesh::System::write_serialized_data(), libMesh::XdrIO::write_serialized_nodes(), libMesh::XdrIO::write_serialized_nodesets(), libMesh::XdrIO::write_serialized_subdomain_names(), libMesh::System::write_serialized_vector(), libMesh::System::write_serialized_vectors(), libMesh::ExodusII_IO_Helper::write_sideset_data(), libMesh::Nemesis_IO_Helper::write_sidesets(), libMesh::ExodusII_IO_Helper::write_sidesets(), libMesh::ExodusII_IO::write_timestep(), libMesh::ExodusII_IO_Helper::write_timestep(), and libMesh::ExodusII_IO::write_timestep_discontinuous().

  { return cast_int<processor_id_type>(_communicator.rank()); }

project_solution() [1/3]

void libMesh::System::project_solution ( FunctionBase< Number > *  f, FunctionBase< Gradient > *  g = nullptr  ) const

inherited

Projects arbitrary functions onto the current solution.

This method projects an arbitrary function onto the solution via L2 projections and nodal interpolations on each element.

The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Definition at line 1041 of file system_projection.C.

Referenced by init_sys(), initialize(), main(), set_initial_condition(), SlitMeshRefinedSystemTest::setUp(), FETestBase< order, family, elem_type, 1 >::setUp(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), MeshFunctionTest::test_subdomain_id_sets(), MeshInputTest::testCopyElementSolutionImpl(), MeshInputTest::testCopyNodalSolutionImpl(), DefaultCouplingTest::testCoupling(), PointNeighborCouplingTest::testCoupling(), SystemsTest::testProjectCubeWithMeshFunction(), MeshInputTest::testProjectionRegression(), EquationSystemsTest::testRepartitionThenReinit(), and libMesh::MeshfreeSolutionTransfer::transfer().

{
  this->project_vector(*solution, f, g);

  solution->localize(*current_local_solution, _dof_map->get_send_list());
}

project_solution() [2/3]

void libMesh::System::project_solution ( FEMFunctionBase< Number > *  f, FEMFunctionBase< Gradient > *  g = nullptr  ) const

inherited

Projects arbitrary functions onto the current solution.

This method projects an arbitrary function onto the solution via L2 projections and nodal interpolations on each element.

The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Definition at line 1054 of file system_projection.C.

{
  this->project_vector(*solution, f, g);

  solution->localize(*current_local_solution, _dof_map->get_send_list());
}

project_solution() [3/3]

void libMesh::System::project_solution ( ValueFunctionPointer  fptr, GradientFunctionPointer  gptr, const Parameters &  parameters  ) const

inherited

This method projects an arbitrary function onto the solution via L2 projections and nodal interpolations on each element.

Definition at line 1027 of file system_projection.C.

References fptr(), and gptr().

{
  WrappedFunction<Number> f(*this, fptr, &function_parameters);
  WrappedFunction<Gradient> g(*this, gptr, &function_parameters);
  this->project_solution(&f, &g);
}

project_solution_on_reinit()

bool& libMesh::System::project_solution_on_reinit ( void  )

inlineinherited

Tells the System whether or not to project the solution vector onto new grids when the system is reinitialized.

The solution will be projected unless project_solution_on_reinit() = false is called.

Definition at line 838 of file system.h.

References libMesh::System::_solution_projection.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), and libMesh::MemoryHistoryData::store_vectors().

  { return _solution_projection; }

project_vector() [1/5]

void libMesh::System::project_vector ( NumericVector< Number > &  new_vector, FunctionBase< Number > *  f, FunctionBase< Gradient > *  g = nullptr, int  is_adjoint = -1  ) const

inherited

Projects arbitrary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary function via L2 projections and nodal interpolations on each element.

The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 1082 of file system_projection.C.

References libMesh::libmesh_assert().

Referenced by main(), libMesh::NewmarkSolver::project_initial_accel(), libMesh::SecondOrderUnsteadySolver::project_initial_rate(), libMesh::InterMeshProjection::project_system_vectors(), and libMesh::System::restrict_vectors().

{
  LOG_SCOPE ("project_vector(FunctionBase)", "System");

  libmesh_assert(f);

  WrappedFunctor<Number> f_fem(*f);

  if (g)
    {
      WrappedFunctor<Gradient> g_fem(*g);

      this->project_vector(new_vector, &f_fem, &g_fem, is_adjoint);
    }
  else
    this->project_vector(new_vector, &f_fem, nullptr, is_adjoint);
}

project_vector() [2/5]

void libMesh::System::project_vector ( NumericVector< Number > &  new_vector, FEMFunctionBase< Number > *  f, FEMFunctionBase< Gradient > *  g = nullptr, int  is_adjoint = -1  ) const

inherited

Projects arbitrary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary function via L2 projections and nodal interpolations on each element.

The function value f and its gradient g are user-provided cloneable functors. A gradient g is only required/used for projecting onto finite element spaces with continuous derivatives.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 1108 of file system_projection.C.

References libMesh::NumericVector< T >::close(), libMesh::FEMFunctionBase< Output >::component(), libMesh::FEType::family, libMesh::Utility::iota(), libMesh::libmesh_assert(), libMesh::libmesh_ignore(), libMesh::make_range(), n_vars, libMesh::NODEELEM, libMesh::FEMContext::pre_fe_reinit(), libMesh::RATIONAL_BERNSTEIN, libMesh::SCALAR, libMesh::DofMap::SCALAR_dof_indices(), libMesh::NumericVector< T >::set(), and libMesh::Variable::type().

{
  LOG_SCOPE ("project_fem_vector()", "System");

  libmesh_assert (f);

  ConstElemRange active_local_range
    (this->get_mesh().active_local_elements_begin(),
     this->get_mesh().active_local_elements_end() );

  VectorSetAction<Number> setter(new_vector);

  const unsigned int n_variables = this->n_vars();

  std::vector<unsigned int> vars(n_variables);
  std::iota(vars.begin(), vars.end(), 0);

  // Use a typedef to make the calling sequence for parallel_for() a bit more readable
  typedef
    GenericProjector<FEMFunctionWrapper<Number>, FEMFunctionWrapper<Gradient>,
                     Number, VectorSetAction<Number>> FEMProjector;

  FEMFunctionWrapper<Number> fw(*f);

  if (g)
    {
      FEMFunctionWrapper<Gradient> gw(*g);

      FEMProjector projector(*this, fw, &gw, setter, vars);
      projector.project(active_local_range);
    }
  else
    {
      FEMProjector projector(*this, fw, nullptr, setter, vars);
      projector.project(active_local_range);
    }

  // Also, load values into the SCALAR dofs
  // Note: We assume that all SCALAR dofs are on the
  // processor with highest ID
  if (this->processor_id() == (this->n_processors()-1))
    {
      // FIXME: Do we want to first check for SCALAR vars before building this? [PB]
      FEMContext context( *this );

      const DofMap & dof_map = this->get_dof_map();
      for (auto var : make_range(this->n_vars()))
        if (this->variable(var).type().family == SCALAR)
          {
            // FIXME: We reinit with an arbitrary element in case the user
            //        doesn't override FEMFunctionBase::component. Is there
            //        any use case we're missing? [PB]
            context.pre_fe_reinit(*this, *(this->get_mesh().active_local_elements_begin()));

            std::vector<dof_id_type> SCALAR_indices;
            dof_map.SCALAR_dof_indices (SCALAR_indices, var);
            const unsigned int n_SCALAR_dofs =
              cast_int<unsigned int>(SCALAR_indices.size());

            for (unsigned int i=0; i<n_SCALAR_dofs; i++)
              {
                const dof_id_type global_index = SCALAR_indices[i];
                const unsigned int component_index =
                  this->variable_scalar_number(var,i);

                new_vector.set(global_index, f->component(context, component_index, Point(), this->time));
              }
          }
    }

  new_vector.close();

  // Look for spline bases, in which case we need to backtrack
  // to calculate the spline DoF values.
  std::vector<const Variable *> rational_vars;
  for (auto varnum : vars)
    {
      const Variable & var = this->get_dof_map().variable(varnum);
      if (var.type().family == RATIONAL_BERNSTEIN)
        rational_vars.push_back(&var);
    }

  // Okay, but are we really using any *spline* bases, or just
  // unconstrained rational bases?
  bool using_spline_bases = false;
  if (!rational_vars.empty())
    {
      // Look for a spline node: a NodeElem with a rational variable
      // on it.
      for (auto & elem : active_local_range)
        if (elem->type() == NODEELEM)
          for (auto rational_var : rational_vars)
            if (rational_var->active_on_subdomain(elem->subdomain_id()))
              {
                using_spline_bases = true;
                goto checked_on_splines;
              }
    }

checked_on_splines:

  // Not every processor may have a NodeElem, especially while
  // we're not partitioning them efficiently yet.
  this->comm().max(using_spline_bases);

  if (using_spline_bases)
    this->solve_for_unconstrained_dofs(new_vector, is_adjoint);

#ifdef LIBMESH_ENABLE_CONSTRAINTS
  if (is_adjoint == -1)
    this->get_dof_map().enforce_constraints_exactly(*this, &new_vector);
  else if (is_adjoint >= 0)
    this->get_dof_map().enforce_adjoint_constraints_exactly(new_vector,
                                                            is_adjoint);
#else
  libmesh_ignore(is_adjoint);
#endif
}

project_vector() [3/5]

void libMesh::System::project_vector ( ValueFunctionPointer  fptr, GradientFunctionPointer  gptr, const Parameters &  parameters, NumericVector< Number > &  new_vector, int  is_adjoint = -1  ) const

inherited

Projects arbitrary functions onto a vector of degree of freedom values for the current system.

This method projects an arbitrary function via L2 projections and nodal interpolations on each element.

The function value fptr and its gradient gptr are represented by function pointers. A gradient gptr is only required/used for projecting onto finite element spaces with continuous derivatives.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 1067 of file system_projection.C.

References fptr(), and gptr().

{
  WrappedFunction<Number> f(*this, fptr, &function_parameters);
  WrappedFunction<Gradient> g(*this, gptr, &function_parameters);
  this->project_vector(new_vector, &f, &g, is_adjoint);
}

project_vector() [4/5]

void libMesh::System::project_vector ( NumericVector< Number > &  vector, int  is_adjoint = -1  ) const

protectedinherited

Projects the vector defined on the old mesh onto the new mesh.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

Definition at line 247 of file system_projection.C.

References libMesh::NumericVector< T >::clone().

{
  // Create a copy of the vector, which currently
  // contains the old data.
  std::unique_ptr<NumericVector<Number>>
    old_vector (vector.clone());

  // Project the old vector to the new vector
  this->project_vector (*old_vector, vector, is_adjoint);
}

project_vector() [5/5]

void libMesh::System::project_vector ( const NumericVector< Number > &  old_v, NumericVector< Number > &  new_v, int  is_adjoint = -1  ) const

protectedinherited

Projects the vector defined on the old mesh onto the new mesh.

This method projects the vector via L2 projections or nodal interpolations on each element.

The original vector is unchanged and the new vector is passed through the second argument.

Constrain the new vector using the requested adjoint rather than primal constraints if is_adjoint is non-negative.

This method projects a solution from an old mesh to a current, refined mesh. The input vector old_v gives the solution on the old mesh, while the new_v gives the solution (to be computed) on the new mesh.

Definition at line 265 of file system_projection.C.

References libMesh::NumericVector< T >::clear(), libMesh::NumericVector< T >::close(), libMesh::NumericVector< T >::get(), libMesh::GHOSTED, libMesh::index_range(), libMesh::NumericVector< T >::init(), libMesh::Utility::iota(), libMesh::libmesh_assert(), libMesh::libmesh_ignore(), libMesh::NumericVector< T >::local_size(), libMesh::NumericVector< T >::localize(), libMesh::make_range(), n_vars, libMesh::PARALLEL, libMesh::Threads::parallel_reduce(), libMesh::SCALAR, libMesh::DofMap::SCALAR_dof_indices(), libMesh::BuildProjectionList::send_list, libMesh::SERIAL, libMesh::NumericVector< T >::set(), libMesh::NumericVector< T >::size(), libMesh::NumericVector< T >::type(), libMesh::TYPE_SCALAR, and libMesh::BuildProjectionList::unique().

{
  LOG_SCOPE ("project_vector(old,new)", "System");

  new_v.clear();

#ifdef LIBMESH_ENABLE_AMR

  // Resize the new vector and get a serial version.
  NumericVector<Number> * new_vector_ptr = nullptr;
  std::unique_ptr<NumericVector<Number>> new_vector_built;
  NumericVector<Number> * local_old_vector;
  std::unique_ptr<NumericVector<Number>> local_old_vector_built;
  const NumericVector<Number> * old_vector_ptr = nullptr;

  ConstElemRange active_local_elem_range
    (this->get_mesh().active_local_elements_begin(),
     this->get_mesh().active_local_elements_end());

  // If the old vector was uniprocessor, make the new
  // vector uniprocessor
  if (old_v.type() == SERIAL)
    {
      new_v.init (this->n_dofs(), false, SERIAL);
      new_vector_ptr = &new_v;
      old_vector_ptr = &old_v;
    }

  // Otherwise it is a parallel, distributed vector, which
  // we need to localize.
  else if (old_v.type() == PARALLEL)
    {
      // Build a send list for efficient localization
      BuildProjectionList projection_list(*this);
      Threads::parallel_reduce (active_local_elem_range,
                                projection_list);

      // Create a sorted, unique send_list
      projection_list.unique();

      new_v.init (this->n_dofs(), this->n_local_dofs(), false, PARALLEL);
      new_vector_built = NumericVector<Number>::build(this->comm());
      local_old_vector_built = NumericVector<Number>::build(this->comm());
      new_vector_ptr = new_vector_built.get();
      local_old_vector = local_old_vector_built.get();
      new_vector_ptr->init(this->n_dofs(), this->n_local_dofs(),
                           this->get_dof_map().get_send_list(), false,
                           GHOSTED);
      local_old_vector->init(old_v.size(), old_v.local_size(),
                             projection_list.send_list, false, GHOSTED);
      old_v.localize(*local_old_vector, projection_list.send_list);
      local_old_vector->close();
      old_vector_ptr = local_old_vector;
    }
  else if (old_v.type() == GHOSTED)
    {
      // Build a send list for efficient localization
      BuildProjectionList projection_list(*this);
      Threads::parallel_reduce (active_local_elem_range,
                                projection_list);

      // Create a sorted, unique send_list
      projection_list.unique();

      new_v.init (this->n_dofs(), this->n_local_dofs(),
                  this->get_dof_map().get_send_list(), false, GHOSTED);

      local_old_vector_built = NumericVector<Number>::build(this->comm());
      new_vector_ptr = &new_v;
      local_old_vector = local_old_vector_built.get();
      local_old_vector->init(old_v.size(), old_v.local_size(),
                             projection_list.send_list, false, GHOSTED);
      old_v.localize(*local_old_vector, projection_list.send_list);
      local_old_vector->close();
      old_vector_ptr = local_old_vector;
    }
  else // unknown old_v.type()
    libmesh_error_msg("ERROR: Unknown old_v.type() == " << old_v.type());

  // Note that the above will have zeroed the new_vector.
  // Just to be sure, assert that new_vector_ptr and old_vector_ptr
  // were successfully set before trying to deref them.
  libmesh_assert(new_vector_ptr);
  libmesh_assert(old_vector_ptr);

  NumericVector<Number> & new_vector = *new_vector_ptr;
  const NumericVector<Number> & old_vector = *old_vector_ptr;

  const unsigned int n_variables = this->n_vars();

  if (n_variables)
    {
      std::vector<unsigned int> vars(n_variables);
      std::iota(vars.begin(), vars.end(), 0);
      std::vector<unsigned int> regular_vars, vector_vars;
      for (auto var : vars)
      {
        if (FEInterface::field_type(this->variable_type(var)) == TYPE_SCALAR)
          regular_vars.push_back(var);
        else
          vector_vars.push_back(var);
      }

      VectorSetAction<Number> setter(new_vector);

      if (!regular_vars.empty())
        {
          // Use a typedef to make the calling sequence for parallel_for() a bit more readable
          typedef
            GenericProjector<OldSolutionValue<Number,   &FEMContext::point_value>,
                             OldSolutionValue<Gradient, &FEMContext::point_gradient>,
                             Number, VectorSetAction<Number>> FEMProjector;

          OldSolutionValue<Number,   &FEMContext::point_value>
            f(*this, old_vector, &regular_vars);
          OldSolutionValue<Gradient, &FEMContext::point_gradient>
            g(*this, old_vector, &regular_vars);

          FEMProjector projector(*this, f, &g, setter, regular_vars);
          projector.project(active_local_elem_range);
        }

      if (!vector_vars.empty())
        {
          typedef
            GenericProjector<OldSolutionValue<Gradient,   &FEMContext::point_value>,
                             OldSolutionValue<Tensor, &FEMContext::point_gradient>,
                             Gradient, VectorSetAction<Number>> FEMVectorProjector;

          OldSolutionValue<Gradient, &FEMContext::point_value> f_vector(*this, old_vector, &vector_vars);
          OldSolutionValue<Tensor, &FEMContext::point_gradient> g_vector(*this, old_vector, &vector_vars);

          FEMVectorProjector vector_projector(*this, f_vector, &g_vector, setter, vector_vars);
          vector_projector.project(active_local_elem_range);
        }

      // Copy the SCALAR dofs from old_vector to new_vector
      // Note: We assume that all SCALAR dofs are on the
      // processor with highest ID
      if (this->processor_id() == (this->n_processors()-1))
        {
          const DofMap & dof_map = this->get_dof_map();
          for (auto var : make_range(this->n_vars()))
            if (this->variable(var).type().family == SCALAR)
              {
                // We can just map SCALAR dofs directly across
                std::vector<dof_id_type> new_SCALAR_indices, old_SCALAR_indices;
                dof_map.SCALAR_dof_indices (new_SCALAR_indices, var, false);
                dof_map.SCALAR_dof_indices (old_SCALAR_indices, var, true);
                for (auto i : index_range(new_SCALAR_indices))
                  new_vector.set(new_SCALAR_indices[i], old_vector(old_SCALAR_indices[i]));
              }
        }
    }

  new_vector.close();

  // If the old vector was serial, we probably need to send our values
  // to other processors
  //
  // FIXME: I'm not sure how to make a NumericVector do that without
  // creating a temporary parallel vector to use localize! - RHS
  if (old_v.type() == SERIAL)
    {
      std::unique_ptr<NumericVector<Number>> dist_v = NumericVector<Number>::build(this->comm());
      dist_v->init(this->n_dofs(), this->n_local_dofs(), false, PARALLEL);
      dist_v->close();

      for (auto i : make_range(dist_v->size()))
        if (new_vector(i) != 0.0)
          dist_v->set(i, new_vector(i));

      dist_v->close();

      dist_v->localize (new_v, this->get_dof_map().get_send_list());
      new_v.close();
    }
  // If the old vector was parallel, we need to update it
  // and free the localized copies
  else if (old_v.type() == PARALLEL)
    {
      // We may have to set dof values that this processor doesn't
      // own in certain special cases, like LAGRANGE FIRST or
      // HERMITE THIRD elements on second-order meshes?
      new_v = new_vector;
      new_v.close();
    }


  // Apply constraints only if we we are asked to
  if(this->project_with_constraints)
  {
    if (is_adjoint == -1)
    {
      this->get_dof_map().enforce_constraints_exactly(*this, &new_v);
    }
    else if (is_adjoint >= 0)
    {
      this->get_dof_map().enforce_adjoint_constraints_exactly(new_v,
                                                            is_adjoint);
    }
  }
#else

  // AMR is disabled: simply copy the vector
  new_v = old_v;

  libmesh_ignore(is_adjoint);

#endif // #ifdef LIBMESH_ENABLE_AMR
}

projection_matrix()

void libMesh::System::projection_matrix ( SparseMatrix< Number > &  proj_mat ) const

inherited

This method creates a projection matrix which corresponds to the operation of project_vector between old and new solution spaces.

Heterogeneous Dirichlet boundary conditions are not taken into account here; if this matrix is used for prolongation (mesh refinement) on a side with a heterogeneous BC, the newly created degrees of freedom on that side will still match the coarse grid approximation of the BC, not the fine grid approximation.

Definition at line 961 of file system_projection.C.

References libMesh::Utility::iota(), libMesh::make_range(), n_vars, libMesh::SCALAR, libMesh::DofMap::SCALAR_dof_indices(), and libMesh::SparseMatrix< T >::set().

Referenced by libMesh::PetscDMWrapper::init_petscdm(), SystemsTest::testProjectMatrix1D(), SystemsTest::testProjectMatrix2D(), and SystemsTest::testProjectMatrix3D().

{
  LOG_SCOPE ("projection_matrix()", "System");

  const unsigned int n_variables = this->n_vars();

  if (n_variables)
    {
      ConstElemRange active_local_elem_range
        (this->get_mesh().active_local_elements_begin(),
         this->get_mesh().active_local_elements_end());

      std::vector<unsigned int> vars(n_variables);
      std::iota(vars.begin(), vars.end(), 0);

      // Use a typedef to make the calling sequence for parallel_for() a bit more readable
      typedef OldSolutionCoefs<Real, &FEMContext::point_value> OldSolutionValueCoefs;
      typedef OldSolutionCoefs<RealGradient, &FEMContext::point_gradient> OldSolutionGradientCoefs;

      typedef
        GenericProjector<OldSolutionValueCoefs,
                         OldSolutionGradientCoefs,
                         DynamicSparseNumberArray<Real,dof_id_type>,
                         MatrixFillAction<Real, Number> > ProjMatFiller;

      OldSolutionValueCoefs    f(*this, &vars);
      OldSolutionGradientCoefs g(*this, &vars);
      MatrixFillAction<Real, Number> setter(proj_mat);

      ProjMatFiller mat_filler(*this, f, &g, setter, vars);
      mat_filler.project(active_local_elem_range);

      // Set the SCALAR dof transfer entries too.
      // Note: We assume that all SCALAR dofs are on the
      // processor with highest ID
      if (this->processor_id() == (this->n_processors()-1))
        {
          const DofMap & dof_map = this->get_dof_map();
          for (auto var : make_range(this->n_vars()))
            if (this->variable(var).type().family == SCALAR)
              {
                // We can just map SCALAR dofs directly across
                std::vector<dof_id_type> new_SCALAR_indices, old_SCALAR_indices;
                dof_map.SCALAR_dof_indices (new_SCALAR_indices, var, false);
                dof_map.SCALAR_dof_indices (old_SCALAR_indices, var, true);
                const unsigned int new_n_dofs =
                  cast_int<unsigned int>(new_SCALAR_indices.size());

                for (unsigned int i=0; i<new_n_dofs; i++)
                  {
                    proj_mat.set( new_SCALAR_indices[i],
                                  old_SCALAR_indices[i], 1);
                  }
              }
        }
    }
}

prolong_vectors()

void libMesh::System::prolong_vectors ( )

virtualinherited

Prolong vectors after the mesh has refined.

Definition at line 444 of file system.C.

References libMesh::System::restrict_vectors().

Referenced by libMesh::EquationSystems::reinit_solutions().

{
#ifdef LIBMESH_ENABLE_AMR
  // Currently project_vector handles both restriction and prolongation
  this->restrict_vectors();
#endif
}

push_physics()

void libMesh::DifferentiableSystem::push_physics ( DifferentiablePhysics &  new_physics )

inherited

Push a clone of a new physics object onto our stack, overriding the current physics until the new physics is popped off again (or until something else is pushed on top of it).

Definition at line 399 of file diff_system.C.

References libMesh::DifferentiableSystem::_diff_physics, libMesh::DifferentiablePhysics::clone_physics(), and libMesh::ImplicitSystem::disable_cache().

Referenced by main().

{
  this->_diff_physics.push(new_physics.clone_physics());

  // If the physics has been changed, we will reassemble
  // the matrix from scratch before doing an adjoint solve
  // rather than just transposing
  this->disable_cache();
}

qoi_parameter_hessian()

void libMesh::ImplicitSystem::qoi_parameter_hessian ( const QoISet &  qoi_indices, const ParameterVector &  parameters, SensitivityData &  hessian  )

overridevirtualinherited

For each of the system's quantities of interest q in qoi[qoi_indices], and for a vector of parameters p, the parameter sensitivity Hessian H_ij is defined as H_ij = (d^2 q)/(d p_i d p_j) This Hessian is the output of this method, where for each q_i, H_jk is stored in hessian.second_derivative(i,j,k).

Note that in some cases only current_local_solution is used during assembly, and, therefore, if solution has been altered without update() being called, then the user must call update() before calling this function.

Reimplemented from libMesh::System.

Definition at line 918 of file implicit_system.C.

References libMesh::ImplicitSystem::adjoint_solve(), libMesh::SensitivityData::allocate_hessian_data(), libMesh::ExplicitSystem::assemble_qoi(), libMesh::ExplicitSystem::assemble_qoi_derivative(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::NumericVector< T >::dot(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_adjoint_solution(), libMesh::System::get_qoi_value(), libMesh::System::get_qoi_values(), libMesh::System::get_sensitivity_solution(), libMesh::QoISet::has_index(), libMesh::System::is_adjoint_already_solved(), libMesh::ImplicitSystem::matrix, libMesh::System::n_qois(), libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::SensitivityData::second_derivative(), libMesh::ImplicitSystem::sensitivity_solve(), libMesh::ParameterVector::size(), libMesh::System::solution, libMesh::TOLERANCE, libMesh::System::update(), and libMesh::SparseMatrix< T >::vector_mult().

{
  // We currently get partial derivatives via finite differencing
  const Real delta_p = TOLERANCE;

  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  // We'll use one temporary vector for matrix-vector-vector products
  std::unique_ptr<NumericVector<Number>> tempvec = this->solution->zero_clone();

  // And another temporary vector to hold a copy of the true solution
  // so we can safely perturb this->solution.
  std::unique_ptr<NumericVector<Number>> oldsolution = this->solution->clone();

  const unsigned int Np = cast_int<unsigned int>
    (parameters_vec.size());
  const unsigned int Nq = this->n_qois();

  // For each quantity of interest q, the parameter sensitivity
  // Hessian is defined as q''_{kl} = {d^2 q}/{d p_k d p_l}.
  //
  // We calculate it from values and partial derivatives of the
  // quantity of interest function Q, solution u, adjoint solution z,
  // and residual R, as:
  //
  // q''_{kl} =
  // Q''_{kl} + Q''_{uk}(u)*u'_l + Q''_{ul}(u) * u'_k +
  // Q''_{uu}(u)*u'_k*u'_l -
  // R''_{kl}(u,z) -
  // R''_{uk}(u,z)*u'_l - R''_{ul}(u,z)*u'_k -
  // R''_{uu}(u,z)*u'_k*u'_l
  //
  // See the adjoints model document for more details.

  // We first do an adjoint solve to get z for each quantity of
  // interest
  // if we haven't already or dont have an initial condition for the adjoint
  if (!this->is_adjoint_already_solved())
    {
      this->adjoint_solve(qoi_indices);
    }

  // And a sensitivity solve to get u_k for each parameter
  this->sensitivity_solve(parameters_vec);

  // Get ready to fill in second derivatives:
  sensitivities.allocate_hessian_data(qoi_indices, *this, parameters_vec);

  for (unsigned int k=0; k != Np; ++k)
    {
      Number old_parameterk = *parameters_vec[k];

      // The Hessian is symmetric, so we just calculate the lower
      // triangle and the diagonal, and we get the upper triangle from
      // the transpose of the lower

      for (unsigned int l=0; l != k+1; ++l)
        {
          // The second partial derivatives with respect to parameters_vec
          // are all calculated via a central finite difference
          // stencil:
          // F''_{kl} ~= (F(p+dp*e_k+dp*e_l) - F(p+dp*e_k-dp*e_l) -
          //              F(p-dp*e_k+dp*e_l) + F(p-dp*e_k-dp*e_l))/(4*dp^2)
          // We will add Q''_{kl}(u) and subtract R''_{kl}(u,z) at the
          // same time.
          //
          // We have to be careful with the perturbations to handle
          // the k=l case

          Number old_parameterl = *parameters_vec[l];

          *parameters_vec[k] += delta_p;
          *parameters_vec[l] += delta_p;
          this->assemble_qoi(qoi_indices);
          this->assembly(true, false, true);
          this->rhs->close();
          std::vector<Number> partial2q_term = this->get_qoi_values();
          std::vector<Number> partial2R_term(this->n_qois());
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              partial2R_term[i] = this->rhs->dot(this->get_adjoint_solution(i));

          *parameters_vec[l] -= 2.*delta_p;
          this->assemble_qoi(qoi_indices);
          this->assembly(true, false, true);
          this->rhs->close();
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                partial2q_term[i] -= this->get_qoi_value(i);
                partial2R_term[i] -= this->rhs->dot(this->get_adjoint_solution(i));
              }

          *parameters_vec[k] -= 2.*delta_p;
          this->assemble_qoi(qoi_indices);
          this->assembly(true, false, true);
          this->rhs->close();
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                partial2q_term[i] += this->get_qoi_value(i);
                partial2R_term[i] += this->rhs->dot(this->get_adjoint_solution(i));
              }

          *parameters_vec[l] += 2.*delta_p;
          this->assemble_qoi(qoi_indices);
          this->assembly(true, false, true);
          this->rhs->close();
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                partial2q_term[i] -= this->get_qoi_value(i);
                partial2R_term[i] -= this->rhs->dot(this->get_adjoint_solution(i));
                partial2q_term[i] /= (4. * delta_p * delta_p);
                partial2R_term[i] /= (4. * delta_p * delta_p);
              }

          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                Number current_terms = partial2q_term[i] - partial2R_term[i];
                sensitivities.second_derivative(i,k,l) += current_terms;
                if (k != l)
                  sensitivities.second_derivative(i,l,k) += current_terms;
              }

          // Don't leave the parameters_vec perturbed
          *parameters_vec[l] = old_parameterl;
          *parameters_vec[k] = old_parameterk;
        }

      // We get (partial q / partial u) and
      // (partial R / partial u) from the user, but centrally
      // difference to get q_uk and R_uk terms:
      // (partial^2 q / partial u partial k)
      // q_uk*u'_l = (q_u(p+dp*e_k)*u'_l - q_u(p-dp*e_k)*u'_l)/(2*dp)
      // R_uk*z*u'_l = (R_u(p+dp*e_k)*z*u'_l - R_u(p-dp*e_k)*z*u'_l)/(2*dp)
      //
      // To avoid creating Nq temporary vectors, we add these
      // subterms to the sensitivities output one by one.
      //
      // FIXME: this is probably a bad order of operations for
      // controlling floating point error.

      *parameters_vec[k] = old_parameterk + delta_p;
      this->assembly(false, true);
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      for (unsigned int l=0; l != Np; ++l)
        {
          this->matrix->vector_mult(*tempvec, this->get_sensitivity_solution(l));
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                this->get_adjoint_rhs(i).close();
                Number current_terms =
                  (this->get_adjoint_rhs(i).dot(this->get_sensitivity_solution(l)) -
                   tempvec->dot(this->get_adjoint_solution(i))) / (2.*delta_p);
                sensitivities.second_derivative(i,k,l) += current_terms;

                // We use the _uk terms twice; symmetry lets us reuse
                // these calculations for the _ul terms.

                sensitivities.second_derivative(i,l,k) += current_terms;
              }
        }

      *parameters_vec[k] = old_parameterk - delta_p;
      this->assembly(false, true);
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      for (unsigned int l=0; l != Np; ++l)
        {
          this->matrix->vector_mult(*tempvec, this->get_sensitivity_solution(l));
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                this->get_adjoint_rhs(i).close();
                Number current_terms =
                  (-this->get_adjoint_rhs(i).dot(this->get_sensitivity_solution(l)) +
                   tempvec->dot(this->get_adjoint_solution(i))) / (2.*delta_p);
                sensitivities.second_derivative(i,k,l) += current_terms;

                // We use the _uk terms twice; symmetry lets us reuse
                // these calculations for the _ul terms.

                sensitivities.second_derivative(i,l,k) += current_terms;
              }
        }

      // Don't leave the parameter perturbed
      *parameters_vec[k] = old_parameterk;

      // Our last remaining terms are -R_uu(u,z)*u_k*u_l and
      // Q_uu(u)*u_k*u_l
      //
      // We take directional central finite differences of R_u and Q_u
      // to approximate these terms, e.g.:
      //
      // Q_uu(u)*u_k ~= (Q_u(u+dp*u_k) - Q_u(u-dp*u_k))/(2*dp)

      *this->solution = this->get_sensitivity_solution(k);
      *this->solution *= delta_p;
      *this->solution += *oldsolution;

      // We've modified solution, so we need to update before calling
      // assembly since assembly may only use current_local_solution
      this->update();
      this->assembly(false, true);
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      // The Hessian is symmetric, so we just calculate the lower
      // triangle and the diagonal, and we get the upper triangle from
      // the transpose of the lower
      //
      // Note that, because we took the directional finite difference
      // with respect to k and not l, we've added an O(delta_p^2)
      // error to any permutational symmetry in the Hessian...
      for (unsigned int l=0; l != k+1; ++l)
        {
          this->matrix->vector_mult(*tempvec, this->get_sensitivity_solution(l));
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                this->get_adjoint_rhs(i).close();
                Number current_terms =
                  (this->get_adjoint_rhs(i).dot(this->get_sensitivity_solution(l)) -
                   tempvec->dot(this->get_adjoint_solution(i))) / (2.*delta_p);
                sensitivities.second_derivative(i,k,l) += current_terms;
                if (k != l)
                  sensitivities.second_derivative(i,l,k) += current_terms;
              }
        }

      *this->solution = this->get_sensitivity_solution(k);
      *this->solution *= -delta_p;
      *this->solution += *oldsolution;

      // We've modified solution, so we need to update before calling
      // assembly since assembly may only use current_local_solution
      this->update();
      this->assembly(false, true);
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      for (unsigned int l=0; l != k+1; ++l)
        {
          this->matrix->vector_mult(*tempvec, this->get_sensitivity_solution(l));
          for (unsigned int i=0; i != Nq; ++i)
            if (qoi_indices.has_index(i))
              {
                this->get_adjoint_rhs(i).close();
                Number current_terms =
                  (-this->get_adjoint_rhs(i).dot(this->get_sensitivity_solution(l)) +
                   tempvec->dot(this->get_adjoint_solution(i))) / (2.*delta_p);
                sensitivities.second_derivative(i,k,l) += current_terms;
                if (k != l)
                  sensitivities.second_derivative(i,l,k) += current_terms;
              }
        }

      // Don't leave the solution perturbed
      *this->solution = *oldsolution;
    }

  // All parameters_vec have been reset.
  // Don't leave the qoi or system changed - principle of least
  // surprise.
  // We've modified solution, so we need to update before calling
  // assembly since assembly may only use current_local_solution
  this->update();
  this->assembly(true, true);
  this->rhs->close();
  this->matrix->close();
  this->assemble_qoi(qoi_indices);
}

qoi_parameter_hessian_vector_product()

void libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product ( const QoISet &  qoi_indices, const ParameterVector &  parameters, const ParameterVector &  vector, SensitivityData &  product  )

overridevirtualinherited

For each of the system's quantities of interest q in qoi[qoi_indices], and for a vector of parameters p, the parameter sensitivity Hessian H_ij is defined as H_ij = (d^2 q)/(d p_i d p_j) The Hessian-vector product, for a vector v_k in parameter space, is S_j = H_jk v_k This product is the output of this method, where for each q_i, S_j is stored in sensitivities[i][j].

Reimplemented from libMesh::System.

Definition at line 713 of file implicit_system.C.

References libMesh::ImplicitSystem::adjoint_solve(), libMesh::SensitivityData::allocate_data(), libMesh::ExplicitSystem::assemble_qoi(), libMesh::ExplicitSystem::assemble_qoi_derivative(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::ParameterVector::deep_copy(), libMesh::NumericVector< T >::dot(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_adjoint_solution(), libMesh::System::get_qoi_value(), libMesh::System::get_qoi_values(), libMesh::System::get_weighted_sensitivity_adjoint_solution(), libMesh::System::get_weighted_sensitivity_solution(), libMesh::QoISet::has_index(), libMesh::System::is_adjoint_already_solved(), libMesh::ImplicitSystem::matrix, libMesh::System::n_qois(), libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::ParameterVector::size(), libMesh::System::solution, libMesh::TOLERANCE, libMesh::ParameterVector::value_copy(), libMesh::SparseMatrix< T >::vector_mult(), libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve(), and libMesh::ImplicitSystem::weighted_sensitivity_solve().

{
  // We currently get partial derivatives via finite differencing
  const Real delta_p = TOLERANCE;

  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  // We'll use a single temporary vector for matrix-vector-vector products
  std::unique_ptr<NumericVector<Number>> tempvec = this->solution->zero_clone();

  const unsigned int Np = cast_int<unsigned int>
    (parameters_vec.size());
  const unsigned int Nq = this->n_qois();

  // For each quantity of interest q, the parameter sensitivity
  // Hessian is defined as q''_{kl} = {d^2 q}/{d p_k d p_l}.
  // Given a vector of parameter perturbation weights w_l, this
  // function evaluates the hessian-vector product sum_l(q''_{kl}*w_l)
  //
  // We calculate it from values and partial derivatives of the
  // quantity of interest function Q, solution u, adjoint solution z,
  // parameter sensitivity adjoint solutions z^l, and residual R, as:
  //
  // sum_l(q''_{kl}*w_l) =
  // sum_l(w_l * Q''_{kl}) + Q''_{uk}(u)*(sum_l(w_l u'_l)) -
  // R'_k(u, sum_l(w_l*z^l)) - R'_{uk}(u,z)*(sum_l(w_l u'_l) -
  // sum_l(w_l*R''_{kl}(u,z))
  //
  // See the adjoints model document for more details.

  // We first do an adjoint solve to get z for each quantity of
  // interest
  // if we haven't already or dont have an initial condition for the adjoint
  if (!this->is_adjoint_already_solved())
    {
      this->adjoint_solve(qoi_indices);
    }

  // Get ready to fill in sensitivities:
  sensitivities.allocate_data(qoi_indices, *this, parameters_vec);

  // We can't solve for all the solution sensitivities u'_l or for all
  // of the parameter sensitivity adjoint solutions z^l without
  // requiring O(Nq*Np) linear solves.  So we'll solve directly for their
  // weighted sum - this is just O(Nq) solves.

  // First solve for sum_l(w_l u'_l).
  this->weighted_sensitivity_solve(parameters_vec, vector);

  // Then solve for sum_l(w_l z^l).
  this->weighted_sensitivity_adjoint_solve(parameters_vec, vector, qoi_indices);

  for (unsigned int k=0; k != Np; ++k)
    {
      // We approximate sum_l(w_l * Q''_{kl}) with a central
      // differencing perturbation:
      // sum_l(w_l * Q''_{kl}) ~=
      // (Q(p + dp*w_l*e_l + dp*e_k) - Q(p - dp*w_l*e_l + dp*e_k) -
      // Q(p + dp*w_l*e_l - dp*e_k) + Q(p - dp*w_l*e_l - dp*e_k))/(4*dp^2)

      // The sum(w_l*R''_kl) term requires the same sort of perturbation,
      // and so we subtract it in at the same time:
      // sum_l(w_l * R''_{kl}) ~=
      // (R(p + dp*w_l*e_l + dp*e_k) - R(p - dp*w_l*e_l + dp*e_k) -
      // R(p + dp*w_l*e_l - dp*e_k) + R(p - dp*w_l*e_l - dp*e_k))/(4*dp^2)

      ParameterVector oldparameters, parameterperturbation;
      parameters_vec.deep_copy(oldparameters);
      vector.deep_copy(parameterperturbation);
      parameterperturbation *= delta_p;
      parameters_vec += parameterperturbation;

      Number old_parameter = *parameters_vec[k];

      *parameters_vec[k] = old_parameter + delta_p;
      this->assemble_qoi(qoi_indices);
      this->assembly(true, false, true);
      this->rhs->close();
      std::vector<Number> partial2q_term = this->get_qoi_values();
      std::vector<Number> partial2R_term(this->n_qois());
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          partial2R_term[i] = this->rhs->dot(this->get_adjoint_solution(i));

      *parameters_vec[k] = old_parameter - delta_p;
      this->assemble_qoi(qoi_indices);
      this->assembly(true, false, true);
      this->rhs->close();
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            partial2q_term[i] -= this->get_qoi_value(i);
            partial2R_term[i] -= this->rhs->dot(this->get_adjoint_solution(i));
          }

      oldparameters.value_copy(parameters_vec);
      parameterperturbation *= -1.0;
      parameters_vec += parameterperturbation;

      // Re-center old_parameter, which may be affected by vector
      old_parameter = *parameters_vec[k];

      *parameters_vec[k] = old_parameter + delta_p;
      this->assemble_qoi(qoi_indices);
      this->assembly(true, false, true);
      this->rhs->close();
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            partial2q_term[i] -= this->get_qoi_value(i);
            partial2R_term[i] -= this->rhs->dot(this->get_adjoint_solution(i));
          }

      *parameters_vec[k] = old_parameter - delta_p;
      this->assemble_qoi(qoi_indices);
      this->assembly(true, false, true);
      this->rhs->close();
      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            partial2q_term[i] += this->get_qoi_value(i);
            partial2R_term[i] += this->rhs->dot(this->get_adjoint_solution(i));
          }

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            partial2q_term[i] /= (4. * delta_p * delta_p);
            partial2R_term[i] /= (4. * delta_p * delta_p);
          }

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          sensitivities[i][k] = partial2q_term[i] - partial2R_term[i];

      // We get (partial q / partial u), R, and
      // (partial R / partial u) from the user, but centrally
      // difference to get q_uk, R_k, and R_uk terms:
      // (partial R / partial k)
      // R_k*sum(w_l*z^l) = (R(p+dp*e_k)*sum(w_l*z^l) - R(p-dp*e_k)*sum(w_l*z^l))/(2*dp)
      // (partial^2 q / partial u partial k)
      // q_uk = (q_u(p+dp*e_k) - q_u(p-dp*e_k))/(2*dp)
      // (partial^2 R / partial u partial k)
      // R_uk*z*sum(w_l*u'_l) = (R_u(p+dp*e_k)*z*sum(w_l*u'_l) - R_u(p-dp*e_k)*z*sum(w_l*u'_l))/(2*dp)

      // To avoid creating Nq temporary vectors for q_uk or R_uk, we add
      // subterms to the sensitivities output one by one.
      //
      // FIXME: this is probably a bad order of operations for
      // controlling floating point error.

      *parameters_vec[k] = old_parameter + delta_p;
      this->assembly(true, true);
      this->rhs->close();
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      this->matrix->vector_mult(*tempvec, this->get_weighted_sensitivity_solution());

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            this->get_adjoint_rhs(i).close();
            sensitivities[i][k] += (this->get_adjoint_rhs(i).dot(this->get_weighted_sensitivity_solution()) -
                                    this->rhs->dot(this->get_weighted_sensitivity_adjoint_solution(i)) -
                                    this->get_adjoint_solution(i).dot(*tempvec)) / (2.*delta_p);
          }

      *parameters_vec[k] = old_parameter - delta_p;
      this->assembly(true, true);
      this->rhs->close();
      this->matrix->close();
      this->assemble_qoi_derivative(qoi_indices,
                                    /* include_liftfunc = */ true,
                                    /* apply_constraints = */ false);

      this->matrix->vector_mult(*tempvec, this->get_weighted_sensitivity_solution());

      for (unsigned int i=0; i != Nq; ++i)
        if (qoi_indices.has_index(i))
          {
            this->get_adjoint_rhs(i).close();
            sensitivities[i][k] += (-this->get_adjoint_rhs(i).dot(this->get_weighted_sensitivity_solution()) +
                                    this->rhs->dot(this->get_weighted_sensitivity_adjoint_solution(i)) +
                                    this->get_adjoint_solution(i).dot(*tempvec)) / (2.*delta_p);
          }
    }

  // All parameters have been reset.
  // Don't leave the qoi or system changed - principle of least
  // surprise.
  this->assembly(true, true);
  this->rhs->close();
  this->matrix->close();
  this->assemble_qoi(qoi_indices);
}

qoi_parameter_sensitivity()

void libMesh::System::qoi_parameter_sensitivity ( const QoISet &  qoi_indices, const ParameterVector &  parameters, SensitivityData &  sensitivities  )

virtualinherited

Solves for the derivative of each of the system's quantities of interest q in qoi[qoi_indices] with respect to each parameter in parameters, placing the result for qoi i and parameter j into sensitivities[i][j].

Note

parameters is a const vector, not a vector-of-const; parameter values in this vector need to be mutable for finite differencing to work.

Automatically chooses the forward method for problems with more quantities of interest than parameters, or the adjoint method otherwise.

This method is only usable in derived classes which override an implementation.

Definition at line 602 of file system.C.

References libMesh::System::adjoint_qoi_parameter_sensitivity(), libMesh::System::forward_qoi_parameter_sensitivity(), libMesh::ParameterVector::size(), and libMesh::QoISet::size().

{
  // Forward sensitivities are more efficient for Nq > Np
  if (qoi_indices.size(*this) > parameters_vec.size())
    forward_qoi_parameter_sensitivity(qoi_indices, parameters_vec, sensitivities);
  // Adjoint sensitivities are more efficient for Np > Nq,
  // and an adjoint may be more reusable than a forward
  // solution sensitivity in the Np == Nq case.
  else
    adjoint_qoi_parameter_sensitivity(qoi_indices, parameters_vec, sensitivities);
}

re_update()

void libMesh::System::re_update ( )

virtualinherited

Re-update the local values when the mesh has changed.

This method takes the data updated by update() and makes it up-to-date on the current mesh.

Reimplemented in libMesh::TransientSystem< RBConstruction >.

Definition at line 533 of file system.C.

References libMesh::System::current_local_solution, libMesh::System::get_dof_map(), libMesh::DofMap::get_send_list(), libMesh::System::n_vars(), and libMesh::System::solution.

{
  parallel_object_only();

  // If this system is empty... don't do anything!
  if (!this->n_vars())
    return;

  const std::vector<dof_id_type> & send_list = this->get_dof_map().get_send_list ();

  // Check sizes
  libmesh_assert_equal_to (current_local_solution->size(), solution->size());
  // Not true with ghosted vectors
  // libmesh_assert_equal_to (current_local_solution->local_size(), solution->size());
  // libmesh_assert (!send_list.empty());
  libmesh_assert_less_equal (send_list.size(), solution->size());

  // Create current_local_solution from solution.  This will
  // put a local copy of solution into current_local_solution.
  solution->localize (*current_local_solution, send_list);
}

read_header()

void libMesh::System::read_header ( Xdr &  io, std::string_view  version, const bool  read_header = true, const bool  read_additional_data = true, const bool  read_legacy_format = false  )

inherited

Reads the basic data header for this System.

Definition at line 97 of file system_io.C.

References libMesh::System::_additional_data_written, libMesh::System::_written_var_indices, libMesh::System::add_variable(), libMesh::System::add_vector(), TIMPI::Communicator::broadcast(), libMesh::System::clear(), libMesh::ParallelObject::comm(), libMesh::Xdr::data(), libMesh::FEType::family, libMesh::System::get_mesh(), libMesh::OrderWrapper::get_order(), libMesh::FEType::inf_map, libMesh::libmesh_assert(), libMesh::MeshBase::mesh_dimension(), libMesh::MONOMIAL, libMesh::on_command_line(), libMesh::FEType::order, libMesh::out, libMesh::ParallelObject::processor_id(), libMesh::FEType::radial_family, libMesh::FEType::radial_order, libMesh::Xdr::reading(), libMesh::System::variable_number(), libMesh::Xdr::version(), and libMesh::XYZ.

Referenced by libMesh::EquationSystems::read(), and libMesh::RBEvaluation::read_in_vectors_from_multiple_files().

{
  // This method implements the input of a
  // System object, embedded in the output of
  // an EquationSystems<T_sys>.  This warrants some
  // documentation.  The output file essentially
  // consists of 5 sections:
  //
  // for this system
  //
  //   5.) The number of variables in the system (unsigned int)
  //
  //   for each variable in the system
  //
  //     6.) The name of the variable (string)
  //
  //     6.1.) Variable subdomains
  //
  //     7.) Combined in an FEType:
  //         - The approximation order(s) of the variable
  //           (Order Enum, cast to int/s)
  //         - The finite element family/ies of the variable
  //           (FEFamily Enum, cast to int/s)
  //
  //   end variable loop
  //
  //   8.) The number of additional vectors (unsigned int),
  //
  //     for each additional vector in the system object
  //
  //     9.) the name of the additional vector  (string)
  //
  // end system
  libmesh_assert (io.reading());

  // Possibly clear data structures and start from scratch.
  if (read_header_in)
    this->clear ();

  // Figure out if we need to read infinite element information.
  // This will be true if the version string contains " with infinite elements"
  const bool read_ifem_info =
    (version.rfind(" with infinite elements") < version.size()) ||
    libMesh::on_command_line ("--read-ifem-systems");


  {
    // 5.)
    // Read the number of variables in the system
    unsigned int nv=0;
    if (this->processor_id() == 0)
      io.data (nv);
    this->comm().broadcast(nv);

    _written_var_indices.clear();
    _written_var_indices.resize(nv, 0);

    for (unsigned int var=0; var<nv; var++)
      {
        // 6.)
        // Read the name of the var-th variable
        std::string var_name;
        if (this->processor_id() == 0)
          io.data (var_name);
        this->comm().broadcast(var_name);

        // 6.1.)
        std::set<subdomain_id_type> domains;
        if (io.version() >= LIBMESH_VERSION_ID(0,7,2))
          {
            std::vector<subdomain_id_type> domain_array;
            if (this->processor_id() == 0)
              io.data (domain_array);
            for (const auto & id : domain_array)
              domains.insert(id);
          }
        this->comm().broadcast(domains);

        // 7.)
        // Read the approximation order(s) of the var-th variable
        int order=0;
        if (this->processor_id() == 0)
          io.data (order);
        this->comm().broadcast(order);


        // do the same for infinite element radial_order
        int rad_order=0;
        if (read_ifem_info)
          {
            if (this->processor_id() == 0)
              io.data(rad_order);
            this->comm().broadcast(rad_order);
          }

        // Read the finite element type of the var-th variable
        int fam=0;
        if (this->processor_id() == 0)
          io.data (fam);
        this->comm().broadcast(fam);
        FEType type;
        type.order  = static_cast<Order>(order);
        type.family = static_cast<FEFamily>(fam);

        // Check for incompatibilities.  The shape function indexing was
        // changed for the monomial and xyz finite element families to
        // simplify extension to arbitrary p.  The consequence is that
        // old restart files will not be read correctly.  This is expected
        // to be an unlikely occurrence, but catch it anyway.
        if (read_legacy_format)
          if ((type.family == MONOMIAL || type.family == XYZ) &&
              ((type.order.get_order() > 2 && this->get_mesh().mesh_dimension() == 2) ||
               (type.order.get_order() > 1 && this->get_mesh().mesh_dimension() == 3)))
            {
              libmesh_here();
              libMesh::out << "*****************************************************************\n"
                           << "* WARNING: reading a potentially incompatible restart file!!!   *\n"
                           << "*  contact [email protected] for more details *\n"
                           << "*****************************************************************"
                           << std::endl;
            }

        // Read additional information for infinite elements
        int radial_fam=0;
        int i_map=0;
        if (read_ifem_info)
          {
            if (this->processor_id() == 0)
              io.data (radial_fam);
            this->comm().broadcast(radial_fam);
            if (this->processor_id() == 0)
              io.data (i_map);
            this->comm().broadcast(i_map);
          }

#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS

        type.radial_order  = static_cast<Order>(rad_order);
        type.radial_family = static_cast<FEFamily>(radial_fam);
        type.inf_map       = static_cast<InfMapType>(i_map);

#endif

        if (read_header_in)
          {
            if (domains.empty())
              _written_var_indices[var] = this->add_variable (var_name, type);
            else
              _written_var_indices[var] = this->add_variable (var_name, type, &domains);
          }
        else
          _written_var_indices[var] = this->variable_number(var_name);
      }
  }

  // 8.)
  // Read the number of additional vectors.
  unsigned int nvecs=0;
  if (this->processor_id() == 0)
    io.data (nvecs);
  this->comm().broadcast(nvecs);

  // If nvecs > 0, this means that write_additional_data
  // was true when this file was written.  We will need to
  // make use of this fact later.
  this->_additional_data_written = nvecs;

  for (unsigned int vec=0; vec<nvecs; vec++)
    {
      // 9.)
      // Read the name of the vec-th additional vector
      std::string vec_name;
      if (this->processor_id() == 0)
        io.data (vec_name);
      this->comm().broadcast(vec_name);
      if (io.version() >= LIBMESH_VERSION_ID(1,7,0))
        {
          int vec_projection = 0;
          if (this->processor_id() == 0)
            io.data (vec_projection);
          this->comm().broadcast(vec_projection);
          int vec_type;
          if (this->processor_id() == 0)
            io.data (vec_type);
          this->comm().broadcast(vec_type);

          if (read_additional_data)
            this->add_vector(vec_name, bool(vec_projection), ParallelType(vec_type));
        }
      else if (read_additional_data)
          // Systems now can handle adding post-initialization vectors
          //  libmesh_assert(this->_can_add_vectors);
          // Some systems may have added their own vectors already
          //  libmesh_assert_equal_to (this->_vectors.count(vec_name), 0);
        this->add_vector(vec_name);
    }
}

read_legacy_data()

void libMesh::System::read_legacy_data ( Xdr &  io, const bool  read_additional_data = true  )

inherited

Reads additional data, namely vectors, for this System.

Deprecated:

The ability to read XDR data files in the old (aka "legacy") XDR format has been deprecated for many years, this capability may soon disappear altogether.

Definition at line 302 of file system_io.C.

References libMesh::System::_additional_data_written, libMesh::System::_vectors, libMesh::System::_written_var_indices, TIMPI::Communicator::broadcast(), libMesh::ParallelObject::comm(), libMesh::Xdr::data(), libMesh::System::get_mesh(), libMesh::DofObject::invalid_id, libMesh::libmesh_assert(), libMesh::make_range(), libMesh::System::n_dofs(), libMesh::System::n_vars(), libMesh::System::number(), libMesh::ParallelObject::processor_id(), libMesh::Xdr::reading(), libMesh::System::solution, and libMesh::zero.

{
  libmesh_deprecated();

  // This method implements the output of the vectors
  // contained in this System object, embedded in the
  // output of an EquationSystems<T_sys>.
  //
  //   10.) The global solution vector, re-ordered to be node-major
  //       (More on this later.)
  //
  //      for each additional vector in the object
  //
  //      11.) The global additional vector, re-ordered to be
  //           node-major (More on this later.)
  libmesh_assert (io.reading());

  // directly-read and reordered buffers, declared here for reuse
  // without heap juggling.
  std::vector<Number> global_vector;
  std::vector<Number> reordered_vector;

  auto reorder_vector_into =
    [this, &global_vector, &reordered_vector]
    (NumericVector<Number> & vec)
  {
    this->comm().broadcast(global_vector);

    // If we have been reading multiple vectors, they should all be
    // the same size.
    libmesh_assert (reordered_vector.empty() ||
                    reordered_vector.size() == global_vector.size());

    // Remember that the stored vector is node-major.
    // We need to put it into whatever application-specific
    // ordering we may have using the dof_map.
    reordered_vector.resize(global_vector.size());

    //libMesh::out << "global_vector.size()=" << global_vector.size() << std::endl;
    //libMesh::out << "this->n_dofs()=" << this->n_dofs() << std::endl;

    libmesh_assert_equal_to (global_vector.size(), this->n_dofs());

    dof_id_type cnt=0;

    const unsigned int sys = this->number();
    const unsigned int nv  = cast_int<unsigned int>
      (this->_written_var_indices.size());
    libmesh_assert_less_equal (nv, this->n_vars());

    for (unsigned int data_var=0; data_var<nv; data_var++)
      {
        const unsigned int var = _written_var_indices[data_var];

        // First reorder the nodal DOF values
        for (auto & node : this->get_mesh().node_ptr_range())
          for (auto index : make_range(node->n_comp(sys,var)))
            {
              libmesh_assert_not_equal_to (node->dof_number(sys, var, index),
                                           DofObject::invalid_id);

              libmesh_assert_less (cnt, global_vector.size());

              reordered_vector[node->dof_number(sys, var, index)] =
                global_vector[cnt++];
            }

        // Then reorder the element DOF values
        for (auto & elem : this->get_mesh().active_element_ptr_range())
          for (auto index : make_range(elem->n_comp(sys,var)))
            {
              libmesh_assert_not_equal_to (elem->dof_number(sys, var, index),
                                           DofObject::invalid_id);

              libmesh_assert_less (cnt, global_vector.size());

              reordered_vector[elem->dof_number(sys, var, index)] =
                global_vector[cnt++];
            }
      }

    // use the overloaded operator=(std::vector) to assign the values
    vec = reordered_vector;
  };

  // 10.)
  // Read and set the solution vector
  if (this->processor_id() == 0)
    io.data (global_vector);
  reorder_vector_into(*(this->solution));

  // For each additional vector, simply go through the list.
  // ONLY attempt to do this IF additional data was actually
  // written to the file for this system (controlled by the
  // _additional_data_written flag).
  if (this->_additional_data_written)
    {
      const std::size_t nvecs = this->_vectors.size();

      // If the number of additional vectors written is non-zero, and
      // the number of additional vectors we have is non-zero, and
      // they don't match, then something is wrong and we can't be
      // sure we're reading data into the correct places.
      if (read_additional_data && nvecs &&
          nvecs != this->_additional_data_written)
        libmesh_error_msg
          ("Additional vectors in file do not match system");

      auto pos = this->_vectors.begin();

      for (std::size_t i = 0; i != this->_additional_data_written; ++i)
        {
          // 11.)
          // Read the values of the vec-th additional vector.
          // Prior do _not_ clear, but fill with zero, since the
          // additional vectors _have_ to have the same size
          // as the solution vector
          std::fill (global_vector.begin(), global_vector.end(), libMesh::zero);

          if (this->processor_id() == 0)
            io.data (global_vector);

          // If read_additional_data==true and we have additional vectors,
          // then we will keep this vector data; otherwise we are going to
          // throw it away.
          if (read_additional_data && nvecs)
            {
              std::fill (reordered_vector.begin(),
                         reordered_vector.end(),
                         libMesh::zero);

              reorder_vector_into(*(pos->second));
            }

          // If we've got vectors then we need to be iterating through
          // those too
          if (pos != this->_vectors.end())
            ++pos;
        }
    } // end if (_additional_data_written)
}

read_parallel_data() [1/2]

template<typename InValType >

void libMesh::System::read_parallel_data ( Xdr &  io, const bool  read_additional_data  )

inherited

Reads additional data, namely vectors, for this System.

This method may safely be called on a distributed-memory mesh. This method will read an individual file for each processor in the simulation where the local solution components for that processor are stored.

This method implements the output of the vectors contained in this System object, embedded in the output of an EquationSystems<T_sys>.

9.) The global solution vector, re-ordered to be node-major (More on this later.)

for each additional vector in the object

10.) The global additional vector, re-ordered to be node-major (More on this later.)

Note that the actual IO is handled through the Xdr class (to be renamed later?) which provides a uniform interface to both the XDR (eXternal Data Representation) interface and standard ASCII output. Thus this one section of code will read XDR or ASCII files with no changes.

Definition at line 449 of file system_io.C.

References libMesh::System::_additional_data_written, libMesh::System::_vectors, libMesh::System::_written_var_indices, libMesh::Xdr::data(), libMesh::FEType::family, libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::DofObject::invalid_id, libMesh::Xdr::is_open(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::ParallelObject::n_processors(), libMesh::System::n_vars(), libMesh::System::number(), libMesh::ParallelObject::processor_id(), libMesh::Xdr::reading(), libMesh::SCALAR, libMesh::DofMap::SCALAR_dof_indices(), libMesh::System::solution, libMesh::Variable::type(), and libMesh::System::variable().

{
  // PerfLog pl("IO Performance",false);
  // pl.push("read_parallel_data");
  dof_id_type total_read_size = 0;

  libmesh_assert (io.reading());
  libmesh_assert (io.is_open());

  // build the ordered nodes and element maps.
  // when writing/reading parallel files we need to iterate
  // over our nodes/elements in order of increasing global id().
  // however, this is not guaranteed to be ordering we obtain
  // by using the node_iterators/element_iterators directly.
  // so build a set, sorted by id(), that provides the ordering.
  // further, for memory economy build the set but then transfer
  // its contents to vectors, which will be sorted.
  std::vector<const DofObject *> ordered_nodes, ordered_elements;
  {
    std::set<const DofObject *, CompareDofObjectsByID>
      ordered_nodes_set (this->get_mesh().local_nodes_begin(),
                         this->get_mesh().local_nodes_end());

    ordered_nodes.insert(ordered_nodes.end(),
                         ordered_nodes_set.begin(),
                         ordered_nodes_set.end());
  }
  {
    std::set<const DofObject *, CompareDofObjectsByID>
      ordered_elements_set (this->get_mesh().local_elements_begin(),
                            this->get_mesh().local_elements_end());

    ordered_elements.insert(ordered_elements.end(),
                            ordered_elements_set.begin(),
                            ordered_elements_set.end());
  }

  //  std::vector<Number> io_buffer;
  std::vector<InValType> io_buffer;

  // 9.)
  //
  // Actually read the solution components
  // for the ith system to disk
  io.data(io_buffer);

  total_read_size += cast_int<dof_id_type>(io_buffer.size());

  const unsigned int sys_num = this->number();
  const unsigned int nv      = cast_int<unsigned int>
    (this->_written_var_indices.size());
  libmesh_assert_less_equal (nv, this->n_vars());

  dof_id_type cnt=0;

  // Loop over each non-SCALAR variable and each node, and read out the value.
  for (unsigned int data_var=0; data_var<nv; data_var++)
    {
      const unsigned int var = _written_var_indices[data_var];
      if (this->variable(var).type().family != SCALAR)
        {
          // First read the node DOF values
          for (const auto & node : ordered_nodes)
            for (auto comp : make_range(node->n_comp(sys_num,var)))
              {
                libmesh_assert_not_equal_to (node->dof_number(sys_num, var, comp),
                                             DofObject::invalid_id);
                libmesh_assert_less (cnt, io_buffer.size());
                this->solution->set(node->dof_number(sys_num, var, comp), io_buffer[cnt++]);
              }

          // Then read the element DOF values
          for (const auto & elem : ordered_elements)
            for (auto comp : make_range(elem->n_comp(sys_num,var)))
              {
                libmesh_assert_not_equal_to (elem->dof_number(sys_num, var, comp),
                                             DofObject::invalid_id);
                libmesh_assert_less (cnt, io_buffer.size());
                this->solution->set(elem->dof_number(sys_num, var, comp), io_buffer[cnt++]);
              }
        }
    }

  // Finally, read the SCALAR variables on the last processor
  for (unsigned int data_var=0; data_var<nv; data_var++)
    {
      const unsigned int var = _written_var_indices[data_var];
      if (this->variable(var).type().family == SCALAR)
        {
          if (this->processor_id() == (this->n_processors()-1))
            {
              const DofMap & dof_map = this->get_dof_map();
              std::vector<dof_id_type> SCALAR_dofs;
              dof_map.SCALAR_dof_indices(SCALAR_dofs, var);

              for (auto dof : SCALAR_dofs)
                this->solution->set(dof, io_buffer[cnt++]);
            }
        }
    }

  // And we're done setting solution entries
  this->solution->close();

  // For each additional vector, simply go through the list.
  // ONLY attempt to do this IF additional data was actually
  // written to the file for this system (controlled by the
  // _additional_data_written flag).
  if (this->_additional_data_written)
    {
      const std::size_t nvecs = this->_vectors.size();

      // If the number of additional vectors written is non-zero, and
      // the number of additional vectors we have is non-zero, and
      // they don't match, then something is wrong and we can't be
      // sure we're reading data into the correct places.
      if (read_additional_data && nvecs &&
          nvecs != this->_additional_data_written)
        libmesh_error_msg
          ("Additional vectors in file do not match system");

      auto pos = _vectors.begin();

      for (std::size_t i = 0; i != this->_additional_data_written; ++i)
        {
          cnt=0;
          io_buffer.clear();

          // 10.)
          //
          // Actually read the additional vector components
          // for the ith system from disk
          io.data(io_buffer);

          total_read_size += cast_int<dof_id_type>(io_buffer.size());

          // If read_additional_data==true and we have additional vectors,
          // then we will keep this vector data; otherwise we are going to
          // throw it away.
          if (read_additional_data && nvecs)
            {
              // Loop over each non-SCALAR variable and each node, and read out the value.
              for (unsigned int data_var=0; data_var<nv; data_var++)
                {
                  const unsigned int var = _written_var_indices[data_var];
                  if (this->variable(var).type().family != SCALAR)
                    {
                      // First read the node DOF values
                      for (const auto & node : ordered_nodes)
                        for (auto comp : make_range(node->n_comp(sys_num,var)))
                          {
                            libmesh_assert_not_equal_to (node->dof_number(sys_num, var, comp),
                                                         DofObject::invalid_id);
                            libmesh_assert_less (cnt, io_buffer.size());
                            pos->second->set(node->dof_number(sys_num, var, comp), io_buffer[cnt++]);
                          }

                      // Then read the element DOF values
                      for (const auto & elem : ordered_elements)
                        for (auto comp : make_range(elem->n_comp(sys_num,var)))
                          {
                            libmesh_assert_not_equal_to (elem->dof_number(sys_num, var, comp),
                                                         DofObject::invalid_id);
                            libmesh_assert_less (cnt, io_buffer.size());
                            pos->second->set(elem->dof_number(sys_num, var, comp), io_buffer[cnt++]);
                          }
                    }
                }

              // Finally, read the SCALAR variables on the last processor
              for (unsigned int data_var=0; data_var<nv; data_var++)
                {
                  const unsigned int var = _written_var_indices[data_var];
                  if (this->variable(var).type().family == SCALAR)
                    {
                      if (this->processor_id() == (this->n_processors()-1))
                        {
                          const DofMap & dof_map = this->get_dof_map();
                          std::vector<dof_id_type> SCALAR_dofs;
                          dof_map.SCALAR_dof_indices(SCALAR_dofs, var);

                          for (auto dof : SCALAR_dofs)
                            pos->second->set(dof, io_buffer[cnt++]);
                        }
                    }
                }

              // And we're done setting entries for this variable
              pos->second->close();
            }

          // If we've got vectors then we need to be iterating through
          // those too
          if (pos != this->_vectors.end())
            ++pos;
        }
    }

  // const Real
  //   dt   = pl.get_elapsed_time(),
  //   rate = total_read_size*sizeof(Number)/dt;

  // libMesh::err << "Read " << total_read_size << " \"Number\" values\n"
  //     << " Elapsed time = " << dt << '\n'
  //     << " Rate = " << rate/1.e6 << "(MB/sec)\n\n";

  // pl.pop("read_parallel_data");
}

read_parallel_data() [2/2]

template LIBMESH_EXPORT void libMesh::System::read_parallel_data< Real > ( Xdr &  io, const bool  read_additional_data  )

inlineinherited

Non-templated version for backward compatibility.

Reads additional data, namely vectors, for this System. This method may safely be called on a distributed-memory mesh. This method will read an individual file for each processor in the simulation where the local solution components for that processor are stored.

Definition at line 1350 of file system.h.

  { read_parallel_data<Number>(io, read_additional_data); }

read_serialized_data() [1/2]

template<typename InValType >

void libMesh::System::read_serialized_data ( Xdr &  io, const bool  read_additional_data = true  )

inherited

Reads additional data, namely vectors, for this System.

This method may safely be called on a distributed-memory mesh.

Definition at line 680 of file system_io.C.

References libMesh::System::_additional_data_written, libMesh::System::_vectors, libMesh::ParallelObject::processor_id(), and libMesh::System::solution.

Referenced by libMesh::TransientRBConstruction::initialize_truth(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), and libMesh::RBConstruction::read_riesz_representors_from_files().

{
  // This method implements the input of the vectors
  // contained in this System object, embedded in the
  // output of an EquationSystems<T_sys>.
  //
  //   10.) The global solution vector, re-ordered to be node-major
  //       (More on this later.)
  //
  //      for each additional vector in the object
  //
  //      11.) The global additional vector, re-ordered to be
  //          node-major (More on this later.)
  parallel_object_only();
  std::string comment;

  // PerfLog pl("IO Performance",false);
  // pl.push("read_serialized_data");
  // std::size_t total_read_size = 0;

  // 10.)
  // Read the global solution vector
  {
    // total_read_size +=
    this->read_serialized_vector<InValType>(io, this->solution.get());

    // get the comment
    if (this->processor_id() == 0)
      io.comment (comment);
  }

  // 11.)
  // Only read additional vectors if data is available, and only use
  // that data to fill our vectors if the user requested it.
  if (this->_additional_data_written)
    {
      const std::size_t nvecs = this->_vectors.size();

      // If the number of additional vectors written is non-zero, and
      // the number of additional vectors we have is non-zero, and
      // they don't match, then we can't read additional vectors
      // and be sure we're reading data into the correct places.
      if (read_additional_data && nvecs &&
          nvecs != this->_additional_data_written)
        libmesh_error_msg
          ("Additional vectors in file do not match system");

      auto pos = _vectors.begin();

      for (std::size_t i = 0; i != this->_additional_data_written; ++i)
        {
          // Read data, but only put it into a vector if we've been
          // asked to and if we have a corresponding vector to read.

          // total_read_size +=
          this->read_serialized_vector<InValType>
            (io, (read_additional_data && nvecs) ? pos->second.get() : nullptr);

          // get the comment
          if (this->processor_id() == 0)
            io.comment (comment);


          // If we've got vectors then we need to be iterating through
          // those too
          if (pos != this->_vectors.end())
            ++pos;
        }
    }

  // const Real
  //   dt   = pl.get_elapsed_time(),
  //   rate = total_read_size*sizeof(Number)/dt;

  // libMesh::out << "Read " << total_read_size << " \"Number\" values\n"
  //     << " Elapsed time = " << dt << '\n'
  //     << " Rate = " << rate/1.e6 << "(MB/sec)\n\n";

  // pl.pop("read_serialized_data");
}

read_serialized_data() [2/2]

template LIBMESH_EXPORT void libMesh::System::read_serialized_data< Real > ( Xdr &  io, const bool  read_additional_data = true  )

inlineinherited

Non-templated version for backward compatibility.

Reads additional data, namely vectors, for this System. This method may safely be called on a distributed-memory mesh.

Definition at line 1308 of file system.h.

  { read_serialized_data<Number>(io, read_additional_data); }

read_serialized_vectors() [1/2]

template<typename InValType >

std::size_t libMesh::System::read_serialized_vectors ( Xdr &  io, const std::vector< NumericVector< Number > *> &  vectors  ) const

inherited

Read a number of identically distributed vectors.

This method allows for optimization for the multiple vector case by only communicating the metadata once.

Definition at line 2165 of file system_io.C.

References libMesh::Xdr::data(), libMesh::System::get_mesh(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::MeshTools::n_elem(), libMesh::MeshBase::n_elem(), n_nodes, libMesh::MeshBase::n_nodes(), libMesh::System::n_vars(), libMesh::ParallelObject::processor_id(), libMesh::System::read_SCALAR_dofs(), libMesh::System::read_serialized_blocked_dof_objects(), libMesh::Xdr::reading(), libMesh::SCALAR, and libMesh::System::variable().

Referenced by libMesh::RBEvaluation::read_in_vectors_from_multiple_files().

{
  parallel_object_only();

  // Error checking
  // #ifndef NDEBUG
  //   // In parallel we better be reading a parallel vector -- if not
  //   // we will not set all of its components below!!
  //   if (this->n_processors() > 1)
  //     {
  //       libmesh_assert (vec.type() == PARALLEL ||
  //       vec.type() == GHOSTED);
  //     }
  // #endif

  libmesh_assert (io.reading());

  if (this->processor_id() == 0)
    {
      // sizes
      unsigned int num_vecs=0;
      dof_id_type vector_length=0;

      // Get the number of vectors
      io.data(num_vecs);
      // Get the buffer size
      io.data(vector_length);

      libmesh_error_msg_if
        (num_vecs != vectors.size(),
         "Xdr file header declares " << num_vecs << " vectors, but we were asked to read " << vectors.size());

      if (num_vecs != 0)
        {
          libmesh_error_msg_if (vectors[0] == nullptr, "vectors[0] should not be null");
          libmesh_error_msg_if (vectors[0]->size() != vector_length, "Inconsistent vector sizes");
        }
    }

  // no need to actually communicate these.
  // this->comm().broadcast(num_vecs);
  // this->comm().broadcast(vector_length);

  // Cache these - they are not free!
  const dof_id_type
    n_nodes = this->get_mesh().n_nodes(),
    n_elem  = this->get_mesh().n_elem();

  std::size_t read_length = 0;

  //---------------------------------
  // Collect the values for all nodes
  read_length +=
    this->read_serialized_blocked_dof_objects (n_nodes,
                                               this->get_mesh().local_nodes_begin(),
                                               this->get_mesh().local_nodes_end(),
                                               InValType(),
                                               io,
                                               vectors);

  //------------------------------------
  // Collect the values for all elements
  read_length +=
    this->read_serialized_blocked_dof_objects (n_elem,
                                               this->get_mesh().local_elements_begin(),
                                               this->get_mesh().local_elements_end(),
                                               InValType(),
                                               io,
                                               vectors);

  //-------------------------------------------
  // Finally loop over all the SCALAR variables
  for (NumericVector<Number> * vec : vectors)
    for (auto var : make_range(this->n_vars()))
      if (this->variable(var).type().family == SCALAR)
        {
          libmesh_assert_not_equal_to (vec, 0);

          read_length +=
            this->read_SCALAR_dofs (var, io, vec);
        }

  //---------------------------------------
  // last step - must close all the vectors
  for (NumericVector<Number> * vec : vectors)
    {
      libmesh_assert_not_equal_to (vec, 0);
      vec->close();
    }

  return read_length;
}

read_serialized_vectors() [2/2]

template LIBMESH_EXPORT std::size_t libMesh::System::read_serialized_vectors< Real > ( Xdr &  io, const std::vector< NumericVector< Number > *> &  vectors  ) const

inlineinherited

Non-templated version for backward compatibility.

Read a number of identically distributed vectors. This method allows for optimization for the multiple vector case by only communicating the metadata once.

Definition at line 1328 of file system.h.

  { return read_serialized_vectors<Number>(io, vectors); }

reinit()

void libMesh::DifferentiableSystem::reinit ( )

overridevirtualinherited

Reinitializes the member data fields associated with the system, so that, e.g., assemble() may be used.

Reimplemented from libMesh::System.

Definition at line 82 of file diff_system.C.

References libMesh::libmesh_assert(), libMesh::System::reinit(), and libMesh::DifferentiableSystem::time_solver.

{
  Parent::reinit();

  libmesh_assert(time_solver.get());
  libmesh_assert_equal_to (&(time_solver->system()), this);

  time_solver->reinit();
}

reinit_constraints()

void libMesh::System::reinit_constraints ( )

virtualinherited

Reinitializes the constraints for this system.

Also prepares the send_list, whether or not constraints have changed.

Definition at line 495 of file system.C.

References libMesh::System::_mesh, libMesh::DofMap::create_dof_constraints(), libMesh::System::get_dof_map(), libMesh::on_command_line(), libMesh::out, libMesh::DofMap::prepare_send_list(), libMesh::DofMap::print_dof_constraints(), libMesh::DofMap::process_constraints(), libMesh::System::time, and libMesh::System::user_constrain().

Referenced by libMesh::EquationSystems::allgather(), libMesh::System::init_data(), libMesh::PetscDMWrapper::init_petscdm(), and libMesh::EquationSystems::reinit_solutions().

{
  parallel_object_only();

#ifdef LIBMESH_ENABLE_CONSTRAINTS
  get_dof_map().create_dof_constraints(_mesh, this->time);
  user_constrain();
  get_dof_map().process_constraints(_mesh);
  if (libMesh::on_command_line ("--print-constraints"))
    get_dof_map().print_dof_constraints(libMesh::out);
#endif
  get_dof_map().prepare_send_list();
}

reinit_mesh()

void libMesh::System::reinit_mesh ( )

virtualinherited

Reinitializes the system with a new mesh.

Definition at line 301 of file system.C.

References libMesh::System::_basic_system_only, libMesh::System::init_data(), libMesh::System::n_vars(), and libMesh::System::user_initialization().

Referenced by libMesh::System::init().

{
  parallel_object_only();

  // First initialize any required data:
  // either only the basic System data
  if (_basic_system_only)
    System::init_data();
  // or all the derived class' data too
  else
    this->init_data();

  // If no variables have been added to this system
  // don't do anything
  if (!this->n_vars())
    return;

  // Then call the user-provided initialization function
  this->user_initialization();

}

release_linear_solver()

void libMesh::ImplicitSystem::release_linear_solver ( LinearSolver< Number > *  ) const

virtualinherited

Currently a no-op.

Deprecated:

This function no longer needs to be called, since get_linear_solver() no longer returns a heap-allocated dumb pointer.

Definition at line 1248 of file implicit_system.C.

{
  // This function was originally paired with get_linear_solver()
  // calls when that returned a dumb pointer which needed to be
  // cleaned up. Since get_linear_solver() now just returns a pointer
  // to a LinearSolver object managed by this class, this function no
  // longer needs to do any cleanup.
  libmesh_deprecated();
}

remove_matrix()

void libMesh::System::remove_matrix ( std::string_view  mat_name )

inherited

Removes the additional matrix mat_name from this system.

Definition at line 1089 of file system.C.

References libMesh::System::_matrices.

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  if (const auto pos = _matrices.find(mat_name);
      pos != _matrices.end())
    _matrices.erase(pos); // erase()'d entries are destroyed
}

remove_vector()

void libMesh::System::remove_vector ( std::string_view  vec_name )

inherited

Removes the additional vector vec_name from this system.

Definition at line 873 of file system.C.

References libMesh::System::_vector_is_adjoint, libMesh::System::_vector_projections, libMesh::System::_vectors, and libMesh::libmesh_assert().

Referenced by libMesh::AdjointRefinementEstimator::estimate_error(), and libMesh::UnsteadySolver::integrate_adjoint_sensitivity().

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  if (const auto pos = _vectors.find(vec_name);
      pos != _vectors.end())
    {
      _vectors.erase(pos);
      auto proj_it = _vector_projections.find(vec_name);
      libmesh_assert(proj_it != _vector_projections.end());
      _vector_projections.erase(proj_it);

      auto adj_it = _vector_is_adjoint.find(vec_name);
      libmesh_assert(adj_it != _vector_is_adjoint.end());
      _vector_is_adjoint.erase(adj_it);
    }
}

request_matrix() [1/2]

const SparseMatrix< Number > * libMesh::System::request_matrix ( std::string_view  mat_name ) const

inherited

Returns

A const pointer to this system's additional matrix named mat_name, or nullptr if no matrix by that name exists.

Definition at line 1100 of file system.C.

References libMesh::System::_matrices.

Referenced by libMesh::EigenSystem::has_matrix_A(), libMesh::EigenSystem::has_matrix_B(), libMesh::EigenSystem::has_precond_matrix(), libMesh::ImplicitSystem::sensitivity_solve(), libMesh::NewtonSolver::solve(), and libMesh::LinearImplicitSystem::solve().

{
  if (const auto pos = _matrices.find(mat_name);
      pos != _matrices.end())
    return pos->second.get();

  // Otherwise, mat_name does not exist
  return nullptr;
}

request_matrix() [2/2]

SparseMatrix< Number > * libMesh::System::request_matrix ( std::string_view  mat_name )

inherited

Returns

A writable pointer to this system's additional matrix named mat_name, or nullptr if no matrix by that name exists.

Definition at line 1112 of file system.C.

References libMesh::System::_matrices.

{
  if (auto pos = _matrices.find(mat_name);
      pos != _matrices.end())
    return pos->second.get();

  // Otherwise, mat_name does not exist
  return nullptr;
}

request_vector() [1/4]

const NumericVector< Number > * libMesh::System::request_vector ( std::string_view  vec_name ) const

inherited

Returns

A const pointer to the vector if this System has a vector associated with the given name, nullptr otherwise.

Definition at line 891 of file system.C.

References libMesh::System::_vectors, and libMesh::NumericVector< T >::get().

Referenced by libMesh::UniformRefinementEstimator::_estimate_error().

{
  if (const auto pos = _vectors.find(vec_name);
      pos != _vectors.end())
    return pos->second.get();

  // Otherwise, vec_name was not found
  return nullptr;
}

request_vector() [2/4]

NumericVector< Number > * libMesh::System::request_vector ( std::string_view  vec_name )

inherited

Returns

A pointer to the vector if this System has a vector associated with the given name, nullptr otherwise.

Definition at line 903 of file system.C.

References libMesh::System::_vectors, and libMesh::NumericVector< T >::get().

{
  if (auto pos = _vectors.find(vec_name);
      pos != _vectors.end())
    return pos->second.get();

  // Otherwise, vec_name was not found
  return nullptr;
}

request_vector() [3/4]

const NumericVector< Number > * libMesh::System::request_vector ( const unsigned int  vec_num ) const

inherited

Returns

A const pointer to this system's additional vector number vec_num (where the vectors are counted starting with 0), or nullptr if the system has no such vector.

Definition at line 915 of file system.C.

References libMesh::System::_vectors, and libMesh::System::vectors_begin().

{
  // If we don't have that many vectors, return nullptr
  if (vec_num >= _vectors.size())
    return nullptr;

  // Otherwise return a pointer to the vec_num'th vector
  auto it = vectors_begin();
  std::advance(it, vec_num);
  return it->second.get();
}

request_vector() [4/4]

NumericVector< Number > * libMesh::System::request_vector ( const unsigned int  vec_num )

inherited

Returns

A writable pointer to this system's additional vector number vec_num (where the vectors are counted starting with 0), or nullptr if the system has no such vector.

Definition at line 929 of file system.C.

References libMesh::System::_vectors, and libMesh::System::vectors_begin().

{
  // If we don't have that many vectors, return nullptr
  if (vec_num >= _vectors.size())
    return nullptr;

  // Otherwise return a pointer to the vec_num'th vector
  auto it = vectors_begin();
  std::advance(it, vec_num);
  return it->second.get();
}

restrict_solve_to()

void libMesh::System::restrict_solve_to ( const SystemSubset *  subset, const SubsetSolveMode  subset_solve_mode = SUBSET_ZERO  )

virtualinherited

After calling this method, any solve will be restricted to the given subdomain.

To disable this mode, call this method with subset being a nullptr.

Reimplemented in libMesh::LinearImplicitSystem.

Definition at line 557 of file system.C.

{
  if (subset != nullptr)
    libmesh_not_implemented();
}

restrict_vectors()

void libMesh::System::restrict_vectors ( )

virtualinherited

Restrict vectors after the mesh has coarsened.

Definition at line 386 of file system.C.

References libMesh::System::_dof_map, libMesh::System::_solution_projection, libMesh::System::_vector_projections, libMesh::System::_vectors, libMesh::System::current_local_solution, libMesh::NumericVector< T >::get(), libMesh::GHOSTED, libMesh::System::n_dofs(), libMesh::System::n_local_dofs(), libMesh::PARALLEL, libMesh::System::project_vector(), libMesh::System::solution, and libMesh::System::vector_is_adjoint().

Referenced by libMesh::System::prolong_vectors(), and libMesh::EquationSystems::reinit_solutions().

{
  parallel_object_only();

#ifdef LIBMESH_ENABLE_AMR
  // Restrict the _vectors on the coarsened cells
  for (auto & [vec_name, vec] : _vectors)
    {
      NumericVector<Number> * v = vec.get();

      if (_vector_projections[vec_name])
        {
          this->project_vector (*v, this->vector_is_adjoint(vec_name));
        }
      else
        {
          const ParallelType type = vec->type();

          if (type == GHOSTED)
            {
#ifdef LIBMESH_ENABLE_GHOSTED
              vec->init (this->n_dofs(), this->n_local_dofs(),
                               _dof_map->get_send_list(), /*fast=*/false,
                               GHOSTED);
#else
              libmesh_error_msg("Cannot initialize ghosted vectors when they are not enabled.");
#endif
            }
          else
            vec->init (this->n_dofs(), this->n_local_dofs(), false, type);
        }
    }

  const std::vector<dof_id_type> & send_list = _dof_map->get_send_list ();

  // Restrict the solution on the coarsened cells
  if (_solution_projection)
    this->project_vector (*solution);
  // Or at least make sure the solution vector is the correct size
  else
    solution->init (this->n_dofs(), this->n_local_dofs(), true, PARALLEL);

#ifdef LIBMESH_ENABLE_GHOSTED
  current_local_solution->init(this->n_dofs(),
                               this->n_local_dofs(), send_list,
                               false, GHOSTED);
#else
  current_local_solution->init(this->n_dofs());
#endif

  if (_solution_projection)
    solution->localize (*current_local_solution, send_list);

#endif // LIBMESH_ENABLE_AMR
}

save_current_solution()

void libMesh::ContinuationSystem::save_current_solution

(

)

Stores the current solution and continuation parameter (as "previous_u" and "old_continuation_parameter") for later referral.

You may need to call this e.g. after the first regular solve, in order to store the first solution, before computing a second solution and beginning arclength continuation.

Definition at line 1364 of file continuation_system.C.

References continuation_parameter, old_continuation_parameter, previous_u, and libMesh::System::solution.

Referenced by update_solution().

{
  // Save the old solution vector
  *previous_u = *solution;

  // Save the old value of lambda
  old_continuation_parameter = *continuation_parameter;
}

sensitivity_solve()

std::pair< unsigned int, Real > libMesh::ImplicitSystem::sensitivity_solve ( const ParameterVector &  parameters )

overridevirtualinherited

Assembles & solves the linear system(s) (dR/du)*u_p = -dR/dp, for those parameters contained within parameters.

Returns

A pair with the total number of linear iterations performed and the (sum of the) final residual norms

Reimplemented from libMesh::System.

Definition at line 136 of file implicit_system.C.

References libMesh::System::add_sensitivity_solution(), libMesh::System::assemble_before_solve, libMesh::ImplicitSystem::assemble_residual_derivatives(), libMesh::ImplicitSystem::assembly(), libMesh::SparseMatrix< T >::close(), libMesh::DofMap::enforce_constraints_exactly(), libMesh::System::get_dof_map(), libMesh::ImplicitSystem::get_linear_solve_parameters(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::System::get_sensitivity_rhs(), libMesh::System::get_sensitivity_solution(), libMesh::make_range(), libMesh::ImplicitSystem::matrix, libMesh::System::request_matrix(), libMesh::ParameterVector::size(), and libMesh::LinearSolver< T >::solve().

Referenced by libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), and libMesh::ImplicitSystem::qoi_parameter_hessian().

{
  // Log how long the linear solve takes.
  LOG_SCOPE("sensitivity_solve()", "ImplicitSystem");

  // The forward system should now already be solved.
  // Now assemble the corresponding sensitivity system.

  if (this->assemble_before_solve)
    {
      // Build the Jacobian
      this->assembly(false, true);
      this->matrix->close();

      // Reset and build the RHS from the residual derivatives
      this->assemble_residual_derivatives(parameters_vec);
    }

  // The sensitivity problem is linear
  LinearSolver<Number> * solver = this->get_linear_solver();

  // Our iteration counts and residuals will be sums of the individual
  // results
  std::pair<unsigned int, Real> solver_params =
    this->get_linear_solve_parameters();
  std::pair<unsigned int, Real> totalrval = std::make_pair(0,0.0);

  // Solve the linear system.
  SparseMatrix<Number> * pc = this->request_matrix("Preconditioner");
  for (auto p : make_range(parameters_vec.size()))
    {
      std::pair<unsigned int, Real> rval =
        solver->solve (*matrix, pc,
                       this->add_sensitivity_solution(p),
                       this->get_sensitivity_rhs(p),
                       double(solver_params.second),
                       solver_params.first);

      totalrval.first  += rval.first;
      totalrval.second += rval.second;
    }

  // The linear solver may not have fit our constraints exactly
#ifdef LIBMESH_ENABLE_CONSTRAINTS
  for (auto p : make_range(parameters_vec.size()))
    this->get_dof_map().enforce_constraints_exactly
      (*this, &this->get_sensitivity_solution(p),
       /* homogeneous = */ true);
#endif

  return totalrval;
}

set_adjoint_already_solved()

void libMesh::System::set_adjoint_already_solved ( bool  setting )

inlineinherited

Setter for the adjoint_already_solved boolean.

Definition at line 415 of file system.h.

References libMesh::System::adjoint_already_solved.

Referenced by main().

  { adjoint_already_solved = setting;}

set_basic_system_only()

void libMesh::System::set_basic_system_only ( )

inlineinherited

Sets the system to be "basic only": i.e.

advanced system components such as ImplicitSystem matrices may not be initialized. This is useful for efficiency in certain utility programs that never use System::solve(). This method must be called after the System or derived class is created but before it is initialized; e.g. from within EquationSystems::read()

Definition at line 2422 of file system.h.

References libMesh::System::_basic_system_only.

Referenced by libMesh::EquationSystems::read().

{
  _basic_system_only = true;
}

set_constrain_in_solver()

void libMesh::DifferentiableSystem::set_constrain_in_solver ( bool  enable )

virtualinherited

set_constrain_in_solver to false to apply constraints only via residual terms in the systems to be solved.

Definition at line 424 of file diff_system.C.

References libMesh::DifferentiableSystem::_constrain_in_solver, and libMesh::DifferentiableSystem::time_solver.

Referenced by main(), and set_system_parameters().

{
  _constrain_in_solver = enable;
  this->time_solver->diff_solver()->set_exact_constraint_enforcement(enable);
}

set_max_arclength_stepsize()

void libMesh::ContinuationSystem::set_max_arclength_stepsize ( Real  maxds )

inline

Sets (initializes) the max-allowable ds value and the current ds value.

Call this before beginning arclength continuation. The default max stepsize is 0.1

Definition at line 132 of file continuation_system.h.

References ds, and ds_current.

{ ds=maxds; ds_current=maxds; }

set_mesh_system()

void libMesh::DifferentiablePhysics::set_mesh_system ( System *  sys )

inlinevirtualinherited

Tells the DifferentiablePhysics that system sys contains the isoparametric Lagrangian variables which correspond to the coordinates of mesh nodes, in problems where the mesh itself is expected to move in time.

The system with mesh coordinate data (which may be this system itself, for fully coupled moving mesh problems) is currently assumed to have new (end of time step) mesh coordinates stored in solution, old (beginning of time step) mesh coordinates stored in _old_nonlinear_solution, and constant velocity motion during each time step.

Activating this function ensures that local (but not neighbor!) element geometry is correctly repositioned when evaluating element residuals.

Currently sys must be *this for a tightly coupled moving mesh problem or nullptr to stop mesh movement; loosely coupled moving mesh problems are not implemented.

This code is experimental. "Trust but verify, and not in that order"

Definition at line 569 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_sys.

Referenced by SolidSystem::init_data().

{
  // For now we assume that we're doing fully coupled mesh motion
  //  if (sys && sys != this)
  //    libmesh_not_implemented();

  // For the foreseeable future we'll assume that we keep these
  // Systems in the same EquationSystems
  // libmesh_assert_equal_to (&this->get_equation_systems(),
  //                          &sys->get_equation_systems());

  // And for the immediate future this code may not even work
  libmesh_experimental();

  _mesh_sys = sys;
}

set_mesh_x_var()

void libMesh::DifferentiablePhysics::set_mesh_x_var ( unsigned int  var )

inlinevirtualinherited

Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the x coordinate of mesh nodes, in problems where the mesh itself is expected to move in time.

The system with mesh coordinate data (which may be this system itself, for fully coupled moving mesh problems) is currently assumed to have new (end of time step) mesh coordinates stored in solution, old (beginning of time step) mesh coordinates stored in _old_nonlinear_solution, and constant velocity motion during each time step.

Activating this function ensures that local (but not neighbor!) element geometry is correctly repositioned when evaluating element residuals.

Definition at line 589 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_x_var.

Referenced by SolidSystem::init_data().

{
  _mesh_x_var = var;
}

set_mesh_y_var()

void libMesh::DifferentiablePhysics::set_mesh_y_var ( unsigned int  var )

inlinevirtualinherited

Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the y coordinate of mesh nodes.

Definition at line 597 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_y_var.

Referenced by SolidSystem::init_data().

{
  _mesh_y_var = var;
}

set_mesh_z_var()

void libMesh::DifferentiablePhysics::set_mesh_z_var ( unsigned int  var )

inlinevirtualinherited

Tells the DifferentiablePhysics that variable var from the mesh system should be used to update the z coordinate of mesh nodes.

Definition at line 605 of file diff_physics.h.

References libMesh::DifferentiablePhysics::_mesh_z_var.

Referenced by SolidSystem::init_data().

{
  _mesh_z_var = var;
}

set_numerical_jacobian_h_for_var()

void FEMSystem::set_numerical_jacobian_h_for_var ( unsigned int  var_num, Real  new_h  )

inlineinherited

Definition at line 275 of file fem_system.h.

References libMesh::FEMSystem::_numerical_jacobian_h_for_var, and libMesh::Real.

{
  if (_numerical_jacobian_h_for_var.size() <= var_num)
    _numerical_jacobian_h_for_var.resize(var_num+1,Real(0));

  libmesh_assert_greater(new_h, Real(0));

  _numerical_jacobian_h_for_var[var_num] = new_h;
}

set_project_with_constraints()

void libMesh::System::set_project_with_constraints ( bool  _project_with_constraints )

inlineinherited

Definition at line 1800 of file system.h.

References libMesh::System::project_with_constraints.

Referenced by libMesh::AdjointRefinementEstimator::estimate_error().

  {
    project_with_constraints = _project_with_constraints;
  }

set_qoi() [1/2]

void libMesh::System::set_qoi ( unsigned int  qoi_index, Number  qoi_value  )

inherited

Definition at line 2378 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::qoi.

Referenced by libMesh::ExplicitSystem::assemble_qoi(), libMesh::FEMSystem::assemble_qoi(), libMesh::Euler2Solver::integrate_qoi_timestep(), libMesh::TwostepTimeSolver::integrate_qoi_timestep(), and libMesh::EulerSolver::integrate_qoi_timestep().

{
  libmesh_assert(qoi_index < qoi.size());

  qoi[qoi_index] = qoi_value;
}

set_qoi() [2/2]

void libMesh::System::set_qoi ( std::vector< Number >  new_qoi )

inherited

Definition at line 2399 of file system.C.

References libMesh::System::qoi.

{
  libmesh_assert_equal_to(this->qoi.size(), new_qoi.size());
  this->qoi = std::move(new_qoi);
}

set_qoi_error_estimate()

void libMesh::System::set_qoi_error_estimate ( unsigned int  qoi_index, Number  qoi_error_estimate  )

inherited

Definition at line 2406 of file system.C.

References libMesh::libmesh_assert(), and libMesh::System::qoi_error_estimates.

Referenced by libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::TwostepTimeSolver::integrate_adjoint_refinement_error_estimate(), and libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate().

{
  libmesh_assert(qoi_index < qoi_error_estimates.size());

  qoi_error_estimates[qoi_index] = qoi_error_estimate;
}

set_Theta()

void libMesh::ContinuationSystem::set_Theta ( )

private

A centralized function for setting the normalization parameter theta.

Definition at line 1065 of file continuation_system.C.

References libMesh::out, quiet, and Theta.

Referenced by initialize_tangent(), and update_solution().

{
  // // Use the norm of the latest solution, squared.
  //const Real normu = solution->l2_norm();
  //libmesh_assert_not_equal_to (normu, 0.0);
  //Theta = 1./normu/normu;

  // // 1.) Use the norm of du, squared
  //   *delta_u = *solution;
  //   delta_u->add(-1, *previous_u);
  //   delta_u->close();
  //   const Real normdu = delta_u->l2_norm();

  //   if (normdu < 1.) // don't divide by zero or make a huge scaling parameter.
  //     Theta = 1.;
  //   else
  //     Theta = 1./normdu/normdu;

  // 2.) Use 1.0, i.e. don't scale
  Theta=1.;

  // 3.) Use a formula which attempts to make the "solution triangle" isosceles.
  //   libmesh_assert_less (std::abs(dlambda_ds), 1.);

  //   *delta_u = *solution;
  //   delta_u->add(-1, *previous_u);
  //   delta_u->close();
  //   const Real normdu = delta_u->l2_norm();

  //   Theta = std::sqrt(1. - dlambda_ds*dlambda_ds) / normdu * tau * ds;


  //   // 4.) Use the norm of du and the norm of du/ds
  //   *delta_u = *solution;
  //   delta_u->add(-1, *previous_u);
  //   delta_u->close();
  //   const Real normdu   = delta_u->l2_norm();
  //   du_ds->close();
  //   const Real normduds = du_ds->l2_norm();

  //   if (normduds < 1.e-12)
  //     {
  //       libMesh::out << "Setting initial Theta= 1./normdu/normdu" << std::endl;
  //       libMesh::out << "normdu=" << normdu << std::endl;

  //       // Don't use this scaling if the solution delta is already O(1)
  //       if (normdu > 1.)
  // Theta = 1./normdu/normdu;
  //       else
  // Theta = 1.;
  //     }
  //   else
  //     {
  //       libMesh::out << "Setting Theta= 1./normdu/normduds" << std::endl;
  //       libMesh::out << "normdu=" << normdu << std::endl;
  //       libMesh::out << "normduds=" << normduds << std::endl;

  //       // Don't use this scaling if the solution delta is already O(1)
  //       if ((normdu>1.) || (normduds>1.))
  // Theta = 1./normdu/normduds;
  //       else
  // Theta = 1.;
  //     }

  if (!quiet)
    libMesh::out << "Setting Normalization Parameter Theta=" << Theta << std::endl;
}

set_Theta_LOCA()

void libMesh::ContinuationSystem::set_Theta_LOCA ( )

private

A centralized function for setting the other normalization parameter, i.e.

the one suggested by the LOCA developers.

Definition at line 1135 of file continuation_system.C.

References dlambda_ds, libMesh::out, quiet, and Theta_LOCA.

Referenced by update_solution().

{
  // We also recompute the LOCA normalization parameter based on the
  // most recently computed value of dlambda_ds
  // if (!quiet)
  //   libMesh::out << "(Theta_LOCA) dlambda_ds=" << dlambda_ds << std::endl;

  // Formula makes no sense if |dlambda_ds| > 1
  libmesh_assert_less (std::abs(dlambda_ds), 1.);

  // 1.) Attempt to implement the method in LOCA paper
  //   const Real g = 1./std::sqrt(2.); // "desired" dlambda_ds

  //   // According to the LOCA people, we only renormalize for
  //   // when |dlambda_ds| exceeds some pre-selected maximum (which they take to be zero, btw).
  //   if (std::abs(dlambda_ds) > .9)
  //     {
  //       // Note the *= ... This is updating the previous value of Theta_LOCA
  //       // Note: The LOCA people actually use Theta_LOCA^2 to normalize their arclength constraint.
  //       Theta_LOCA *= std::abs( (dlambda_ds/g)*std::sqrt( (1.-g*g) / (1.-dlambda_ds*dlambda_ds) ) );

  //       // Suggested max-allowable value for Theta_LOCA
  //       if (Theta_LOCA > 1.e8)
  // {
  //   Theta_LOCA = 1.e8;

  //   if (!quiet)
  //     libMesh::out << "max Theta_LOCA=" << Theta_LOCA << " has been selected." << std::endl;
  // }
  //     }
  //   else
  //     Theta_LOCA=1.0;

  // 2.) FIXME: Should we do *= or just =?  This function is of dlambda_ds is
  //  < 1,  |dlambda_ds| < 1/sqrt(2) ~~ .7071
  //  > 1,  |dlambda_ds| > 1/sqrt(2) ~~ .7071
  Theta_LOCA *= std::abs( dlambda_ds / std::sqrt( (1.-dlambda_ds*dlambda_ds) ) );

  // Suggested max-allowable value for Theta_LOCA.  I've never come close
  // to this value in my code.
  if (Theta_LOCA > 1.e8)
    {
      Theta_LOCA = 1.e8;

      if (!quiet)
        libMesh::out << "max Theta_LOCA=" << Theta_LOCA << " has been selected." << std::endl;
    }

  // 3.) Use 1.0, i.e. don't scale
  //Theta_LOCA=1.0;

  if (!quiet)
    libMesh::out << "Setting Theta_LOCA=" << Theta_LOCA << std::endl;
}

set_time_solver()

void libMesh::DifferentiableSystem::set_time_solver ( std::unique_ptr< TimeSolver >  _time_solver )

inlineinherited

Sets the time_solver FIXME: This code is a little dangerous as it transfers ownership from the TimeSolver creator to this class.

The user must no longer access his original TimeSolver object after calling this function.

Definition at line 261 of file diff_system.h.

References libMesh::DifferentiableSystem::time_solver.

  {
    time_solver.reset(_time_solver.release());
  }

set_vector_as_adjoint()

void libMesh::System::set_vector_as_adjoint ( const std::string &  vec_name, int  qoi_num  )

inherited

Allows one to set the QoI index controlling whether the vector identified by vec_name represents a solution from the adjoint (qoi_num >= 0) or primal (qoi_num == -1) space.

This becomes significant if those spaces have differing heterogeneous Dirichlet constraints.

qoi_num == -2 can be used to indicate a vector which should not be affected by constraints during projection operations.

Definition at line 1160 of file system.C.

References libMesh::System::_vector_is_adjoint.

Referenced by libMesh::System::add_adjoint_solution(), and libMesh::System::add_weighted_sensitivity_adjoint_solution().

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  // We reserve -1 for vectors which get primal constraints, -2 for
  // vectors which get no constraints
  libmesh_assert_greater_equal(qoi_num, -2);
  _vector_is_adjoint[vec_name] = qoi_num;
}

set_vector_preservation()

void libMesh::System::set_vector_preservation ( const std::string &  vec_name, bool  preserve  )

inherited

Allows one to set the boolean controlling whether the vector identified by vec_name should be "preserved": projected to new meshes, saved, etc.

Definition at line 1138 of file system.C.

References libMesh::System::_vector_projections.

Referenced by libMesh::AdjointRefinementEstimator::estimate_error(), and main().

{
  parallel_object_only();  // Not strictly needed, but the only safe way to keep in sync

  _vector_projections[vec_name] = preserve;
}

setup_static_condensation_preconditioner()

template<typename T >

template void libMesh::ImplicitSystem::setup_static_condensation_preconditioner ( T &  solver )

protectedinherited

Sets up the static condensation preconditioner for the supplied solver.

Definition at line 71 of file implicit_system.C.

References libMesh::ImplicitSystem::_sc_system_matrix, libMesh::StaticCondensation::get_preconditioner(), and libMesh::libmesh_assert().

Referenced by libMesh::LinearImplicitSystem::create_static_condensation(), libMesh::NonlinearImplicitSystem::create_static_condensation(), libMesh::LinearImplicitSystem::LinearImplicitSystem(), and libMesh::NonlinearImplicitSystem::NonlinearImplicitSystem().

{
  libmesh_assert(_sc_system_matrix);
  solver.attach_preconditioner(&_sc_system_matrix->get_preconditioner());
}

side_constraint()

virtual bool libMesh::DifferentiablePhysics::side_constraint ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds the constraint contribution on side of elem to elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Users may need to reimplement this for their particular PDE depending on the boundary conditions.

To implement a weak form of the constraint 0 = G(u), the user should examine u = elem_solution and add (G(u), phi_i) boundary integral contributions to elem_residual in side_constraint().

Reimplemented in LaplaceSystem, LaplaceSystem, LaplaceSystem, and NavierSystem.

Definition at line 195 of file diff_physics.h.

Referenced by libMesh::EulerSolver::side_residual(), libMesh::SteadySolver::side_residual(), libMesh::Euler2Solver::side_residual(), libMesh::EigenTimeSolver::side_residual(), and libMesh::NewmarkSolver::side_residual().

  {
    return request_jacobian;
  }

side_damping_residual()

virtual bool libMesh::DifferentiablePhysics::side_damping_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Subtracts a damping vector contribution on side of elem from elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

For most problems, the default implementation of "do nothing" is correct; users with boundary conditions including first time derivatives may need to reimplement this themselves.

Definition at line 378 of file diff_physics.h.

Referenced by libMesh::EulerSolver::side_residual(), libMesh::Euler2Solver::side_residual(), and libMesh::NewmarkSolver::side_residual().

  {
    return request_jacobian;
  }

side_mass_residual()

virtual bool libMesh::DifferentiablePhysics::side_mass_residual ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Subtracts a mass vector contribution on side of elem from elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

For most problems, the default implementation of "do nothing" is correct; users with boundary conditions including time derivatives may need to reimplement this themselves.

Definition at line 320 of file diff_physics.h.

Referenced by libMesh::EulerSolver::side_residual(), libMesh::Euler2Solver::side_residual(), libMesh::EigenTimeSolver::side_residual(), and libMesh::NewmarkSolver::side_residual().

  {
    return request_jacobian;
  }

side_postprocess()

virtual void libMesh::DifferentiableSystem::side_postprocess ( DiffContext &  )

inlinevirtualinherited

Does any work that needs to be done on side of elem in a postprocessing loop.

Reimplemented in LaplaceSystem, and LaplaceSystem.

Definition at line 307 of file diff_system.h.

{}

side_qoi()

virtual void libMesh::DifferentiableQoI::side_qoi ( DiffContext &  , const QoISet &    )

inlinevirtualinherited

Does any work that needs to be done on side of elem in a quantity of interest assembly loop, outputting to elem_qoi.

Only qois included in the supplied QoISet need to be assembled.

Reimplemented in CoupledSystemQoI.

Definition at line 147 of file diff_qoi.h.

  {}

side_qoi_derivative()

virtual void libMesh::DifferentiableQoI::side_qoi_derivative ( DiffContext &  , const QoISet &    )

inlinevirtualinherited

Does any work that needs to be done on side of elem in a quantity of interest derivative assembly loop, outputting to elem_qoi_derivative.

Only qois included in the supplied QoISet need their derivatives assembled.

Reimplemented in LaplaceSystem, LaplaceSystem, and CoupledSystemQoI.

Definition at line 159 of file diff_qoi.h.

  {}

side_time_derivative()

virtual bool libMesh::DifferentiablePhysics::side_time_derivative ( bool  request_jacobian, DiffContext &    )

inlinevirtualinherited

Adds the time derivative contribution on side of elem to elem_residual.

If this method receives request_jacobian = true, then it should compute elem_jacobian and return true if possible. If elem_jacobian has not been computed then the method should return false.

Users may need to reimplement this for their particular PDE depending on the boundary conditions.

To implement a weak form of the source term du/dt = F(u) on sides, such as might arise in a flux boundary condition, the user should examine u = elem_solution and add (F(u), phi_i) boundary integral contributions to elem_residual in side_constraint().

Reimplemented in ElasticitySystem, ElasticitySystem, CurlCurlSystem, CurlCurlSystem, and SolidSystem.

Definition at line 174 of file diff_physics.h.

Referenced by libMesh::EulerSolver::side_residual(), libMesh::SteadySolver::side_residual(), libMesh::Euler2Solver::side_residual(), libMesh::EigenTimeSolver::side_residual(), and libMesh::NewmarkSolver::side_residual().

  {
    return request_jacobian;
  }

solve()

void libMesh::ContinuationSystem::solve ( )

overridevirtual

Perform a standard "solve" of the system, without doing continuation.

Reimplemented from libMesh::FEMSystem.

Definition at line 122 of file continuation_system.C.

References Residual, rhs_mode, and libMesh::DifferentiableSystem::solve().

{
  // Set the Residual RHS mode, and call the normal solve routine.
  rhs_mode      = Residual;
  DifferentiableSystem::solve();
}

solve_for_unconstrained_dofs()

void libMesh::System::solve_for_unconstrained_dofs ( NumericVector< Number > &  vec, int  is_adjoint = -1  ) const

protectedinherited

Definition at line 2041 of file system_projection.C.

References libMesh::DofMap::build_sparsity(), libMesh::DofMap::computed_sparsity_already(), libMesh::DofMapBase::end_dof(), libMesh::DofMapBase::first_dof(), libMesh::NumericVector< T >::get(), libMesh::DofMap::heterogenously_constrain_element_matrix_and_vector(), libMesh::DofMap::is_constrained_dof(), libMesh::NumericVector< T >::local_size(), libMesh::DofMap::n_dofs(), libMesh::DofMap::n_local_dofs(), libMesh::PARALLEL, libMesh::Real, libMesh::NumericVector< T >::size(), and libMesh::DofMap::update_sparsity_pattern().

{
  const DofMap & dof_map = this->get_dof_map();

  std::unique_ptr<SparseMatrix<Number>> mat =
    SparseMatrix<Number>::build(this->comm());

  std::unique_ptr<SparsityPattern::Build> sp;

  if (dof_map.computed_sparsity_already())
    dof_map.update_sparsity_pattern(*mat);
  else
    {
      mat->attach_dof_map(dof_map);
      sp = dof_map.build_sparsity(this->get_mesh());
      mat->attach_sparsity_pattern(*sp);
    }

  mat->init();

  libmesh_assert_equal_to(vec.size(), dof_map.n_dofs());
  libmesh_assert_equal_to(vec.local_size(), dof_map.n_local_dofs());

  std::unique_ptr<NumericVector<Number>> rhs =
    NumericVector<Number>::build(this->comm());

  rhs->init(dof_map.n_dofs(), dof_map.n_local_dofs(), false,
            PARALLEL);

  // Here we start with the unconstrained (and indeterminate) linear
  // system, K*u = f, where K is the identity matrix for constrained
  // DoFs and 0 elsewhere, and f is the current solution values for
  // constrained DoFs and 0 elsewhere.
  // We then apply the usual heterogeneous constraint matrix C and
  // offset h, where u = C*x + h,
  // to get C^T*K*C*x = C^T*f - C^T*K*h
  // - a constrained and no-longer-singular system that finds the
  // closest approximation for the unconstrained degrees of freedom.
  //
  // Here, though "closest" is in an algebraic sense; we're
  // effectively using a pseudoinverse that optimizes in a
  // discretization-dependent norm.  That only seems to give ~0.1%
  // excess error even in coarse unit test cases, but at some point it
  // might be reasonable to weight K and f properly.

  for (dof_id_type d : IntRange<dof_id_type>(dof_map.first_dof(),
                                             dof_map.end_dof()))
    {
      if (dof_map.is_constrained_dof(d))
        {
          DenseMatrix<Number> K(1,1);
          DenseVector<Number> F(1);
          std::vector<dof_id_type> dof_indices(1, d);
          K(0,0) = 1;
          F(0) = (*this->solution)(d);
          dof_map.heterogenously_constrain_element_matrix_and_vector
            (K, F, dof_indices, false, is_adjoint);
          mat->add_matrix(K, dof_indices);
          rhs->add_vector(F, dof_indices);
        }
    }

  std::unique_ptr<LinearSolver<Number>> linear_solver =
    LinearSolver<Number>::build(this->comm());

  linear_solver->solve(*mat, vec, *rhs,
                       double(this->get_equation_systems().parameters.get<Real>("linear solver tolerance")),
                       this->get_equation_systems().parameters.get<unsigned int>("linear solver maximum iterations"));
}

solve_tangent()

void libMesh::ContinuationSystem::solve_tangent ( )

private

Special solve algorithm for solving the tangent system.

Definition at line 956 of file continuation_system.C.

References libMesh::NumericVector< T >::add(), libMesh::FEMSystem::assembly(), libMesh::NumericVector< T >::close(), continuation_parameter, delta_u, dlambda_ds, libMesh::NumericVector< T >::dot(), du_ds, G_Lambda, libMesh::NumericVector< T >::l2_norm(), libMesh::libmesh_assert(), libMesh::libmesh_real(), libMesh::ImplicitSystem::linear_solver, libMesh::ImplicitSystem::matrix, libMesh::DiffSolver::max_linear_iterations, newton_solver, old_continuation_parameter, libMesh::out, previous_dlambda_ds, previous_du_ds, previous_u, quiet, libMesh::Real, libMesh::ExplicitSystem::rhs, rhs_mode, libMesh::NumericVector< T >::scale(), libMesh::System::solution, tangent_initialized, Theta, Theta_LOCA, libMesh::DifferentiableSystem::time_solver, y, and libMesh::NumericVector< T >::zero().

Referenced by advance_arcstep(), and initialize_tangent().

{
  // We shouldn't call this unless the current tangent already makes sense.
  libmesh_assert (tangent_initialized);

  // Set pointer to underlying Newton solver
  if (!newton_solver)
    newton_solver =
      cast_ptr<NewtonSolver *> (this->time_solver->diff_solver().get());

  // Assemble the system matrix AND rhs, with rhs = G_{\lambda}
  this->rhs_mode = G_Lambda;

  // Assemble Residual and Jacobian
  this->assembly(true,   // Residual
                 true); // Jacobian

  // Not sure if this is really necessary
  rhs->close();

  // Solve G_u*y =  G_{\lambda}
  std::pair<unsigned int, Real> rval =
    linear_solver->solve(*matrix,
                         *y,
                         *rhs,
                         1.e-12, // relative linear tolerance
                         2*newton_solver->max_linear_iterations);   // max linear iterations

  // FIXME: If this doesn't converge at all, the new tangent vector is
  // going to be really bad...

  if (!quiet)
    libMesh::out << "G_u*y = G_{lambda} solver converged at step "
                 << rval.first
                 << " linear tolerance = "
                 << rval.second
                 << "."
                 << std::endl;

  // Save old solution and parameter tangents for possible use in higher-order
  // predictor schemes.
  previous_dlambda_ds = dlambda_ds;
  *previous_du_ds     = *du_ds;


  // 1.) Previous, probably wrong, technique!
  //   // Solve for the updated d(lambda)/ds
  //   // denom = N_{lambda}   - (du_ds)^t y
  //   //       = d(lambda)/ds - (du_ds)^t y
  //   Real denom = dlambda_ds - du_ds->dot(*y);

  //   //libMesh::out << "denom=" << denom << std::endl;
  //   libmesh_assert_not_equal_to (denom, 0.0);

  //   dlambda_ds = 1.0 / denom;


  //   if (!quiet)
  //     libMesh::out << "dlambda_ds=" << dlambda_ds << std::endl;

  //   // Compute the updated value of du/ds = -_dlambda_ds * y
  //   du_ds->zero();
  //   du_ds->add(-dlambda_ds, *y);
  //   du_ds->close();


  // 2.) From Brian Carnes' paper...
  // According to Carnes, y comes from solving G_u * y = -G_{\lambda}
  y->scale(-1.);
  const Real ynorm = y->l2_norm();
  dlambda_ds = 1. / std::sqrt(1. + Theta_LOCA*Theta_LOCA*Theta*ynorm*ynorm);

  // Determine the correct sign for dlambda_ds.

  // We will use delta_u to temporarily compute this sign.
  *delta_u = *solution;
  delta_u->add(-1., *previous_u);
  delta_u->close();

  const Real sgn_dlambda_ds =
    libmesh_real(Theta_LOCA*Theta_LOCA*Theta*y->dot(*delta_u) +
                 (*continuation_parameter-old_continuation_parameter));

  if (sgn_dlambda_ds < 0.)
    {
      if (!quiet)
        libMesh::out << "dlambda_ds is negative." << std::endl;

      dlambda_ds *= -1.;
    }

  // Finally, set the new tangent vector, du/ds = dlambda/ds * y.
  du_ds->zero();
  du_ds->add(dlambda_ds, *y);
  du_ds->close();

  if (!quiet)
    {
      libMesh::out << "d(lambda)/ds = " << dlambda_ds << std::endl;
      libMesh::out << "||du_ds||    = " << du_ds->l2_norm() << std::endl;
    }

  // Our next solve expects y ~ -du/dlambda, so scale it back by -1 again now.
  y->scale(-1.);
  y->close();
}

swap_physics()

void libMesh::DifferentiableSystem::swap_physics ( DifferentiablePhysics *&  swap_physics )

inherited

Swap current physics object with external object.

This is

Deprecated:

for being too unsafe for easy use.

Definition at line 350 of file diff_system.C.

References libMesh::DifferentiableSystem::_diff_physics, libMesh::ImplicitSystem::disable_cache(), and libMesh::libmesh_assert().

{
  // This isn't safe if users aren't very careful about memory
  // management and they don't (or aren't able to due to an exception)
  // swap back.
  libmesh_deprecated();

  // A mess of code for backwards compatibility
  if (this->_diff_physics.empty())
    {
      // Swap-something-else-for-self
      std::unique_ptr<DifferentiablePhysics> scary_hack(swap_physics);
      this->_diff_physics.push(std::move(scary_hack));
      swap_physics = this;
    }
  else if (swap_physics == this)
    {
      // The user must be cleaning up after a previous
      // swap-something-else-for-self
      libmesh_assert(!this->_diff_physics.empty());

      // So we don't want to delete what got swapped in, but we do
      // want to put it back into their pointer
      DifferentiablePhysics * old_p = this->_diff_physics.top().release();
      this->_diff_physics.pop();
      swap_physics = old_p;

      // And if the user is doing anything more sophisticated than
      // that then the user is sophisticated enough to upgrade to
      // push/pop.
      libmesh_assert(this->_diff_physics.empty());
    }
  else
    {
      // Swapping one external physics for another
      DifferentiablePhysics * old_p = this->_diff_physics.top().release();
      std::swap(old_p, swap_physics);
      this->_diff_physics.top().reset(old_p);
    }

  // If the physics has been swapped, we will reassemble
  // the matrix from scratch before doing an adjoint solve
  // rather than just transposing
  this->disable_cache();
}

system()

sys_type& libMesh::ImplicitSystem::system ( )

inlineinherited

Returns

A reference to *this.

Definition at line 87 of file implicit_system.h.

{ return *this; }

system_type()

virtual std::string libMesh::ImplicitSystem::system_type ( ) const

inlineoverridevirtualinherited

Returns

"Implicit". Helps in identifying the system type in an equation system file.

Reimplemented from libMesh::ExplicitSystem.

Reimplemented in libMesh::NonlinearImplicitSystem, libMesh::OptimizationSystem, libMesh::LinearImplicitSystem, libMesh::RBConstruction, libMesh::FrequencySystem, libMesh::TransientSystem< RBConstruction >, libMesh::NewmarkSystem, libMesh::ClawSystem, and SolidSystem.

Definition at line 117 of file implicit_system.h.

{ return "Implicit"; }

thread_join()

void libMesh::DifferentiableQoI::thread_join ( std::vector< Number > &  qoi, const std::vector< Number > &  other_qoi, const QoISet &  qoi_indices  )

virtualinherited

Method to combine thread-local qois.

By default, simply sums thread qois.

Definition at line 33 of file diff_qoi.C.

References libMesh::index_range().

{
  for (auto i : index_range(qoi))
    qoi[i] += other_qoi[i];
}

time_evolving()

void libMesh::DifferentiablePhysics::time_evolving ( unsigned int  var, unsigned int  order  )

virtualinherited

Tells the DiffSystem that variable var is evolving with respect to time.

In general, the user's init() function should call time_evolving() with order 1 for any variables which behave like du/dt = F(u), with order 2 for any variables that behave like d^2u/dt^2 = F(u), and should not call time_evolving() for any variables which behave like 0 = G(u).

Most derived systems will not have to reimplement this function; however any system which reimplements mass_residual() may have to reimplement time_evolving() to prepare data structures.

Definition at line 41 of file diff_physics.C.

References libMesh::DifferentiablePhysics::_first_order_vars, libMesh::DifferentiablePhysics::_second_order_vars, and libMesh::DifferentiablePhysics::_time_evolving.

Referenced by libMesh::DifferentiableSystem::add_second_order_dot_vars(), SigmaPhysics::init_data(), CurlCurlSystem::init_data(), and HeatSystem::init_data().

{
  libmesh_error_msg_if(order != 1 && order != 2, "Input order must be 1 or 2!");

  if (_time_evolving.size() <= var)
    _time_evolving.resize(var+1, 0);

  _time_evolving[var] = order;

  if (order == 1)
    _first_order_vars.insert(var);
  else
    _second_order_vars.insert(var);
}

update()

void libMesh::System::update ( )

virtualinherited

Update the local values to reflect the solution on neighboring processors.

Reimplemented in SolidSystem.

Definition at line 510 of file system.C.

References libMesh::System::_dof_map, libMesh::System::current_local_solution, libMesh::libmesh_assert(), and libMesh::System::solution.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), libMesh::__libmesh_petsc_diff_solver_residual(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::FEMSystem::assemble_qoi(), libMesh::FEMSystem::assemble_qoi_derivative(), libMesh::NonlinearImplicitSystem::assembly(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::NewmarkSolver::compute_initial_accel(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::Problem_Interface::computeF(), libMesh::Problem_Interface::computeJacobian(), libMesh::Problem_Interface::computePreconditioner(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::GMVIO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::Nemesis_IO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), DMlibMeshFunction(), DMlibMeshJacobian(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::CondensedEigenSystem::get_eigenpair(), libMesh::TransientRBConstruction::initialize_truth(), libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate(), libMesh::libmesh_petsc_snes_fd_residual(), libMesh::libmesh_petsc_snes_jacobian(), libMesh::libmesh_petsc_snes_mffd_residual(), libMesh::libmesh_petsc_snes_residual(), libMesh::libmesh_petsc_snes_residual_helper(), libMesh::NewtonSolver::line_search(), libMesh::RBConstruction::load_basis_function(), libMesh::TransientRBConstruction::load_rb_solution(), libMesh::RBConstruction::load_rb_solution(), main(), libMesh::FEMSystem::mesh_position_get(), HeatSystem::perturb_accumulate_residuals(), libMesh::FEMSystem::postprocess(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::MemorySolutionHistory::retrieve(), libMesh::FileSolutionHistory::retrieve(), libMesh::NewtonSolver::solve(), libMesh::ExplicitSystem::solve(), libMesh::LinearImplicitSystem::solve(), libMesh::OptimizationSystem::solve(), libMesh::NonlinearImplicitSystem::solve(), libMesh::ClawSystem::solve_conservation_law(), libMesh::RBConstruction::solve_for_matrix_and_rhs(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::DirectSolutionTransfer::transfer(), and update_current_local_solution().

{
  parallel_object_only();

  libmesh_assert(solution->closed());

  const std::vector<dof_id_type> & send_list = _dof_map->get_send_list ();

  // Check sizes
  libmesh_assert_equal_to (current_local_solution->size(), solution->size());
  // More processors than elements => empty send_list
  //  libmesh_assert (!send_list.empty());
  libmesh_assert_less_equal (send_list.size(), solution->size());

  // Create current_local_solution from solution.  This will
  // put a local copy of solution into current_local_solution.
  // Only the necessary values (specified by the send_list)
  // are copied to minimize communication
  solution->localize (*current_local_solution, send_list);
}

update_global_solution() [1/2]

void libMesh::System::update_global_solution ( std::vector< Number > &  global_soln ) const

inherited

Fill the input vector global_soln so that it contains the global solution on all processors.

Requires communication with all other processors.

Definition at line 745 of file system.C.

References libMesh::System::solution.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::ExactErrorEstimator::estimate_error(), main(), and libMesh::InterMeshProjection::project_system_vectors().

{
  parallel_object_only();

  global_soln.resize (solution->size());

  solution->localize (global_soln);
}

update_global_solution() [2/2]

void libMesh::System::update_global_solution ( std::vector< Number > &  global_soln, const processor_id_type  dest_proc  ) const

inherited

Fill the input vector global_soln so that it contains the global solution on processor dest_proc.

Requires communication with all other processors.

Definition at line 756 of file system.C.

References libMesh::System::solution.

{
  parallel_object_only();

  global_soln.resize        (solution->size());

  solution->localize_to_one (global_soln, dest_proc);
}

update_solution()

void libMesh::ContinuationSystem::update_solution ( )

private

This function (which assumes the most recent tangent vector has been computed) updates the solution and the control parameter with the initial guess for the next point on the continuation path.

Definition at line 1192 of file continuation_system.C.

References libMesh::NumericVector< T >::add(), apply_predictor(), libMesh::NumericVector< T >::close(), continuation_parameter, delta_u, libMesh::NumericVector< T >::dot(), ds, ds_current, ds_min, libMesh::NumericVector< T >::l2_norm(), libMesh::libmesh_assert(), libMesh::DiffSolver::max_nonlinear_iterations, newton_solver, newton_step, newton_stepgrowth_aggressiveness, old_continuation_parameter, libMesh::out, libMesh::BasicOStreamProxy< charT, traits >::precision(), previous_ds, previous_u, quiet, libMesh::Real, save_current_solution(), set_Theta(), set_Theta_LOCA(), libMesh::BasicOStreamProxy< charT, traits >::setf(), libMesh::System::solution, tangent_initialized, Theta, Theta_LOCA, libMesh::BasicOStreamProxy< charT, traits >::unsetf(), y, and y_old.

Referenced by advance_arcstep(), and initialize_tangent().

{
  // Set some stream formatting flags
  std::streamsize old_precision = libMesh::out.precision();
  libMesh::out.precision(16);
  libMesh::out.setf(std::ios_base::scientific);

  // We must have a tangent that makes sense before we can update the solution.
  libmesh_assert (tangent_initialized);

  // Compute tau, the stepsize scaling parameter which attempts to
  // reduce ds when the angle between the most recent two tangent
  // vectors becomes large.  tau is actually the (absolute value of
  // the) cosine of the angle between these two vectors... so if tau ~
  // 0 the angle is ~ 90 degrees, while if tau ~ 1 the angle is ~ 0
  // degrees.
  y_old->close();
  y->close();
  const Real yoldnorm = y_old->l2_norm();
  const Real ynorm = y->l2_norm();
  const Number yoldy = y_old->dot(*y);
  const Real yold_over_y = yoldnorm/ynorm;

  if (!quiet)
    {
      libMesh::out << "yoldnorm=" << yoldnorm << std::endl;
      libMesh::out << "ynorm="    << ynorm << std::endl;
      libMesh::out << "yoldy="    << yoldy << std::endl;
      libMesh::out << "yoldnorm/ynorm=" << yoldnorm/ynorm << std::endl;
    }

  // Save the current value of ds before updating it
  previous_ds = ds_current;

  // // 1.) Cosine method (for some reason this always predicts the angle is ~0)
  // // Don't try dividing by zero
  // if ((yoldnorm > 1.e-12) && (ynorm > 1.e-12))
  //   tau = std::abs(yoldy) / yoldnorm  / ynorm;
  // else
  //   tau = 1.;

  // // 2.) Relative size of old and new du/dlambda method with cutoff of 0.9
  // if ((yold_over_y < 0.9) && (yold_over_y > 1.e-6))
  //   tau = yold_over_y;
  // else
  //   tau = 1.;

  // 3.) Grow (or shrink) the arclength stepsize by the ratio of du/dlambda, but do not
  // exceed the user-specified value of ds.
  if (yold_over_y > 1.e-6)
    {
      // // 1.) Scale current ds by the ratio of successive tangents.
      //       ds_current *= yold_over_y;
      //       if (ds_current > ds)
      // ds_current = ds;

      // 2.) Technique 1 tends to shrink the step fairly well (and even if it doesn't
      // get very small, we still have step reduction) but it seems to grow the step
      // very slowly.  Another possible technique is step-doubling:
      //       if (yold_over_y > 1.)
      //       ds_current *= 2.;
      //       else
      // ds_current *= yold_over_y;

      // 3.) Technique 2 may over-zealous when we are also using the Newton stepgrowth
      // factor.  For technique 3 we multiply by yold_over_y unless yold_over_y > 2
      // in which case we use 2.
      //       if (yold_over_y > 2.)
      // ds_current *= 2.;
      //       else
      // ds_current *= yold_over_y;

      // 4.) Double-or-halve.  We double the arc-step if the ratio of successive tangents
      // is larger than 'double_threshold', halve it if it is less than 'halve_threshold'
      const Real double_threshold = 0.5;
      const Real halve_threshold  = 0.5;
      if (yold_over_y > double_threshold)
        ds_current *= 2.;
      else if (yold_over_y < halve_threshold)
        ds_current *= 0.5;


      // Also possibly use the number of Newton iterations required to compute the previous
      // step (relative to the maximum-allowed number of Newton iterations) to grow the step.
      if (newton_stepgrowth_aggressiveness > 0.)
        {
          libmesh_assert(newton_solver);
          const unsigned int Nmax = newton_solver->max_nonlinear_iterations;

          // // The LOCA Newton step growth technique (note: only grows step length)
          // const Real stepratio = static_cast<Real>(Nmax-(newton_step+1))/static_cast<Real>(Nmax-1.);
          // const Real newtonstep_growthfactor = 1. + newton_stepgrowth_aggressiveness*stepratio*stepratio;

          // The "Nopt/N" method, may grow or shrink the step.  Assume Nopt=Nmax/2.
          const Real newtonstep_growthfactor =
            newton_stepgrowth_aggressiveness * 0.5 *
            static_cast<Real>(Nmax) / static_cast<Real>(newton_step+1);

          if (!quiet)
            libMesh::out << "newtonstep_growthfactor=" << newtonstep_growthfactor << std::endl;

          ds_current *= newtonstep_growthfactor;
        }
    }


  // Don't let the stepsize get above the user's maximum-allowed stepsize.
  if (ds_current > ds)
    ds_current = ds;

  // Check also for a minimum allowed stepsize.
  if (ds_current < ds_min)
    {
      libMesh::out << "Enforcing minimum-allowed arclength stepsize of " << ds_min << std::endl;
      ds_current = ds_min;
    }

  if (!quiet)
    {
      libMesh::out << "Current step size: ds_current=" << ds_current << std::endl;
    }

  // Recompute scaling factor Theta for
  // the current solution before updating.
  set_Theta();

  // Also, recompute the LOCA scaling factor, which attempts to
  // maintain a reasonable value of dlambda/ds
  set_Theta_LOCA();

  libMesh::out << "Theta*Theta_LOCA^2=" << Theta*Theta_LOCA*Theta_LOCA << std::endl;

  // Based on the asymptotic singular behavior of du/dlambda near simple turning points,
  // we can compute a single parameter which may suggest that we are close to a singularity.
  *delta_u = *solution;
  delta_u->add(-1, *previous_u);
  delta_u->close();
  const Real normdu   = delta_u->l2_norm();
  const Real C = (std::log (Theta_LOCA*normdu) /
                  std::log (std::abs(*continuation_parameter-old_continuation_parameter))) - 1.0;
  if (!quiet)
    libMesh::out << "C=" << C << std::endl;

  // Save the current value of u and lambda before updating.
  save_current_solution();

  if (!quiet)
    {
      libMesh::out << "Updating the solution with the tangent guess." << std::endl;
      libMesh::out << "||u_old||=" << this->solution->l2_norm() << std::endl;
      libMesh::out << "lambda_old=" << *continuation_parameter << std::endl;
    }

  // Since we solved for the tangent vector, now we can compute an
  // initial guess for the new solution, and an initial guess for the
  // new value of lambda.
  apply_predictor();

  if (!quiet)
    {
      libMesh::out << "||u_new||=" << this->solution->l2_norm() << std::endl;
      libMesh::out << "lambda_new=" << *continuation_parameter << std::endl;
    }

  // Unset previous stream flags
  libMesh::out.precision(old_precision);
  libMesh::out.unsetf(std::ios_base::scientific);
}

user_assembly()

void libMesh::System::user_assembly ( )

virtualinherited

Calls user's attached assembly function, or is overridden by the user in derived classes.

Definition at line 2311 of file system.C.

References libMesh::System::_assemble_system_function, libMesh::System::_assemble_system_object, libMesh::System::_equation_systems, libMesh::System::Assembly::assemble(), and libMesh::System::name().

Referenced by libMesh::System::assemble().

{
  // Call the user-provided assembly function,
  // if it was provided
  if (_assemble_system_function != nullptr)
    this->_assemble_system_function (_equation_systems, this->name());

  // ...or the user-provided assembly object.
  else if (_assemble_system_object != nullptr)
    this->_assemble_system_object->assemble();
}

user_constrain()

void libMesh::System::user_constrain ( )

virtualinherited

Calls user's attached constraint function, or is overridden by the user in derived classes.

Definition at line 2325 of file system.C.

References libMesh::System::_constrain_system_function, libMesh::System::_constrain_system_object, libMesh::System::_equation_systems, libMesh::System::Constraint::constrain(), and libMesh::System::name().

Referenced by libMesh::System::reinit_constraints().

{
  // Call the user-provided constraint function,
  // if it was provided
  if (_constrain_system_function!= nullptr)
    this->_constrain_system_function(_equation_systems, this->name());

  // ...or the user-provided constraint object.
  else if (_constrain_system_object != nullptr)
    this->_constrain_system_object->constrain();
}

user_initialization()

void libMesh::System::user_initialization ( )

virtualinherited

Calls user's attached initialization function, or is overridden by the user in derived classes.

Definition at line 2297 of file system.C.

References libMesh::System::_equation_systems, libMesh::System::_init_system_function, libMesh::System::_init_system_object, libMesh::System::Initialization::initialize(), and libMesh::System::name().

Referenced by libMesh::NewmarkSystem::initial_conditions(), and libMesh::System::reinit_mesh().

{
  // Call the user-provided initialization function,
  // if it was provided
  if (_init_system_function != nullptr)
    this->_init_system_function (_equation_systems, this->name());

  // ...or the user-provided initialization object.
  else if (_init_system_object != nullptr)
    this->_init_system_object->initialize();
}

user_QOI()

void libMesh::System::user_QOI ( const QoISet &  qoi_indices )

virtualinherited

Calls user's attached quantity of interest function, or is overridden by the user in derived classes.

Definition at line 2339 of file system.C.

References libMesh::System::_equation_systems, libMesh::System::_qoi_evaluate_function, libMesh::System::_qoi_evaluate_object, libMesh::System::name(), and libMesh::System::QOI::qoi().

Referenced by libMesh::System::assemble_qoi().

{
  // Call the user-provided quantity of interest function,
  // if it was provided
  if (_qoi_evaluate_function != nullptr)
    this->_qoi_evaluate_function(_equation_systems, this->name(), qoi_indices);

  // ...or the user-provided QOI function object.
  else if (_qoi_evaluate_object != nullptr)
    this->_qoi_evaluate_object->qoi(qoi_indices);
}

user_QOI_derivative()

void libMesh::System::user_QOI_derivative ( const QoISet &  qoi_indices = QoISet(), bool  include_liftfunc = true, bool  apply_constraints = true  )

virtualinherited

Calls user's attached quantity of interest derivative function, or is overridden by the user in derived classes.

Definition at line 2353 of file system.C.

References libMesh::System::_equation_systems, libMesh::System::_qoi_evaluate_derivative_function, libMesh::System::_qoi_evaluate_derivative_object, libMesh::System::name(), and libMesh::System::QOIDerivative::qoi_derivative().

Referenced by libMesh::System::assemble_qoi_derivative().

{
  // Call the user-provided quantity of interest derivative,
  // if it was provided
  if (_qoi_evaluate_derivative_function != nullptr)
    this->_qoi_evaluate_derivative_function
      (_equation_systems, this->name(), qoi_indices, include_liftfunc,
       apply_constraints);

  // ...or the user-provided QOI derivative function object.
  else if (_qoi_evaluate_derivative_object != nullptr)
    this->_qoi_evaluate_derivative_object->qoi_derivative
      (qoi_indices, include_liftfunc, apply_constraints);
}

variable()

const Variable & libMesh::System::variable ( unsigned int  var ) const

inlineinherited

Return a constant reference to Variable var.

Definition at line 2458 of file system.h.

References libMesh::System::_variables.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::PetscDMWrapper::add_dofs_to_section(), libMesh::DifferentiableSystem::add_second_order_dot_vars(), libMesh::System::add_variable(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::find_dofs_to_send(), libMesh::DifferentiableSystem::have_first_order_scalar_vars(), libMesh::DifferentiableSystem::have_second_order_scalar_vars(), main(), libMesh::DifferentiablePhysics::nonlocal_mass_residual(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SortAndCopy::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectVertices::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectEdges::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectSides::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectInteriors::operator()(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::System::read_parallel_data(), libMesh::System::read_SCALAR_dofs(), libMesh::System::read_serialized_vector(), libMesh::System::read_serialized_vectors(), libMesh::PetscDMWrapper::set_point_range_in_section(), libMesh::System::write_header(), libMesh::Nemesis_IO_Helper::write_nodal_solution(), libMesh::System::write_parallel_data(), libMesh::System::write_serialized_vector(), and libMesh::System::write_serialized_vectors().

{
  libmesh_assert_less (i, _variables.size());

  return _variables[i];
}

variable_group()

const VariableGroup & libMesh::System::variable_group ( unsigned int  vg ) const

inlineinherited

Return a constant reference to VariableGroup vg.

Definition at line 2468 of file system.h.

References libMesh::System::_variable_groups.

Referenced by libMesh::FEMSystem::assembly(), libMesh::System::get_info(), and libMesh::System::init_data().

{
  libmesh_assert_less (vg, _variable_groups.size());

  return _variable_groups[vg];
}

variable_name()

const std::string & libMesh::System::variable_name ( const unsigned int  i ) const

inlineinherited

Returns

The name of variable i.

Definition at line 2478 of file system.h.

References libMesh::System::_variables.

Referenced by libMesh::System::add_variable(), libMesh::System::add_variables(), libMesh::PetscDMWrapper::build_section(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::ExactSolution::ExactSolution(), libMesh::EquationSystems::find_variable_numbers(), main(), output_norms(), libMesh::petsc_auto_fieldsplit(), libMesh::InterMeshProjection::project_system_vectors(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), libMesh::System::write_header(), and libMesh::Nemesis_IO_Helper::write_nodal_solution().

{
  libmesh_assert_less (i, _variables.size());

  return _variables[i].name();
}

variable_number()

unsigned int libMesh::System::variable_number ( std::string_view  var ) const

inherited

Returns

The variable number associated with the user-specified variable named var.

Definition at line 1609 of file system.C.

References libMesh::System::_variable_numbers, libMesh::System::_variables, and libMesh::System::name().

Referenced by libMesh::ExactSolution::_compute_error(), alternative_fe_assembly(), LinearElasticity::assemble(), AssembleOptimization::assemble_A_and_F(), assemble_divgrad(), assemble_elasticity(), assemble_graddiv(), assemble_matrix_and_rhs(), assemble_shell(), assemble_stokes(), compute_enriched_soln(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::GMVIO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::Nemesis_IO::copy_nodal_solution(), libMesh::ExactErrorEstimator::estimate_error(), fe_assembly(), libMesh::ExactErrorEstimator::find_squared_element_error(), CoupledSystemQoI::init_context(), libMesh::HDGProblem::jacobian(), LargeDeformationElasticity::jacobian(), line_print(), main(), LinearElasticityWithContact::move_mesh(), libMesh::System::read_header(), libMesh::HDGProblem::residual(), LargeDeformationElasticity::residual(), LinearElasticityWithContact::residual_and_jacobian(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), OverlappingTestBase::setup_coupling_matrix(), libMesh::DTKAdapter::update_variable_values(), libMesh::System::variable_scalar_number(), libMesh::System::variable_type(), libMesh::EnsightIO::write_scalar_ascii(), and libMesh::EnsightIO::write_vector_ascii().

{
  auto var_num = libmesh_map_find(_variable_numbers, var);
  libmesh_assert_equal_to (_variables[var_num].name(), var);
  return var_num;
}

variable_scalar_number() [1/2]

unsigned int libMesh::System::variable_scalar_number ( std::string_view  var, unsigned int  component  ) const

inlineinherited

Returns

An index, starting from 0 for the first component of the first variable, and incrementing for each component of each (potentially vector-valued) variable in the system in order. For systems with only scalar-valued variables, this will be the same as variable_number(var)

Irony: currently our only non-scalar-valued variable type is SCALAR.

Definition at line 2489 of file system.h.

References libMesh::System::variable_number().

Referenced by libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectVertices::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectEdges::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectSides::operator()(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectInteriors::operator()().

{
  return variable_scalar_number(this->variable_number(var), component);
}

variable_scalar_number() [2/2]

unsigned int libMesh::System::variable_scalar_number ( unsigned int  var_num, unsigned int  component  ) const

inlineinherited

Returns

An index, starting from 0 for the first component of the first variable, and incrementing for each component of each (potentially vector-valued) variable in the system in order. For systems with only scalar-valued variables, this will be the same as var_num

Irony: currently our only non-scalar-valued variable type is SCALAR.

Definition at line 2499 of file system.h.

References libMesh::System::_variables.

{
  return _variables[var_num].first_scalar_number() + component;
}

variable_type() [1/2]

const FEType & libMesh::System::variable_type ( const unsigned int  i ) const

inlineinherited

Returns

The finite element type variable number i.

Definition at line 2508 of file system.h.

References libMesh::System::_variables.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::System::add_variable(), libMesh::System::add_variables(), alternative_fe_assembly(), assemble(), libMesh::ClawSystem::assemble_advection_matrices(), libMesh::ClawSystem::assemble_avg_coupling_matrices(), libMesh::ClawSystem::assemble_boundary_condition_matrices(), assemble_ellipticdg(), libMesh::ClawSystem::assemble_jump_coupling_matrix(), libMesh::ClawSystem::assemble_mass_matrix(), assemble_shell(), assemble_stokes(), libMesh::FEMContext::attach_quadrature_rules(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::GMVIO::copy_nodal_solution(), libMesh::DGFEMContext::DGFEMContext(), fe_assembly(), libMesh::FEMContext::find_hardest_fe_type(), libMesh::EquationSystems::find_variable_numbers(), form_functionA(), form_functionB(), form_matrixA(), libMesh::FEMSystem::init_context(), libMesh::FEMContext::init_internal_data(), RationalMapTest< elem_type >::setUp(), FETestBase< order, family, elem_type, 1 >::setUp(), EquationSystemsTest::testBadVarNames(), libMesh::Nemesis_IO_Helper::write_element_values(), libMesh::System::write_header(), libMesh::Nemesis_IO_Helper::write_nodal_solution(), libMesh::EnsightIO::write_scalar_ascii(), and libMesh::EnsightIO::write_vector_ascii().

{
  libmesh_assert_less (i, _variables.size());

  return _variables[i].type();
}

variable_type() [2/2]

const FEType & libMesh::System::variable_type ( std::string_view  var ) const

inlineinherited

Returns

The finite element type for variable var.

Definition at line 2518 of file system.h.

References libMesh::System::_variables, and libMesh::System::variable_number().

{
  return _variables[this->variable_number(var)].type();
}

vector_is_adjoint()

int libMesh::System::vector_is_adjoint ( std::string_view  vec_name ) const

inherited

Returns

The integer describing whether the vector identified by vec_name represents a solution from an adjoint (non-negative) or the primal (-1) space.

Definition at line 1173 of file system.C.

References libMesh::System::_vector_is_adjoint, and libMesh::libmesh_assert().

Referenced by libMesh::InterMeshProjection::project_system_vectors(), and libMesh::System::restrict_vectors().

{
  const auto it = _vector_is_adjoint.find(vec_name);
  libmesh_assert(it != _vector_is_adjoint.end());
  return it->second;
}

vector_name() [1/2]

const std::string & libMesh::System::vector_name ( const unsigned int  vec_num ) const

inherited

Returns

The name of this system's additional vector number vec_num (where the vectors are counted starting with 0).

Definition at line 983 of file system.C.

References libMesh::System::_vectors, and libMesh::System::vectors_begin().

Referenced by libMesh::AdjointRefinementEstimator::estimate_error(), and main().

{
  // If we don't have that many vectors, throw an error
  libmesh_assert_less(vec_num, _vectors.size());

  // Otherwise return a reference to the vec_num'th vector name
  auto it = vectors_begin();
  std::advance(it, vec_num);
  return it->first;
}

vector_name() [2/2]

const std::string & libMesh::System::vector_name ( const NumericVector< Number > &  vec_reference ) const

inherited

Returns

The name of a system vector, given a reference to that vector

Definition at line 994 of file system.C.

References libMesh::System::_vectors, libMesh::NumericVector< T >::get(), libMesh::libmesh_assert(), libMesh::System::vectors_begin(), and libMesh::System::vectors_end().

{
  // Linear search for a vector whose pointer matches vec_reference
  auto it = std::find_if(vectors_begin(), vectors_end(),
                         [&vec_reference](const decltype(_vectors)::value_type & pr)
                         { return &vec_reference == pr.second.get(); });

  // Before returning, make sure we didn't loop till the end and not find any match
  libmesh_assert (it != vectors_end());

  // Return the string associated with the current vector
  return it->first;
}

vector_preservation()

bool libMesh::System::vector_preservation ( std::string_view  vec_name ) const

inherited

Returns

The boolean describing whether the vector identified by vec_name should be "preserved": projected to new meshes, saved, etc.

Definition at line 1148 of file system.C.

References libMesh::System::_vector_projections.

Referenced by libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::MemoryHistoryData::store_vectors(), SystemsTest::testAddVectorProjChange(), SystemsTest::testAddVectorTypeChange(), and SystemsTest::testPostInitAddVectorTypeChange().

{
  if (auto it = _vector_projections.find(vec_name);
      it != _vector_projections.end())
    return it->second;

  // vec_name was not in the map, return false
  return false;
}

vectors_begin() [1/2]

System::vectors_iterator libMesh::System::vectors_begin ( )

inlineinherited

Beginning of vectors container.

Definition at line 2564 of file system.h.

References libMesh::System::_vectors.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::System::get_vector(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::System::request_vector(), libMesh::MemoryHistoryData::store_vectors(), and libMesh::System::vector_name().

{
  return _vectors.begin();
}

vectors_begin() [2/2]

System::const_vectors_iterator libMesh::System::vectors_begin ( ) const

inlineinherited

Beginning of vectors container.

Definition at line 2570 of file system.h.

References libMesh::System::_vectors.

{
  return _vectors.begin();
}

vectors_end() [1/2]

System::vectors_iterator libMesh::System::vectors_end ( )

inlineinherited

End of vectors container.

Definition at line 2576 of file system.h.

References libMesh::System::_vectors.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::MemoryHistoryData::store_vectors(), and libMesh::System::vector_name().

{
  return _vectors.end();
}

vectors_end() [2/2]

System::const_vectors_iterator libMesh::System::vectors_end ( ) const

inlineinherited

End of vectors container.

Definition at line 2582 of file system.h.

References libMesh::System::_vectors.

{
  return _vectors.end();
}

weighted_sensitivity_adjoint_solve()

std::pair< unsigned int, Real > libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve ( const ParameterVector &  parameters, const ParameterVector &  weights, const QoISet &  qoi_indices = QoISet()  )

overridevirtualinherited

Assembles & solves the linear system(s) (dR/du)^T*z_w = sum(w_p*(d^2q/dudp - d^2R/dudp*z)), for those parameters p contained within parameters, weighted by the values w_p found within weights.

Assumes that adjoint_solve has already calculated z for each qoi in qoi_indices.

Returns

A pair with the total number of linear iterations performed and the (sum of the) final residual norms

Reimplemented from libMesh::System.

Definition at line 243 of file implicit_system.C.

References libMesh::System::add_weighted_sensitivity_adjoint_solution(), libMesh::ExplicitSystem::assemble_qoi_derivative(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::ParameterVector::deep_copy(), libMesh::DofMap::enforce_constraints_exactly(), libMesh::System::get_adjoint_rhs(), libMesh::System::get_adjoint_solution(), libMesh::System::get_dof_map(), libMesh::ImplicitSystem::get_linear_solve_parameters(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::SparseMatrix< T >::get_transpose(), libMesh::System::get_weighted_sensitivity_adjoint_solution(), libMesh::DofMap::has_adjoint_dirichlet_boundaries(), libMesh::QoISet::has_index(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::ImplicitSystem::matrix, libMesh::System::n_qois(), libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::LinearSolver< T >::solve(), libMesh::TOLERANCE, libMesh::ParameterVector::value_copy(), libMesh::SparseMatrix< T >::vector_mult_add(), and libMesh::NumericVector< T >::zero_clone().

Referenced by libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product().

{
  // Log how long the linear solve takes.
  LOG_SCOPE("weighted_sensitivity_adjoint_solve()", "ImplicitSystem");

  // We currently get partial derivatives via central differencing
  const Real delta_p = TOLERANCE;

  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  // The forward system should now already be solved.
  // The adjoint system should now already be solved.
  // Now we're assembling a weighted sum of adjoint-adjoint systems:
  //
  // dR/du (u, sum_l(w_l*z^l)) = sum_l(w_l*(Q''_ul - R''_ul (u, z)))

  // FIXME: The derivation here does not yet take adjoint boundary
  // conditions into account.
#ifdef LIBMESH_ENABLE_DIRICHLET
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      libmesh_assert(!this->get_dof_map().has_adjoint_dirichlet_boundaries(i));
#endif

  // We'll assemble the rhs first, because the R'' term will require
  // perturbing the jacobian

  // We'll use temporary rhs vectors, because we haven't (yet) found
  // any good reasons why users might want to save these:

  std::vector<std::unique_ptr<NumericVector<Number>>> temprhs(this->n_qois());
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      temprhs[i] = this->rhs->zero_clone();

  // We approximate the _l partial derivatives via a central
  // differencing perturbation in the w_l direction:
  //
  // sum_l(w_l*v_l) ~= (v(p + dp*w_l*e_l) - v(p - dp*w_l*e_l))/(2*dp)

  // PETSc doesn't implement SGEMX, so neither does NumericVector,
  // so we want to avoid calculating f -= R'*z.  We'll thus evaluate
  // the above equation by first adding -v(p+dp...), then multiplying
  // the intermediate result vectors by -1, then adding -v(p-dp...),
  // then finally dividing by 2*dp.

  ParameterVector oldparameters, parameterperturbation;
  parameters_vec.deep_copy(oldparameters);
  weights.deep_copy(parameterperturbation);
  parameterperturbation *= delta_p;
  parameters_vec += parameterperturbation;

  this->assembly(false, true);
  this->matrix->close();

  // Take the discrete adjoint, so that we can calculate R_u(u,z) with
  // a matrix-vector product of R_u and z.
  matrix->get_transpose(*matrix);

  this->assemble_qoi_derivative(qoi_indices,
                                /* include_liftfunc = */ false,
                                /* apply_constraints = */ true);
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      {
        this->get_adjoint_rhs(i).close();
        *(temprhs[i]) -= this->get_adjoint_rhs(i);
        this->matrix->vector_mult_add(*(temprhs[i]), this->get_adjoint_solution(i));
        *(temprhs[i]) *= -1.0;
      }

  oldparameters.value_copy(parameters_vec);
  parameterperturbation *= -1.0;
  parameters_vec += parameterperturbation;

  this->assembly(false, true);
  this->matrix->close();
  matrix->get_transpose(*matrix);

  this->assemble_qoi_derivative(qoi_indices,
                                /* include_liftfunc = */ false,
                                /* apply_constraints = */ true);
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      {
        this->get_adjoint_rhs(i).close();
        *(temprhs[i]) -= this->get_adjoint_rhs(i);
        this->matrix->vector_mult_add(*(temprhs[i]), this->get_adjoint_solution(i));
        *(temprhs[i]) /= (2.0*delta_p);
      }

  // Finally, assemble the jacobian at the non-perturbed parameter
  // values.  Ignore assemble_before_solve; if we had a good
  // non-perturbed matrix before we've already overwritten it.
  oldparameters.value_copy(parameters_vec);

  // if (this->assemble_before_solve)
  {
    // Build the Jacobian
    this->assembly(false, true);
    this->matrix->close();

    // Take the discrete adjoint
    matrix->get_transpose(*matrix);
  }

  // The weighted adjoint-adjoint problem is linear
  LinearSolver<Number> * solver = this->get_linear_solver();

  // Our iteration counts and residuals will be sums of the individual
  // results
  std::pair<unsigned int, Real> solver_params =
    this->get_linear_solve_parameters();
  std::pair<unsigned int, Real> totalrval = std::make_pair(0,0.0);

  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      {
        const std::pair<unsigned int, Real> rval =
          solver->solve (*matrix, this->add_weighted_sensitivity_adjoint_solution(i),
                         *(temprhs[i]),
                         double(solver_params.second),
                         solver_params.first);

        totalrval.first  += rval.first;
        totalrval.second += rval.second;
      }

  // The linear solver may not have fit our constraints exactly
#ifdef LIBMESH_ENABLE_CONSTRAINTS
  for (auto i : make_range(this->n_qois()))
    if (qoi_indices.has_index(i))
      this->get_dof_map().enforce_constraints_exactly
        (*this, &this->get_weighted_sensitivity_adjoint_solution(i),
         /* homogeneous = */ true);
#endif

  return totalrval;
}

weighted_sensitivity_solve()

std::pair< unsigned int, Real > libMesh::ImplicitSystem::weighted_sensitivity_solve ( const ParameterVector &  parameters, const ParameterVector &  weights  )

overridevirtualinherited

Assembles & solves the linear system(s) (dR/du)*u_w = sum(w_p*-dR/dp), for those parameters p contained within parameters weighted by the values w_p found within weights.

Returns

A pair with the total number of linear iterations performed and the (sum of the) final residual norms

Reimplemented from libMesh::System.

Definition at line 389 of file implicit_system.C.

References libMesh::System::add_weighted_sensitivity_solution(), libMesh::ImplicitSystem::assembly(), libMesh::NumericVector< T >::clone(), libMesh::NumericVector< T >::close(), libMesh::SparseMatrix< T >::close(), libMesh::ParameterVector::deep_copy(), libMesh::DofMap::enforce_constraints_exactly(), libMesh::System::get_dof_map(), libMesh::ImplicitSystem::get_linear_solve_parameters(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::System::get_weighted_sensitivity_solution(), libMesh::ImplicitSystem::matrix, libMesh::Real, libMesh::ExplicitSystem::rhs, libMesh::LinearSolver< T >::solve(), libMesh::TOLERANCE, and libMesh::ParameterVector::value_copy().

Referenced by libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product().

{
  // Log how long the linear solve takes.
  LOG_SCOPE("weighted_sensitivity_solve()", "ImplicitSystem");

  // We currently get partial derivatives via central differencing
  const Real delta_p = TOLERANCE;

  ParameterVector & parameters_vec =
    const_cast<ParameterVector &>(parameters_in);

  // The forward system should now already be solved.

  // Now we're assembling a weighted sum of sensitivity systems:
  //
  // dR/du (u, v)(sum(w_l*u'_l)) = -sum_l(w_l*R'_l (u, v)) forall v

  // We'll assemble the rhs first, because the R' term will require
  // perturbing the system, and some applications may not be able to
  // assemble a perturbed residual without simultaneously constructing
  // a perturbed jacobian.

  // We approximate the _l partial derivatives via a central
  // differencing perturbation in the w_l direction:
  //
  // sum_l(w_l*v_l) ~= (v(p + dp*w_l*e_l) - v(p - dp*w_l*e_l))/(2*dp)

  ParameterVector oldparameters, parameterperturbation;
  parameters_vec.deep_copy(oldparameters);
  weights.deep_copy(parameterperturbation);
  parameterperturbation *= delta_p;
  parameters_vec += parameterperturbation;

  this->assembly(true, false, true);
  this->rhs->close();

  std::unique_ptr<NumericVector<Number>> temprhs = this->rhs->clone();

  oldparameters.value_copy(parameters_vec);
  parameterperturbation *= -1.0;
  parameters_vec += parameterperturbation;

  this->assembly(true, false, true);
  this->rhs->close();

  *temprhs -= *(this->rhs);
  *temprhs /= (2.0*delta_p);

  // Finally, assemble the jacobian at the non-perturbed parameter
  // values
  oldparameters.value_copy(parameters_vec);

  // Build the Jacobian
  this->assembly(false, true);
  this->matrix->close();

  // The weighted sensitivity problem is linear
  LinearSolver<Number> * solver = this->get_linear_solver();

  std::pair<unsigned int, Real> solver_params =
    this->get_linear_solve_parameters();

  const std::pair<unsigned int, Real> rval =
    solver->solve (*matrix, this->add_weighted_sensitivity_solution(),
                   *temprhs,
                   double(solver_params.second),
                   solver_params.first);

  // The linear solver may not have fit our constraints exactly
#ifdef LIBMESH_ENABLE_CONSTRAINTS
  this->get_dof_map().enforce_constraints_exactly
    (*this, &this->get_weighted_sensitivity_solution(),
     /* homogeneous = */ true);
#endif

  return rval;
}

write_header()

void libMesh::System::write_header ( Xdr &  io, std::string_view  version, const bool  write_additional_data  ) const

inherited

Writes the basic data header for this System.

This method implements the output of a System object, embedded in the output of an EquationSystems<T_sys>. This warrants some documentation. The output of this part consists of 5 sections:

for this system

5.) The number of variables in the system (unsigned int)

for each variable in the system

6.) The name of the variable (string)

6.1.) subdomain where the variable lives

7.) Combined in an FEType:

• The approximation order(s) of the variable (Order Enum, cast to int/s)
• The finite element family/ies of the variable (FEFamily Enum, cast to int/s)

end variable loop

8.) The number of additional vectors (unsigned int),

for each additional vector in the system object

9.) the name of the additional vector (string)

end system

Definition at line 1267 of file system_io.C.

References libMesh::System::_vector_projections, libMesh::System::_vectors, libMesh::Variable::active_subdomains(), libMesh::Xdr::data(), libMesh::FEType::family, libMesh::System::get_mesh(), libMesh::FEType::inf_map, libMesh::libmesh_assert(), libMesh::make_range(), libMesh::System::n_vars(), libMesh::System::n_vectors(), libMesh::System::name(), libMesh::FEType::order, libMesh::ParallelObject::processor_id(), libMesh::FEType::radial_family, libMesh::FEType::radial_order, libMesh::System::variable(), libMesh::System::variable_name(), libMesh::System::variable_type(), and libMesh::Xdr::writing().

Referenced by libMesh::RBEvaluation::write_out_vectors().

{
  libmesh_assert (io.writing());


  // Only write the header information
  // if we are processor 0.
  if (this->get_mesh().processor_id() != 0)
    return;

  std::string comment;

  // 5.)
  // Write the number of variables in the system

  {
    // set up the comment
    comment = "# No. of Variables in System \"";
    comment += this->name();
    comment += "\"";

    unsigned int nv = this->n_vars();
    io.data (nv, comment);
  }


  for (auto var : make_range(this->n_vars()))
    {
      // 6.)
      // Write the name of the var-th variable
      {
        // set up the comment
        comment  = "#   Name, Variable No. ";
        comment += std::to_string(var);
        comment += ", System \"";
        comment += this->name();
        comment += "\"";

        std::string var_name = this->variable_name(var);
        io.data (var_name, comment);
      }

      // 6.1.) Variable subdomains
      {
        // set up the comment
        comment  = "#     Subdomains, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        const std::set<subdomain_id_type> & domains = this->variable(var).active_subdomains();
        std::vector<subdomain_id_type> domain_array;
        domain_array.assign(domains.begin(), domains.end());
        io.data (domain_array, comment);
      }

      // 7.)
      // Write the approximation order of the var-th variable
      // in this system
      {
        // set up the comment
        comment = "#     Approximation Order, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        int order = static_cast<int>(this->variable_type(var).order);
        io.data (order, comment);
      }


#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS

      // do the same for radial_order
      {
        comment = "#     Radial Approximation Order, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        int rad_order = static_cast<int>(this->variable_type(var).radial_order);
        io.data (rad_order, comment);
      }

#endif

      // Write the Finite Element type of the var-th variable
      // in this System
      {
        // set up the comment
        comment = "#     FE Family, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        const FEType & type = this->variable_type(var);
        int fam = static_cast<int>(type.family);
        io.data (fam, comment);

#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS

        comment = "#     Radial FE Family, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        int radial_fam = static_cast<int>(type.radial_family);
        io.data (radial_fam, comment);

        comment = "#     Infinite Mapping Type, Variable \"";
        comment += this->variable_name(var);
        comment += "\", System \"";
        comment += this->name();
        comment += "\"";

        int i_map = static_cast<int>(type.inf_map);
        io.data (i_map, comment);
#endif
      }
    } // end of the variable loop

  // 8.)
  // Write the number of additional vectors in the System.
  // If write_additional_data==false, then write zero for
  // the number of additional vectors.
  {
    {
      // set up the comment
      comment = "# No. of Additional Vectors, System \"";
      comment += this->name();
      comment += "\"";

      unsigned int nvecs = write_additional_data ? this->n_vectors () : 0;
      io.data (nvecs, comment);
    }

    if (write_additional_data)
      {
        unsigned int cnt=0;
        for (const auto & [vec_name, vec] : _vectors)
          {
            // 9.)
            // write the name of the cnt-th additional vector
            const std::string dth_vector = std::to_string(cnt++)+"th vector";
            comment =  "# Name of " + dth_vector;
            std::string nonconst_vec_name = vec_name; // Stupid XDR API

            io.data (nonconst_vec_name, comment);
            int vec_projection = _vector_projections.at(vec_name);
            comment = "# Whether to do projections for " + dth_vector;
            io.data (vec_projection, comment);
            int vec_type = vec->type();
            comment = "# Parallel type of " + dth_vector;
            io.data (vec_type, comment);
          }
      }
  }
}

write_parallel_data()

void libMesh::System::write_parallel_data ( Xdr &  io, const bool  write_additional_data  ) const

inherited

Writes additional data, namely vectors, for this System.

This method may safely be called on a distributed-memory mesh. This method will create an individual file for each processor in the simulation where the local solution components for that processor will be stored.

This method implements the output of the vectors contained in this System object, embedded in the output of an EquationSystems<T_sys>.

9.) The global solution vector, re-ordered to be node-major (More on this later.)

for each additional vector in the object

10.) The global additional vector, re-ordered to be node-major (More on this later.)

Note that the actual IO is handled through the Xdr class (to be renamed later?) which provides a uniform interface to both the XDR (eXternal Data Representation) interface and standard ASCII output. Thus this one section of code will read XDR or ASCII files with no changes.

Definition at line 1468 of file system_io.C.

References libMesh::System::_vectors, libMesh::Xdr::data(), libMesh::FEType::family, libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::DofObject::invalid_id, libMesh::libmesh_assert(), libMesh::make_range(), libMesh::ParallelObject::n_processors(), libMesh::System::n_vars(), libMesh::System::name(), libMesh::System::number(), libMesh::ParallelObject::processor_id(), libMesh::SCALAR, libMesh::DofMap::SCALAR_dof_indices(), libMesh::System::solution, libMesh::Variable::type(), libMesh::System::variable(), and libMesh::Xdr::writing().

{
  // PerfLog pl("IO Performance",false);
  // pl.push("write_parallel_data");
  // std::size_t total_written_size = 0;

  std::string comment;

  libmesh_assert (io.writing());

  std::vector<Number> io_buffer; io_buffer.reserve(this->solution->local_size());

  // build the ordered nodes and element maps.
  // when writing/reading parallel files we need to iterate
  // over our nodes/elements in order of increasing global id().
  // however, this is not guaranteed to be ordering we obtain
  // by using the node_iterators/element_iterators directly.
  // so build a set, sorted by id(), that provides the ordering.
  // further, for memory economy build the set but then transfer
  // its contents to vectors, which will be sorted.
  std::vector<const DofObject *> ordered_nodes, ordered_elements;
  {
    std::set<const DofObject *, CompareDofObjectsByID>
      ordered_nodes_set (this->get_mesh().local_nodes_begin(),
                         this->get_mesh().local_nodes_end());

    ordered_nodes.insert(ordered_nodes.end(),
                         ordered_nodes_set.begin(),
                         ordered_nodes_set.end());
  }
  {
    std::set<const DofObject *, CompareDofObjectsByID>
      ordered_elements_set (this->get_mesh().local_elements_begin(),
                            this->get_mesh().local_elements_end());

    ordered_elements.insert(ordered_elements.end(),
                            ordered_elements_set.begin(),
                            ordered_elements_set.end());
  }

  const unsigned int sys_num = this->number();
  const unsigned int nv      = this->n_vars();

  // Loop over each non-SCALAR variable and each node, and write out the value.
  for (unsigned int var=0; var<nv; var++)
    if (this->variable(var).type().family != SCALAR)
      {
        // First write the node DOF values
        for (const auto & node : ordered_nodes)
          for (auto comp : make_range(node->n_comp(sys_num,var)))
            {
              libmesh_assert_not_equal_to (node->dof_number(sys_num, var, comp),
                                           DofObject::invalid_id);

              io_buffer.push_back((*this->solution)(node->dof_number(sys_num, var, comp)));
            }

        // Then write the element DOF values
        for (const auto & elem : ordered_elements)
          for (auto comp : make_range(elem->n_comp(sys_num,var)))
            {
              libmesh_assert_not_equal_to (elem->dof_number(sys_num, var, comp),
                                           DofObject::invalid_id);

              io_buffer.push_back((*this->solution)(elem->dof_number(sys_num, var, comp)));
            }
      }

  // Finally, write the SCALAR data on the last processor
  for (auto var : make_range(this->n_vars()))
    if (this->variable(var).type().family == SCALAR)
      {
        if (this->processor_id() == (this->n_processors()-1))
          {
            const DofMap & dof_map = this->get_dof_map();
            std::vector<dof_id_type> SCALAR_dofs;
            dof_map.SCALAR_dof_indices(SCALAR_dofs, var);

            for (auto dof : SCALAR_dofs)
              io_buffer.push_back((*this->solution)(dof));
          }
      }

  // 9.)
  //
  // Actually write the reordered solution vector
  // for the ith system to disk

  // set up the comment
  {
    comment = "# System \"";
    comment += this->name();
    comment += "\" Solution Vector";
  }

  io.data (io_buffer, comment);

  // total_written_size += io_buffer.size();

  // Only write additional vectors if wanted
  if (write_additional_data)
    {
      for (auto & [vec_name, vec] : _vectors)
        {
          io_buffer.clear();
          io_buffer.reserve(vec->local_size());

          // Loop over each non-SCALAR variable and each node, and write out the value.
          for (unsigned int var=0; var<nv; var++)
            if (this->variable(var).type().family != SCALAR)
              {
                // First write the node DOF values
                for (const auto & node : ordered_nodes)
                  for (auto comp : make_range(node->n_comp(sys_num,var)))
                    {
                      libmesh_assert_not_equal_to (node->dof_number(sys_num, var, comp),
                                                   DofObject::invalid_id);

                      io_buffer.push_back((*vec)(node->dof_number(sys_num, var, comp)));
                    }

                // Then write the element DOF values
                for (const auto & elem : ordered_elements)
                  for (auto comp : make_range(elem->n_comp(sys_num,var)))
                    {
                      libmesh_assert_not_equal_to (elem->dof_number(sys_num, var, comp),
                                                   DofObject::invalid_id);

                      io_buffer.push_back((*vec)(elem->dof_number(sys_num, var, comp)));
                    }
              }

          // Finally, write the SCALAR data on the last processor
          for (auto var : make_range(this->n_vars()))
            if (this->variable(var).type().family == SCALAR)
              {
                if (this->processor_id() == (this->n_processors()-1))
                  {
                    const DofMap & dof_map = this->get_dof_map();
                    std::vector<dof_id_type> SCALAR_dofs;
                    dof_map.SCALAR_dof_indices(SCALAR_dofs, var);

                    for (auto dof : SCALAR_dofs)
                      io_buffer.push_back((*vec)(dof));
                  }
              }

          // 10.)
          //
          // Actually write the reordered additional vector
          // for this system to disk

          // set up the comment
          {
            comment = "# System \"";
            comment += this->name();
            comment += "\" Additional Vector \"";
            comment += vec_name;
            comment += "\"";
          }

          io.data (io_buffer, comment);

          // total_written_size += io_buffer.size();
        }
    }

  // const Real
  //   dt   = pl.get_elapsed_time(),
  //   rate = total_written_size*sizeof(Number)/dt;

  // libMesh::err << "Write " << total_written_size << " \"Number\" values\n"
  //     << " Elapsed time = " << dt << '\n'
  //     << " Rate = " << rate/1.e6 << "(MB/sec)\n\n";

  // pl.pop("write_parallel_data");
}

write_serialized_data()

void libMesh::System::write_serialized_data ( Xdr &  io, const bool  write_additional_data = true  ) const

inherited

Writes additional data, namely vectors, for this System.

This method may safely be called on a distributed-memory mesh.

This method implements the output of the vectors contained in this System object, embedded in the output of an EquationSystems<T_sys>.

9.) The global solution vector, re-ordered to be node-major (More on this later.)

for each additional vector in the object

10.) The global additional vector, re-ordered to be node-major (More on this later.)

Definition at line 1668 of file system_io.C.

References libMesh::System::_vectors, libMesh::Xdr::comment(), libMesh::System::name(), libMesh::ParallelObject::processor_id(), libMesh::System::solution, and libMesh::System::write_serialized_vector().

Referenced by libMesh::TransientRBConstruction::write_riesz_representors_to_files(), and libMesh::RBConstruction::write_riesz_representors_to_files().

{
  parallel_object_only();
  std::string comment;

  // PerfLog pl("IO Performance",false);
  // pl.push("write_serialized_data");
  // std::size_t total_written_size = 0;

  // total_written_size +=
  this->write_serialized_vector(io, *this->solution);

  // set up the comment
  if (this->processor_id() == 0)
    {
      comment = "# System \"";
      comment += this->name();
      comment += "\" Solution Vector";

      io.comment (comment);
    }

  // Only write additional vectors if wanted
  if (write_additional_data)
    {
      for (auto & pair : this->_vectors)
        {
          // total_written_size +=
          this->write_serialized_vector(io, *pair.second);

          // set up the comment
          if (this->processor_id() == 0)
            {
              comment = "# System \"";
              comment += this->name();
              comment += "\" Additional Vector \"";
              comment += pair.first;
              comment += "\"";
              io.comment (comment);
            }
        }
    }

  // const Real
  //   dt   = pl.get_elapsed_time(),
  //   rate = total_written_size*sizeof(Number)/dt;

  // libMesh::out << "Write " << total_written_size << " \"Number\" values\n"
  //     << " Elapsed time = " << dt << '\n'
  //     << " Rate = " << rate/1.e6 << "(MB/sec)\n\n";

  // pl.pop("write_serialized_data");




  // // test the new method
  // {
  //   std::vector<std::string> names;
  //   std::vector<NumericVector<Number> *> vectors_to_write;

  //   names.push_back("Solution Vector");
  //   vectors_to_write.push_back(this->solution.get());

  //   // Only write additional vectors if wanted
  //   if (write_additional_data)
  //     {
  // std::map<std::string, NumericVector<Number> *>::const_iterator
  //   pos = _vectors.begin();

  // for (; pos != this->_vectors.end(); ++pos)
  //   {
  //     names.push_back("Additional Vector " + pos->first);
  //     vectors_to_write.push_back(pos->second);
  //   }
  //     }

  //   total_written_size =
  //     this->write_serialized_vectors (io, names, vectors_to_write);

  //   const Real
  //     dt2   = pl.get_elapsed_time(),
  //     rate2 = total_written_size*sizeof(Number)/(dt2-dt);

  //   libMesh::out << "Write (new) " << total_written_size << " \"Number\" values\n"
  //       << " Elapsed time = " << (dt2-dt) << '\n'
  //       << " Rate = " << rate2/1.e6 << "(MB/sec)\n\n";

  // }
}

write_serialized_vectors()

std::size_t libMesh::System::write_serialized_vectors ( Xdr &  io, const std::vector< const NumericVector< Number > *> &  vectors  ) const

inherited

Serialize & write a number of identically distributed vectors.

This method allows for optimization for the multiple vector case by only communicating the metadata once.

Definition at line 2261 of file system_io.C.

References libMesh::Xdr::data(), libMesh::System::get_mesh(), libMesh::libmesh_assert(), libMesh::make_range(), libMesh::MeshTools::n_elem(), libMesh::MeshBase::n_elem(), n_nodes, libMesh::MeshBase::n_nodes(), libMesh::System::n_vars(), libMesh::ParallelObject::processor_id(), libMesh::SCALAR, libMesh::System::variable(), libMesh::System::write_SCALAR_dofs(), libMesh::System::write_serialized_blocked_dof_objects(), and libMesh::Xdr::writing().

Referenced by libMesh::RBEvaluation::write_out_vectors().

{
  parallel_object_only();

  libmesh_assert (io.writing());

  // Cache these - they are not free!
  const dof_id_type
    n_nodes       = this->get_mesh().n_nodes(),
    n_elem        = this->get_mesh().n_elem();

  std::size_t written_length = 0;

  if (this->processor_id() == 0)
    {
      unsigned int
        n_vec    = cast_int<unsigned int>(vectors.size());
      dof_id_type
        vec_size = vectors.empty() ? 0 : vectors[0]->size();
      // Set the number of vectors
      io.data(n_vec, "# number of vectors");
      // Set the buffer size
      io.data(vec_size, "# vector length");
    }

  //---------------------------------
  // Collect the values for all nodes
  written_length +=
    this->write_serialized_blocked_dof_objects (vectors,
                                                n_nodes,
                                                this->get_mesh().local_nodes_begin(),
                                                this->get_mesh().local_nodes_end(),
                                                io);

  //------------------------------------
  // Collect the values for all elements
  written_length +=
    this->write_serialized_blocked_dof_objects (vectors,
                                                n_elem,
                                                this->get_mesh().local_elements_begin(),
                                                this->get_mesh().local_elements_end(),
                                                io);

  //-------------------------------------------
  // Finally loop over all the SCALAR variables
  for (const NumericVector<Number> * vec : vectors)
    for (auto var : make_range(this->n_vars()))
      if (this->variable(var).type().family == SCALAR)
        {
          libmesh_assert_not_equal_to (vec, 0);

          written_length +=
            this->write_SCALAR_dofs (*vec, var, io);
        }

  return written_length;
}

zero_variable()

void libMesh::System::zero_variable ( NumericVector< Number > &  v, unsigned int  var_num  ) const

inherited

Zeroes all dofs in v that correspond to variable number var_num.

Definition at line 1668 of file system.C.

References libMesh::System::get_mesh(), mesh, libMesh::System::n_vars(), libMesh::System::number(), and libMesh::NumericVector< T >::set().

{
  /* Make sure the call makes sense.  */
  libmesh_assert_less (var_num, this->n_vars());

  /* Get a reference to the mesh.  */
  const MeshBase & mesh = this->get_mesh();

  /* Check which system we are.  */
  const unsigned int sys_num = this->number();

  // Loop over nodes.
  for (const auto & node : mesh.local_node_ptr_range())
    {
      unsigned int n_comp = node->n_comp(sys_num,var_num);
      for (unsigned int i=0; i<n_comp; i++)
        {
          const dof_id_type index = node->dof_number(sys_num,var_num,i);
          v.set(index,0.0);
        }
    }

  // Loop over elements.
  for (const auto & elem : mesh.active_local_element_ptr_range())
    {
      unsigned int n_comp = elem->n_comp(sys_num,var_num);
      for (unsigned int i=0; i<n_comp; i++)
        {
          const dof_id_type index = elem->dof_number(sys_num,var_num,i);
          v.set(index,0.0);
        }
    }
}

Member Data Documentation

_communicator

const Parallel::Communicator& libMesh::ParallelObject::_communicator

protectedinherited

Definition at line 120 of file parallel_object.h.

Referenced by libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::StaticCondensation::close(), libMesh::ParallelObject::comm(), libMesh::CondensedEigenSystem::initialize_condensed_matrices(), libMesh::ParallelObject::n_processors(), libMesh::ParallelObject::operator=(), libMesh::ParallelObject::processor_id(), libMesh::BoundaryInfo::regenerate_id_sets(), and libMesh::StaticCondensationDofMap::reinit().

_constrain_in_solver

bool libMesh::DifferentiableSystem::_constrain_in_solver

protectedinherited

_constrain_in_solver defaults to true; if false then we apply constraints only via residual terms in the systems to be solved.

Definition at line 432 of file diff_system.h.

Referenced by libMesh::DifferentiableSystem::get_constrain_in_solver(), and libMesh::DifferentiableSystem::set_constrain_in_solver().

_counts

ReferenceCounter::Counts libMesh::ReferenceCounter::_counts

staticprotectedinherited

Actually holds the data.

Definition at line 124 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::get_info().

_enable_print_counter

bool libMesh::ReferenceCounter::_enable_print_counter = true

staticprotectedinherited

Flag to control whether reference count information is printed when print_info is called.

Definition at line 143 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::disable_print_counter_info(), libMesh::ReferenceCounter::enable_print_counter_info(), and libMesh::ReferenceCounter::print_info().

_first_order_vars

std::set<unsigned int> libMesh::DifferentiablePhysics::_first_order_vars

protectedinherited

Variable indices for those variables that are first order in time.

Definition at line 548 of file diff_physics.h.

Referenced by libMesh::DifferentiablePhysics::get_first_order_vars(), libMesh::DifferentiablePhysics::have_first_order_vars(), libMesh::DifferentiablePhysics::is_first_order_var(), and libMesh::DifferentiablePhysics::time_evolving().

_mesh_sys

System* libMesh::DifferentiablePhysics::_mesh_sys

protectedinherited

System from which to acquire moving mesh information.

Definition at line 531 of file diff_physics.h.

Referenced by libMesh::FEMPhysics::eulerian_residual(), libMesh::DifferentiablePhysics::get_mesh_system(), libMesh::FEMSystem::mesh_position_get(), libMesh::FEMSystem::mesh_position_set(), libMesh::FEMSystem::numerical_jacobian(), and libMesh::DifferentiablePhysics::set_mesh_system().

_mesh_x_var

unsigned int libMesh::DifferentiablePhysics::_mesh_x_var

protectedinherited

Variables from which to acquire moving mesh information.

Definition at line 536 of file diff_physics.h.

Referenced by libMesh::FEMPhysics::eulerian_residual(), libMesh::DifferentiablePhysics::get_mesh_x_var(), libMesh::FEMSystem::mesh_position_get(), libMesh::FEMSystem::numerical_jacobian(), and libMesh::DifferentiablePhysics::set_mesh_x_var().

_mesh_y_var

unsigned int libMesh::DifferentiablePhysics::_mesh_y_var

protectedinherited

Definition at line 536 of file diff_physics.h.

Referenced by libMesh::FEMPhysics::eulerian_residual(), libMesh::DifferentiablePhysics::get_mesh_y_var(), libMesh::FEMSystem::mesh_position_get(), libMesh::FEMSystem::numerical_jacobian(), and libMesh::DifferentiablePhysics::set_mesh_y_var().

_mesh_z_var

unsigned int libMesh::DifferentiablePhysics::_mesh_z_var

protectedinherited

Definition at line 536 of file diff_physics.h.

Referenced by libMesh::FEMPhysics::eulerian_residual(), libMesh::DifferentiablePhysics::get_mesh_z_var(), libMesh::FEMSystem::mesh_position_get(), libMesh::FEMSystem::numerical_jacobian(), and libMesh::DifferentiablePhysics::set_mesh_z_var().

_mutex

Threads::spin_mutex libMesh::ReferenceCounter::_mutex

staticprotectedinherited

Mutual exclusion object to enable thread-safe reference counting.

Definition at line 137 of file reference_counter.h.

_n_objects

Threads::atomic< unsigned int > libMesh::ReferenceCounter::_n_objects

staticprotectedinherited

The number of objects.

Print the reference count information when the number returns to 0.

Definition at line 132 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::n_objects(), libMesh::ReferenceCounter::ReferenceCounter(), and libMesh::ReferenceCounter::~ReferenceCounter().

_second_order_dot_vars

std::map<unsigned int,unsigned int> libMesh::DifferentiablePhysics::_second_order_dot_vars

protectedinherited

If the user adds any second order variables, then we need to also cache the map to their corresponding dot variable that will be added by this TimeSolver class.

Definition at line 560 of file diff_physics.h.

Referenced by libMesh::DifferentiableSystem::add_second_order_dot_vars(), and libMesh::DifferentiableSystem::get_second_order_dot_var().

_second_order_vars

std::set<unsigned int> libMesh::DifferentiablePhysics::_second_order_vars

protectedinherited

Variable indices for those variables that are second order in time.

Definition at line 553 of file diff_physics.h.

Referenced by libMesh::DifferentiablePhysics::get_second_order_vars(), libMesh::DifferentiablePhysics::have_second_order_vars(), libMesh::DifferentiablePhysics::is_second_order_var(), and libMesh::DifferentiablePhysics::time_evolving().

_time_evolving

std::vector<unsigned int> libMesh::DifferentiablePhysics::_time_evolving

protectedinherited

Stores unsigned int to tell us which variables are evolving as first order in time (1), second order in time (2), or are not time evolving (0).

Definition at line 543 of file diff_physics.h.

Referenced by libMesh::DifferentiablePhysics::clear_physics(), libMesh::DifferentiablePhysics::init_physics(), libMesh::DifferentiablePhysics::is_time_evolving(), and libMesh::DifferentiablePhysics::time_evolving().

assemble_before_solve

bool libMesh::System::assemble_before_solve

inherited

Flag which tells the system to whether or not to call the user assembly function during each call to solve().

By default, every call to solve() begins with a call to the user assemble, so this flag is true. (For explicit systems, "solving" the system occurs during the assembly step, so this flag is always true for explicit systems.)

You will only want to set this to false if you need direct control over when the system is assembled, and are willing to track the state of its assembly yourself. An example of such a case is an implicit system with multiple right hand sides. In this instance, a single assembly would likely be followed with multiple calls to solve.

The frequency system and Newmark system have their own versions of this flag, called _finished_assemble, which might be able to be replaced with this more general concept.

Definition at line 1547 of file system.h.

Referenced by libMesh::ImplicitSystem::adjoint_solve(), libMesh::ClawSystem::ClawSystem(), libMesh::ImplicitSystem::disable_cache(), libMesh::System::disable_cache(), main(), libMesh::RBConstruction::RBConstruction(), libMesh::RBSCMConstruction::RBSCMConstruction(), libMesh::ImplicitSystem::sensitivity_solve(), libMesh::EigenSystem::solve(), libMesh::CondensedEigenSystem::solve(), and libMesh::LinearImplicitSystem::solve().

assemble_qoi_elements

bool libMesh::DifferentiableQoI::assemble_qoi_elements

inherited

If assemble_qoi_elements is false (it is true by default), the assembly loop for a quantity of interest or its derivatives will skip computing on mesh elements, and will only compute on mesh sides.

Definition at line 115 of file diff_qoi.h.

assemble_qoi_internal_sides

bool libMesh::DifferentiableQoI::assemble_qoi_internal_sides

inherited

If assemble_qoi_internal_sides is true (it is false by default), the assembly loop for a quantity of interest or its derivatives will loop over element sides which do not fall on domain boundaries.

Definition at line 107 of file diff_qoi.h.

assemble_qoi_sides

bool libMesh::DifferentiableQoI::assemble_qoi_sides

inherited

If assemble_qoi_sides is true (it is false by default), the assembly loop for a quantity of interest or its derivatives will loop over domain boundary sides.

To add domain interior sides, also set assemble_qoi_internal_sides to true.

Definition at line 99 of file diff_qoi.h.

Referenced by main().

compute_internal_sides

bool libMesh::DifferentiablePhysics::compute_internal_sides

inherited

compute_internal_sides is false by default, indicating that side_* computations will only be done on boundary sides.

If compute_internal_sides is true, computations will be done on sides between elements as well.

Definition at line 156 of file diff_physics.h.

continuation_parameter

Real* libMesh::ContinuationSystem::continuation_parameter

The continuation parameter must be a member variable of the derived class, and the "continuation_parameter" pointer defined here must be a pointer to that variable.

This is how the continuation system updates the derived class's continuation parameter.

Also sometimes referred to as "lambda" in the code comments.

Definition at line 119 of file continuation_system.h.

Referenced by apply_predictor(), continuation_solve(), initialize_tangent(), save_current_solution(), solve_tangent(), and update_solution().

continuation_parameter_tolerance

double libMesh::ContinuationSystem::continuation_parameter_tolerance

How tightly should the Newton iterations attempt to converge delta_lambda.

Defaults to 1.e-6.

Definition at line 138 of file continuation_system.h.

Referenced by continuation_solve().

current_local_solution

std::unique_ptr<NumericVector<Number> > libMesh::System::current_local_solution

inherited

All the values I need to compute my contribution to the simulation at hand.

Think of this as the current solution with any ghost values needed from other processors. This vector is necessarily larger than the solution vector in the case of a parallel simulation. The update() member is used to synchronize the contents of the solution and current_local_solution vectors.

Definition at line 1605 of file system.h.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), libMesh::__libmesh_petsc_diff_solver_residual(), libMesh::UniformRefinementEstimator::_estimate_error(), alternative_fe_assembly(), libMesh::VariationalSmootherSystem::assembly(), libMesh::NonlinearImplicitSystem::assembly(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::System::clear(), libMesh::Problem_Interface::computeF(), libMesh::Problem_Interface::computeJacobian(), libMesh::Problem_Interface::computePreconditioner(), libMesh::System::current_solution(), DMlibMeshFunction(), DMlibMeshJacobian(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), fe_assembly(), libMesh::StaticCondensation::init(), libMesh::System::init_data(), libMesh::libmesh_petsc_snes_fd_residual(), libMesh::libmesh_petsc_snes_jacobian(), libMesh::libmesh_petsc_snes_mffd_residual(), libMesh::libmesh_petsc_snes_residual(), libMesh::libmesh_petsc_snes_residual_helper(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::System::point_value(), libMesh::FEMContext::pre_fe_reinit(), libMesh::System::re_update(), libMesh::System::reinit(), libMesh::System::restrict_vectors(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), SolidSystem::save_initial_mesh(), libMesh::RBConstruction::set_context_solution_vec(), setup(), MeshFunctionTest::test_subdomain_id_sets(), MeshInputTest::testCopyElementVectorImpl(), libMesh::BoundaryVolumeSolutionTransfer::transfer_boundary_volume(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::TransientRBConstruction::truth_solve(), libMesh::System::update(), libMesh::Nemesis_IO_Helper::write_element_values(), and libMesh::Nemesis_IO_Helper::write_nodal_solution().

delta_u

NumericVector<Number>* libMesh::ContinuationSystem::delta_u

private

Temporary vector "delta u" ...

the Newton step update in our custom augmented PDE solve.

Definition at line 374 of file continuation_system.h.

Referenced by continuation_solve(), init_data(), solve_tangent(), and update_solution().

deltat

Real libMesh::DifferentiableSystem::deltat

inherited

For time-dependent problems, this is the amount delta t to advance the solution in time.

Definition at line 280 of file diff_system.h.

Referenced by libMesh::EulerSolver::_general_residual(), libMesh::Euler2Solver::_general_residual(), libMesh::NewmarkSolver::_general_residual(), libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::UnsteadySolver::adjoint_solve(), libMesh::NewmarkSolver::advance_timestep(), libMesh::UnsteadySolver::advance_timestep(), libMesh::FEMSystem::build_context(), libMesh::DifferentiableSystem::build_context(), libMesh::FEMSystem::init_context(), SolidSystem::init_data(), libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate(), libMesh::UnsteadySolver::integrate_adjoint_sensitivity(), libMesh::Euler2Solver::integrate_qoi_timestep(), libMesh::EulerSolver::integrate_qoi_timestep(), main(), HeatSystem::perturb_accumulate_residuals(), libMesh::MemorySolutionHistory::retrieve(), libMesh::FileSolutionHistory::retrieve(), set_system_parameters(), libMesh::TwostepTimeSolver::solve(), and libMesh::UnsteadySolver::solve().

dlambda_ds

Real libMesh::ContinuationSystem::dlambda_ds

private

The most recent value of the derivative of the continuation parameter with respect to s.

We use "lambda" here for shortness of notation, lambda always refers to the continuation parameter.

Definition at line 393 of file continuation_system.h.

Referenced by apply_predictor(), continuation_solve(), initialize_tangent(), set_Theta_LOCA(), and solve_tangent().

ds

Real libMesh::ContinuationSystem::ds

private

The initial arclength stepsize, selected by the user.

This is the max-allowable arclength stepsize, but the algorithm may frequently reduce ds near turning points.

Definition at line 400 of file continuation_system.h.

Referenced by set_max_arclength_stepsize(), and update_solution().

ds_current

Real libMesh::ContinuationSystem::ds_current

private

Value of stepsize currently in use.

Will not exceed user-provided maximum arclength stepsize ds.

Definition at line 406 of file continuation_system.h.

Referenced by apply_predictor(), continuation_solve(), initialize_tangent(), set_max_arclength_stepsize(), and update_solution().

ds_min

Real libMesh::ContinuationSystem::ds_min

The minimum-allowed steplength, defaults to 1.e-8.

Definition at line 218 of file continuation_system.h.

Referenced by update_solution().

du_ds

NumericVector<Number>* libMesh::ContinuationSystem::du_ds

private

Extra work vectors used by the continuation algorithm.

These are added to the system by the init_data() routine.

The "solution" tangent vector du/ds.

Definition at line 342 of file continuation_system.h.

Referenced by apply_predictor(), continuation_solve(), init_data(), initialize_tangent(), and solve_tangent().

extra_quadrature_order

int libMesh::System::extra_quadrature_order

inherited

A member int that can be employed to indicate increased or reduced quadrature order.

Note

For FEMSystem users, by default, when calling the user-defined residual functions, the FEMSystem will first set up an appropriate FEType::default_quadrature_rule() object for performing the integration. This rule will integrate elements of order up to 2*p+1 exactly (where p is the sum of the base FEType and local p refinement levels), but if additional (or reduced) quadrature accuracy is desired then this extra_quadrature_order (default 0) will be added.

Definition at line 1578 of file system.h.

Referenced by CurlCurlSystem::init_data(), and set_system_parameters().

fe_reinit_during_postprocess

bool libMesh::FEMSystem::fe_reinit_during_postprocess

inherited

If fe_reinit_during_postprocess is true (it is true by default), FE objects will be reinit()ed with their default quadrature rules.

If false, FE objects will need to be reinit()ed by the user or will be in an undefined state.

Definition at line 176 of file fem_system.h.

initial_newton_tolerance

double libMesh::ContinuationSystem::initial_newton_tolerance

How much to try to reduce the residual by at the first (inexact) Newton step.

This is frequently something large like 1/2 in an inexact Newton method, to prevent oversolving.

Definition at line 151 of file continuation_system.h.

Referenced by continuation_solve().

linear_solver

std::unique_ptr<LinearSolver<Number> > libMesh::ImplicitSystem::linear_solver

mutableinherited

This class handles all the details of interfacing with various linear algebra packages like PETSc or LASPACK.

This is a public member for backwards compatibility reasons, but in general it's better to use get_linear_solver() to access this member, since that function will also handle initialization if it hasn't already been taken care of.

Definition at line 339 of file implicit_system.h.

Referenced by libMesh::LinearImplicitSystem::clear(), libMesh::RBConstruction::compute_output_dual_innerprods(), continuation_solve(), ContinuationSystem(), libMesh::LinearImplicitSystem::create_static_condensation(), libMesh::ImplicitSystem::get_linear_solver(), libMesh::LinearImplicitSystem::get_linear_solver(), libMesh::LinearImplicitSystem::init_data(), libMesh::LinearImplicitSystem::LinearImplicitSystem(), libMesh::LinearImplicitSystem::reinit(), libMesh::FrequencySystem::solve(), libMesh::LinearImplicitSystem::solve(), libMesh::ClawSystem::solve_conservation_law(), solve_tangent(), and libMesh::TransientRBConstruction::truth_solve().

matrix

SparseMatrix<Number>* libMesh::ImplicitSystem::matrix

inherited

The system matrix.

Implicit systems are characterized by the need to solve the linear system Ax=b. This is the system matrix A.

Public access to this member variable will be deprecated in the future! Use get_system_matrix() instead.

Definition at line 322 of file implicit_system.h.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), add_M_C_K_helmholtz(), libMesh::ImplicitSystem::add_matrices(), libMesh::ImplicitSystem::adjoint_solve(), libMesh::ImplicitSystem::assemble(), assemble_func(), libMesh::FEMSystem::assembly(), libMesh::LinearImplicitSystem::assembly(), libMesh::NonlinearImplicitSystem::assembly(), libMesh::ImplicitSystem::clear(), libMesh::NewmarkSystem::compute_matrix(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), continuation_solve(), libMesh::ImplicitSystem::create_static_condensation_system_matrix(), DMCreateMatrix_libMesh(), DMlibMeshJacobian(), libMesh::RBConstruction::enrich_basis_from_rhs_terms(), fill_dirichlet_bc(), libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::ImplicitSystem::get_system_matrix(), main(), periodic_bc_test_poisson(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), libMesh::ImplicitSystem::sensitivity_solve(), libMesh::NewtonSolver::solve(), libMesh::PetscDiffSolver::solve(), libMesh::NoxNonlinearSolver< Number >::solve(), libMesh::EigenTimeSolver::solve(), libMesh::FrequencySystem::solve(), libMesh::LinearImplicitSystem::solve(), libMesh::NonlinearImplicitSystem::solve(), libMesh::ClawSystem::solve_conservation_law(), solve_tangent(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::RBConstruction::truth_assembly(), libMesh::TransientRBConstruction::truth_solve(), libMesh::RBConstruction::truth_solve(), libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve(), and libMesh::ImplicitSystem::weighted_sensitivity_solve().

max_continuation_parameter

Real libMesh::ContinuationSystem::max_continuation_parameter

The maximum-allowable value of the continuation parameter.

The Newton iterations will quit if the continuation parameter goes above this value. If this value is zero, there is no maximum value for the continuation parameter.

Definition at line 178 of file continuation_system.h.

Referenced by continuation_solve().

min_continuation_parameter

Real libMesh::ContinuationSystem::min_continuation_parameter

The minimum-allowable value of the continuation parameter.

The Newton iterations will quit if the continuation parameter falls below this value.

Definition at line 171 of file continuation_system.h.

Referenced by continuation_solve().

n_arclength_reductions

unsigned int libMesh::ContinuationSystem::n_arclength_reductions

Number of arclength reductions to try when Newton fails to reduce the residual.

For each arclength reduction, the arcstep size is cut in half.

Definition at line 213 of file continuation_system.h.

Referenced by continuation_solve().

n_backtrack_steps

unsigned int libMesh::ContinuationSystem::n_backtrack_steps

Another scaling parameter suggested by the LOCA people.

This one attempts to shrink the stepsize ds whenever the angle between the previous two tangent vectors gets large. Number of (Newton) backtracking steps to attempt if a Newton step does not reduce the residual. This is backtracking within a single Newton step, if you want to try a smaller arcstep, set n_arclength_reductions > 0.

Definition at line 206 of file continuation_system.h.

Referenced by continuation_solve().

newton_progress_check

bool libMesh::ContinuationSystem::newton_progress_check

True by default, the Newton progress check allows the Newton loop to exit if half the allowed iterations have elapsed without a reduction in the initial residual.

In our experience this usually means the Newton steps are going to fail eventually and we could save some time by quitting early.

Definition at line 260 of file continuation_system.h.

Referenced by continuation_solve().

newton_solver

NewtonSolver* libMesh::ContinuationSystem::newton_solver

private

A pointer to the underlying Newton solver used by the DiffSystem.

From this pointer, we can get access to all the parameters and options which are available to the "normal" Newton solver.

Definition at line 386 of file continuation_system.h.

Referenced by continuation_solve(), solve_tangent(), and update_solution().

newton_step

unsigned int libMesh::ContinuationSystem::newton_step

private

Loop counter for nonlinear (Newton) iteration loop.

Definition at line 421 of file continuation_system.h.

Referenced by continuation_solve(), and update_solution().

newton_stepgrowth_aggressiveness

Real libMesh::ContinuationSystem::newton_stepgrowth_aggressiveness

A measure of how rapidly one should attempt to grow the arclength stepsize based on the number of Newton iterations required to solve the problem.

Default value is 1.0, if set to zero, will not try to grow or shrink the arclength stepsize based on the number of Newton iterations required.

Definition at line 251 of file continuation_system.h.

Referenced by update_solution().

numerical_jacobian_h

Real libMesh::FEMSystem::numerical_jacobian_h

inherited

If calculating numeric jacobians is required, the FEMSystem will perturb each solution vector entry by numerical_jacobian_h when calculating finite differences.

This defaults to the libMesh TOLERANCE but can be set manually.

For ALE terms, the FEMSystem will perturb each mesh point in an element by numerical_jacobian_h * Elem::hmin()

Definition at line 187 of file fem_system.h.

Referenced by libMesh::FEMSystem::numerical_jacobian(), libMesh::FEMSystem::numerical_jacobian_h_for_var(), and set_system_parameters().

old_continuation_parameter

Real libMesh::ContinuationSystem::old_continuation_parameter

The system also keeps track of the old value of the continuation parameter.

Definition at line 165 of file continuation_system.h.

Referenced by continuation_solve(), initialize_tangent(), save_current_solution(), solve_tangent(), and update_solution().

parameters

Parameters libMesh::System::parameters

inherited

Parameters for the system. If a parameter is not provided, it should be retrieved from the EquationSystems.

Definition at line 1526 of file system.h.

Referenced by libMesh::ImplicitSystem::get_linear_solve_parameters(), libMesh::FrequencySystem::init_data(), libMesh::NonlinearImplicitSystem::set_solver_parameters(), libMesh::EigenSystem::solve(), libMesh::CondensedEigenSystem::solve(), and libMesh::EigenSystem::solve_helper().

postprocess_sides

bool libMesh::DifferentiableSystem::postprocess_sides

inherited

If postprocess_sides is true (it is false by default), the postprocessing loop will loop over all sides as well as all elements.

Definition at line 334 of file diff_system.h.

Referenced by main().

predictor

Predictor libMesh::ContinuationSystem::predictor

Definition at line 242 of file continuation_system.h.

Referenced by apply_predictor().

previous_dlambda_ds

Real libMesh::ContinuationSystem::previous_dlambda_ds

private

The old parameter tangent value.

Definition at line 411 of file continuation_system.h.

Referenced by apply_predictor(), and solve_tangent().

previous_ds

Real libMesh::ContinuationSystem::previous_ds

private

The previous arcstep length used.

Definition at line 416 of file continuation_system.h.

Referenced by apply_predictor(), and update_solution().

previous_du_ds

NumericVector<Number>* libMesh::ContinuationSystem::previous_du_ds

private

The value of du_ds from the previous solution.

Definition at line 347 of file continuation_system.h.

Referenced by apply_predictor(), init_data(), and solve_tangent().

previous_u

NumericVector<Number>* libMesh::ContinuationSystem::previous_u

private

The solution at the previous value of the continuation variable.

Definition at line 352 of file continuation_system.h.

Referenced by continuation_solve(), init_data(), initialize_tangent(), save_current_solution(), solve_tangent(), and update_solution().

print_element_jacobians

bool libMesh::DifferentiableSystem::print_element_jacobians

inherited

Set print_element_jacobians to true to print each J_elem contribution.

Definition at line 381 of file diff_system.h.

Referenced by CurlCurlSystem::init_data(), main(), and set_system_parameters().

print_element_residuals

bool libMesh::DifferentiableSystem::print_element_residuals

inherited

Set print_element_residuals to true to print each R_elem contribution.

Definition at line 376 of file diff_system.h.

Referenced by main(), and set_system_parameters().

print_element_solutions

bool libMesh::DifferentiableSystem::print_element_solutions

inherited

Set print_element_solutions to true to print each U_elem input.

Definition at line 371 of file diff_system.h.

Referenced by main().

print_jacobian_norms

bool libMesh::DifferentiableSystem::print_jacobian_norms

inherited

Set print_jacobian_norms to true to print |J| whenever it is assembled.

Definition at line 361 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), main(), and set_system_parameters().

print_jacobians

bool libMesh::DifferentiableSystem::print_jacobians

inherited

Set print_jacobians to true to print J whenever it is assembled.

Definition at line 366 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), CurlCurlSystem::init_data(), main(), and set_system_parameters().

print_residual_norms

bool libMesh::DifferentiableSystem::print_residual_norms

inherited

Set print_residual_norms to true to print |F| whenever it is assembled.

Definition at line 351 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), main(), and set_system_parameters().

print_residuals

bool libMesh::DifferentiableSystem::print_residuals

inherited

Set print_residuals to true to print F whenever it is assembled.

Definition at line 356 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), main(), and set_system_parameters().

print_solution_norms

bool libMesh::DifferentiableSystem::print_solution_norms

inherited

Set print_residual_norms to true to print |U| whenever it is used in an assembly() call.

Definition at line 340 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), main(), and set_system_parameters().

print_solutions

bool libMesh::DifferentiableSystem::print_solutions

inherited

Set print_solutions to true to print U whenever it is used in an assembly() call.

Definition at line 346 of file diff_system.h.

Referenced by libMesh::FEMSystem::assembly(), main(), and set_system_parameters().

quiet

bool libMesh::ContinuationSystem::quiet

If quiet==false, the System prints extra information about what it is doing.

Definition at line 125 of file continuation_system.h.

Referenced by continuation_solve(), initialize_tangent(), set_Theta(), set_Theta_LOCA(), solve_tangent(), and update_solution().

rhs

NumericVector<Number>* libMesh::ExplicitSystem::rhs

inherited

The system matrix.

Implicit systems are characterized by the need to solve the linear system Ax=b. This is the right-hand-side vector b.

Definition at line 124 of file explicit_system.h.

Referenced by libMesh::__libmesh_petsc_diff_solver_residual(), add_M_C_K_helmholtz(), libMesh::ExplicitSystem::add_system_rhs(), assemble(), libMesh::ImplicitSystem::assemble(), LinearElasticity::assemble(), assemble_1D(), assemble_biharmonic(), libMesh::AdvectionSystem::assemble_claw_rhs(), assemble_divgrad(), assemble_elasticity(), assemble_ellipticdg(), assemble_func(), assemble_graddiv(), assemble_laplace(), assemble_matrix_and_rhs(), assemble_poisson(), libMesh::ImplicitSystem::assemble_residual_derivatives(), assemble_shell(), assemble_stokes(), assemble_wave(), libMesh::FEMSystem::assembly(), libMesh::LinearImplicitSystem::assembly(), libMesh::NonlinearImplicitSystem::assembly(), assembly_with_dg_fem_context(), libMesh::RBConstruction::compute_Fq_representor_innerprods(), libMesh::RBConstruction::compute_output_dual_innerprods(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), libMesh::Problem_Interface::computeF(), continuation_solve(), DMlibMeshFunction(), libMesh::RBConstruction::enrich_basis_from_rhs_terms(), fill_dirichlet_bc(), libMesh::ImplicitSystem::forward_qoi_parameter_sensitivity(), libMesh::NewtonSolver::line_search(), periodic_bc_test_poisson(), HeatSystem::perturb_accumulate_residuals(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), libMesh::NewtonSolver::solve(), libMesh::PetscDiffSolver::solve(), libMesh::FrequencySystem::solve(), libMesh::LinearImplicitSystem::solve(), libMesh::NonlinearImplicitSystem::solve(), solve_tangent(), libMesh::TransientRBConstruction::truth_assembly(), libMesh::RBConstruction::truth_assembly(), libMesh::TransientRBConstruction::truth_solve(), libMesh::RBConstruction::truth_solve(), libMesh::TransientRBConstruction::update_residual_terms(), libMesh::RBConstruction::update_residual_terms(), libMesh::NewmarkSystem::update_rhs(), libMesh::ImplicitSystem::weighted_sensitivity_adjoint_solve(), and libMesh::ImplicitSystem::weighted_sensitivity_solve().

rhs_mode

RHS_Mode libMesh::ContinuationSystem::rhs_mode

protected

Definition at line 293 of file continuation_system.h.

Referenced by continuation_solve(), solve(), and solve_tangent().

solution

std::unique_ptr<NumericVector<Number> > libMesh::System::solution

inherited

Data structure to hold solution values.

Definition at line 1593 of file system.h.

Referenced by libMesh::__libmesh_petsc_diff_solver_jacobian(), libMesh::__libmesh_petsc_diff_solver_residual(), libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::TransientRBConstruction::add_IC_to_RB_space(), libMesh::NewmarkSolver::advance_timestep(), libMesh::AdaptiveTimeSolver::advance_timestep(), libMesh::UnsteadySolver::advance_timestep(), apply_predictor(), libMesh::TransientRBConstruction::assemble_affine_expansion(), libMesh::VariationalSmootherSystem::assembly(), libMesh::FEMSystem::assembly(), libMesh::LinearImplicitSystem::assembly(), libMesh::EquationSystems::build_parallel_elemental_solution_vector(), libMesh::EquationSystems::build_parallel_solution_vector(), libMesh::RBConstruction::check_if_zero_truth_solve(), libMesh::System::clear(), libMesh::System::compare(), compute_enriched_soln(), libMesh::RBConstruction::compute_Fq_representor_innerprods(), libMesh::NewmarkSolver::compute_initial_accel(), libMesh::RBConstruction::compute_output_dual_innerprods(), libMesh::RBConstruction::compute_residual_dual_norm_slow(), compute_stresses(), LinearElasticityWithContact::compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::Problem_Interface::computeF(), libMesh::Problem_Interface::computeJacobian(), libMesh::Problem_Interface::computePreconditioner(), continuation_solve(), libMesh::ExodusII_IO::copy_elemental_solution(), libMesh::Nemesis_IO::copy_elemental_solution(), libMesh::GMVIO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_nodal_solution(), libMesh::Nemesis_IO::copy_nodal_solution(), libMesh::ExodusII_IO::copy_scalar_solution(), libMesh::Nemesis_IO::copy_scalar_solution(), create_wrapped_function(), DMCreateGlobalVector_libMesh(), DMlibMeshFunction(), DMlibMeshJacobian(), libMesh::UnsteadySolver::du(), libMesh::RBConstruction::enrich_RB_space(), libMesh::PatchRecoveryErrorEstimator::estimate_error(), libMesh::WeightedPatchRecoveryErrorEstimator::estimate_error(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::AdjointRefinementEstimator::estimate_error(), libMesh::AdjointResidualErrorEstimator::estimate_error(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::RBSCMConstruction::evaluate_stability_constant(), libMesh::EigenSystem::get_eigenpair(), libMesh::CondensedEigenSystem::get_eigenpair(), LinearElasticityWithContact::get_least_and_max_gap_function(), libMesh::VariationalSmootherSystem::init_data(), libMesh::System::init_data(), initialize_tangent(), libMesh::TransientRBConstruction::initialize_truth(), libMesh::libmesh_petsc_snes_fd_residual(), libMesh::libmesh_petsc_snes_jacobian(), libMesh::libmesh_petsc_snes_mffd_residual(), libMesh::libmesh_petsc_snes_residual(), libMesh::libmesh_petsc_snes_residual_helper(), libMesh::RBConstruction::load_basis_function(), libMesh::TransientRBConstruction::load_rb_solution(), libMesh::RBConstruction::load_rb_solution(), main(), libMesh::DofMap::max_constraint_error(), libMesh::FEMSystem::mesh_position_get(), libMesh::ErrorVector::plot_error(), libMesh::RBConstruction::print_basis_function_orthogonality(), libMesh::InterMeshProjection::project_system_vectors(), libMesh::ImplicitSystem::qoi_parameter_hessian(), libMesh::ImplicitSystem::qoi_parameter_hessian_vector_product(), libMesh::System::re_update(), libMesh::System::read_legacy_data(), libMesh::System::read_parallel_data(), libMesh::TransientRBConstruction::read_riesz_representors_from_files(), libMesh::RBConstruction::read_riesz_representors_from_files(), libMesh::System::read_serialized_data(), libMesh::System::reinit(), libMesh::System::restrict_vectors(), libMesh::MemoryHistoryData::retrieve_vectors(), OverlappingAlgebraicGhostingTest::run_ghosting_test(), OverlappingCouplingGhostingTest::run_sparsity_pattern_test(), save_current_solution(), libMesh::TransientRBConstruction::set_error_temporal_data(), setup(), WriteVecAndScalar::setupTests(), libMesh::TwostepTimeSolver::solve(), libMesh::NewtonSolver::solve(), libMesh::PetscDiffSolver::solve(), libMesh::FrequencySystem::solve(), libMesh::LinearImplicitSystem::solve(), libMesh::NonlinearImplicitSystem::solve(), libMesh::ClawSystem::solve_conservation_law(), libMesh::RBConstruction::solve_for_matrix_and_rhs(), solve_tangent(), libMesh::MemoryHistoryData::store_vectors(), ConstraintOperatorTest::test1DCoarseningOperator(), MeshfunctionDFEM::test_mesh_function_dfem(), MeshfunctionDFEM::test_mesh_function_dfem_grad(), MeshFunctionTest::test_p_level(), SystemsTest::testBoundaryProjectCube(), ConstraintOperatorTest::testCoreform(), SystemsTest::testDofCouplingWithVarGroups(), MeshInputTest::testExodusWriteElementDataFromDiscontinuousNodalData(), SystemsTest::testPostInitAddVector(), SystemsTest::testProjectCubeWithMeshFunction(), MeshInputTest::testProjectionRegression(), WriteVecAndScalar::testSolution(), libMesh::RBConstruction::train_reduced_basis_with_POD(), libMesh::MeshFunctionSolutionTransfer::transfer(), libMesh::DirectSolutionTransfer::transfer(), libMesh::MeshfreeSolutionTransfer::transfer(), libMesh::BoundaryVolumeSolutionTransfer::transfer_boundary_volume(), libMesh::BoundaryVolumeSolutionTransfer::transfer_volume_boundary(), libMesh::TransientRBConstruction::truth_solve(), libMesh::RBConstruction::truth_solve(), libMesh::System::update(), update_current_local_solution(), libMesh::System::update_global_solution(), libMesh::TransientRBConstruction::update_RB_initial_condition_all_N(), libMesh::TransientRBConstruction::update_residual_terms(), libMesh::RBConstruction::update_residual_terms(), update_solution(), libMesh::NewmarkSystem::update_u_v_a(), libMesh::DTKAdapter::update_variable_values(), libMesh::System::write_parallel_data(), libMesh::TransientRBConstruction::write_riesz_representors_to_files(), libMesh::RBConstruction::write_riesz_representors_to_files(), and libMesh::System::write_serialized_data().

solution_tolerance

double libMesh::ContinuationSystem::solution_tolerance

How tightly should the Newton iterations attempt to converge ||delta_u|| Defaults to 1.e-6.

Definition at line 144 of file continuation_system.h.

Referenced by continuation_solve().

tangent_initialized

bool libMesh::ContinuationSystem::tangent_initialized

private

False until initialize_tangent() is called.

Definition at line 379 of file continuation_system.h.

Referenced by continuation_solve(), initialize_tangent(), solve_tangent(), and update_solution().

Theta

Real libMesh::ContinuationSystem::Theta

Arclength normalization parameter.

Defaults to 1.0 (no normalization). Used to ensure that one term in the arclength constraint equation does not wash out all the others.

Definition at line 185 of file continuation_system.h.

Referenced by continuation_solve(), initialize_tangent(), set_Theta(), solve_tangent(), and update_solution().

Theta_LOCA

Real libMesh::ContinuationSystem::Theta_LOCA

Another normalization parameter, which is described in the LOCA manual.

This one is designed to maintain a relatively "fixed" value of d(lambda)/ds. It is initially 1.0 and is updated after each solve.

Definition at line 192 of file continuation_system.h.

Referenced by continuation_solve(), initialize_tangent(), set_Theta_LOCA(), solve_tangent(), and update_solution().

time

Real libMesh::System::time

inherited

For time-dependent problems, this is the time t at the beginning of the current timestep.

Note

For DifferentiableSystem users: do not access this time during an assembly! Use the DiffContext::time value instead to get correct results.

Definition at line 1615 of file system.h.

Referenced by libMesh::AdaptiveTimeSolver::adjoint_advance_timestep(), libMesh::UnsteadySolver::adjoint_advance_timestep(), libMesh::TwostepTimeSolver::adjoint_solve(), libMesh::AdaptiveTimeSolver::advance_timestep(), libMesh::UnsteadySolver::advance_timestep(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubProjector::construct_projection(), HeatSystem::element_qoi(), fill_dirichlet_bc(), libMesh::ExactErrorEstimator::find_squared_element_error(), initialize(), libMesh::Euler2Solver::integrate_adjoint_refinement_error_estimate(), libMesh::EulerSolver::integrate_adjoint_refinement_error_estimate(), libMesh::UnsteadySolver::integrate_adjoint_sensitivity(), libMesh::Euler2Solver::integrate_qoi_timestep(), libMesh::EulerSolver::integrate_qoi_timestep(), main(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectVertices::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectEdges::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectSides::operator()(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::ProjectInteriors::operator()(), libMesh::System::reinit_constraints(), libMesh::UnsteadySolver::retrieve_timestep(), and libMesh::TwostepTimeSolver::solve().

time_solver

std::unique_ptr<TimeSolver> libMesh::DifferentiableSystem::time_solver

inherited

A pointer to the solver object we're going to use.

This must be instantiated by the user before solving!

Definition at line 253 of file diff_system.h.

Referenced by libMesh::DifferentiableSystem::adjoint_solve(), libMesh::FEMSystem::assembly(), continuation_solve(), libMesh::DifferentiableSystem::get_linear_solve_parameters(), libMesh::DifferentiableSystem::get_linear_solver(), libMesh::DifferentiableSystem::get_second_order_dot_var(), libMesh::DifferentiableSystem::get_time_solver(), SolidSystem::init_data(), libMesh::DifferentiableSystem::init_data(), main(), libMesh::DifferentiableSystem::reinit(), libMesh::DifferentiableSystem::set_constrain_in_solver(), set_system_parameters(), libMesh::DifferentiableSystem::set_time_solver(), libMesh::VariationalMeshSmoother::smooth(), SolidSystem::SolidSystem(), libMesh::DifferentiableSystem::solve(), solve_tangent(), libMesh::MemoryHistoryData::store_primal_solution(), and libMesh::FileHistoryData::store_primal_solution().

use_fixed_solution

bool libMesh::System::use_fixed_solution

inherited

A boolean to be set to true by systems using elem_fixed_solution, for optional use by e.g.

stabilized methods. False by default.

Note

For FEMSystem users, if this variable is set to true, it must be before init_data() is called.

Definition at line 1563 of file system.h.

Referenced by libMesh::EulerSolver::_general_residual(), libMesh::Euler2Solver::_general_residual(), libMesh::SteadySolver::_general_residual(), libMesh::NewmarkSolver::_general_residual(), libMesh::DifferentiableSystem::clear(), libMesh::DiffContext::DiffContext(), and libMesh::FEMContext::pre_fe_reinit().

verify_analytic_jacobians

Real libMesh::FEMSystem::verify_analytic_jacobians

inherited

If verify_analytic_jacobian is equal to zero (as it is by default), no numeric jacobians will be calculated unless an overridden element_time_derivative(), element_constraint(), side_time_derivative(), or side_constraint() function cannot provide an analytic jacobian upon request.

If verify_analytic_jacobian is equal to the positive value tol, then any time a full analytic element jacobian can be calculated it will be tested against a numerical jacobian on the same element, and the program will abort if the relative error (in matrix l1 norms) exceeds tol.

Definition at line 215 of file fem_system.h.

Referenced by libMesh::FEMSystem::assembly(), CurlCurlSystem::init_data(), and set_system_parameters().

y

NumericVector<Number>* libMesh::ContinuationSystem::y

private

Temporary vector "y" ...

stores -du/dlambda, the solution of \( Ay=G_{\lambda} \).

Definition at line 357 of file continuation_system.h.

Referenced by continuation_solve(), init_data(), initialize_tangent(), solve_tangent(), and update_solution().

y_old

NumericVector<Number>* libMesh::ContinuationSystem::y_old

private

Temporary vector "y_old" ...

stores the previous value of -du/dlambda, which is the solution of \( Ay=G_{\lambda} \).

Definition at line 363 of file continuation_system.h.

Referenced by continuation_solve(), init_data(), and update_solution().

z

NumericVector<Number>* libMesh::ContinuationSystem::z

private

Temporary vector "z" ...

the solution of \( Az = -G \)

Definition at line 368 of file continuation_system.h.

Referenced by continuation_solve(), and init_data().

zero_out_matrix_and_rhs

bool libMesh::ImplicitSystem::zero_out_matrix_and_rhs

inherited

By default, the system will zero out the matrix and the right hand side.

If this flag is false, it is the responsibility of the client code to take care of setting these to zero before assembly begins

Definition at line 329 of file implicit_system.h.

Referenced by libMesh::ImplicitSystem::assemble().

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The documentation for this class was generated from the following files:

• include/systems/continuation_system.h
• src/systems/continuation_system.C