NonlinearEigen

Executioner for eigenvalue problems.

Overview

Eigenvalue executioners such as this one intend on solving the eigenvalue problem described by:

var element = document.getElementById("moose-equation-e3f11f8e-e47a-49fe-bb8c-4416f2d5c0d8");katex.render("Ax = \\frac{1}{k}Bx,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-74c59506-0fd5-4532-b654-9ede28bd783e");katex.render("A", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-25c41b43-7e1e-404f-a437-774eb22568dd");katex.render("B", element, {displayMode:false,throwOnError:false});$ are linear or nonlinear operators represented by kernels. To differentiate the $var element = document.getElementById("moose-equation-49d08cfe-8e6d-4ef6-9129-a03cfafccff4");katex.render("B", element, {displayMode:false,throwOnError:false});$ kernels from the $var element = document.getElementById("moose-equation-ffcbd2e0-852b-4435-a12d-bc1c1b6f399a");katex.render("A", element, {displayMode:false,throwOnError:false});$ kernels, we must derive all $var element = document.getElementById("moose-equation-b7f1f274-e232-4704-b33b-8998892be565");katex.render("B", element, {displayMode:false,throwOnError:false});$ kernels from EigenKernel. Currently we are only interested in the absolute minimum eigenvalue $var element = document.getElementById("moose-equation-cff7569f-4597-45d1-82cf-365f33f731ce");katex.render("\\frac{1}{k}", element, {displayMode:false,throwOnError:false});$ and the corresponding eigenvector $var element = document.getElementById("moose-equation-a4d5b9dd-f039-4358-84d8-9e8596a70947");katex.render("x", element, {displayMode:false,throwOnError:false});$ of the system. We are also not seeking the solutions of a general nonlinear eigenvalue problem, where the operators have nonlinear dependency on the eigenvalue.

The nonlinear Newton method

From the above section, we can see the eigenvalue problem can be viewed as a nonlinear problem

var element = document.getElementById("moose-equation-193b31d3-5ca7-4143-aa8a-2d3ec67b7a66");katex.render("\\begin{aligned} &Ax = \\frac{1}{k}Bx, \\\\ &k = |Bx|, \\end{aligned}", element, {displayMode:true,throwOnError:false});

so we can use the Newton method to solve it. However, to make the solving converge, we need to have a fairly close initial guess to the fundamental mode. This can be achieved with several free power iterations before the Newton iteration. We do not have to have $var element = document.getElementById("moose-equation-b40fdad3-101c-40df-b206-04647a713aac");katex.render("k", element, {displayMode:false,throwOnError:false});$ as part of the solution vector. Instead we can apply the elimination technique and view the equation as

var element = document.getElementById("moose-equation-25c22d32-cb74-4f8c-b604-c88e734bd7df");katex.render("Ax = \\frac{Bx}{|Bx|}.", element, {displayMode:true,throwOnError:false});

Again we can use PJFNK (preconditioned Jacobian-free Newton Krylov) method to solve this nonlinear problem. The preconditioning matrix can affect the linear convergence in each Newton iteration. If there is a convergence issue, it is suggested to use $var element = document.getElementById("moose-equation-951cf188-5603-4309-b032-28aa251a9372");katex.render("A-\\frac{B}{|Bx|}", element, {displayMode:false,throwOnError:false});$ and gradually reduce its complexity as the preconditioning matrix.

Input Parameters

bx_normTo evaluate |Bx| for the eigenvalue
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:To evaluate |Bx| for the eigenvalue

Required Parameters

free_l_tol0.01Relative linear tolerance in free power iteration
Default:0.01
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative linear tolerance in free power iteration
free_power_iterations4The number of free power iterations
Default:4
C++ Type:unsigned int
Controllable:No
Description:The number of free power iterations
k01Initial guess of the eigenvalue
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial guess of the eigenvalue
output_after_power_iterationsTrueTrue to output solution after free power iterations
Default:True
C++ Type:bool
Controllable:No
Description:True to output solution after free power iterations
verboseFalseSet to true to print additional information
Default:False
C++ Type:bool
Controllable:No
Description:Set to true to print additional information

Optional Parameters

accept_on_max_fixed_point_iterationFalseTrue to treat reaching the maximum number of fixed point iterations as converged.
Default:False
C++ Type:bool
Controllable:No
Description:True to treat reaching the maximum number of fixed point iterations as converged.
auto_advanceFalseWhether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
custom_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
custom_ppPostprocessor for custom fixed point convergence check.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor for custom fixed point convergence check.
custom_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
direct_pp_valueFalseTrue to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
Default:False
C++ Type:bool
Controllable:No
Description:True to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
disable_fixed_point_residual_norm_checkFalseDisable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
Default:False
C++ Type:bool
Controllable:No
Description:Disable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
fixed_point_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
fixed_point_algorithmpicardThe fixed point algorithm to converge the sequence of problems.
Default:picard
C++ Type:MooseEnum
Options:picard, secant, steffensen
Controllable:No
Description:The fixed point algorithm to converge the sequence of problems.
fixed_point_force_normsFalseForce the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
Default:False
C++ Type:bool
Controllable:No
Description:Force the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
fixed_point_max_its1Specifies the maximum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Specifies the maximum number of fixed point iterations.
fixed_point_min_its1Specifies the minimum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Specifies the minimum number of fixed point iterations.
fixed_point_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
multiapp_fixed_point_convergenceName of the Convergence object to use to assess convergence of the MultiApp fixed point solve. If not provided, a default Convergence will be constructed internally from the executioner parameters.
C++ Type:ConvergenceName
Controllable:No
Description:Name of the Convergence object to use to assess convergence of the MultiApp fixed point solve. If not provided, a default Convergence will be constructed internally from the executioner parameters.
relaxation_factor1Fraction of newly computed value to keep.Set between 0 and 2.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of newly computed value to keep.Set between 0 and 2.
transformed_postprocessorsList of main app postprocessors to transform during fixed point iterations
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:List of main app postprocessors to transform during fixed point iterations
transformed_variablesList of main app variables to transform during fixed point iterations
C++ Type:std::vector<std::string>
Controllable:No
Description:List of main app variables to transform during fixed point iterations

Fixed Point Iterations Parameters

auto_initializationTrueTrue to ask the solver to set initial
Default:True
C++ Type:bool
Controllable:No
Description:True to ask the solver to set initial
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
skip_exception_checkFalseSpecifies whether or not to skip exception check
Default:False
C++ Type:bool
Controllable:No
Description:Specifies whether or not to skip exception check
time0System time
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:System time

Advanced Parameters

automatic_scalingFalseWhether to use automatic scaling for the variables.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic scaling for the variables.
compute_scaling_once1 Whether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step. Vector entries correspond to each nonlinear system.
Default:1
C++ Type:std::vector<bool>
Controllable:No
Description:Whether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step. Vector entries correspond to each nonlinear system.
ignore_variables_for_autoscalingList of variables that do not participate in autoscaling. Vector entries correspond to each nonlinear system.
C++ Type:std::vector<std::vector<std::string>>
Controllable:No
Description:List of variables that do not participate in autoscaling. Vector entries correspond to each nonlinear system.
off_diagonals_in_auto_scaling0 Whether to consider off-diagonals when determining automatic scaling factors. Vector entries correspond to each nonlinear system.
Default:0
C++ Type:std::vector<bool>
Controllable:No
Description:Whether to consider off-diagonals when determining automatic scaling factors. Vector entries correspond to each nonlinear system.
resid_vs_jac_scaling_param0 A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling. Vector entries correspond to each nonlinear system.
Default:0
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling. Vector entries correspond to each nonlinear system.
scaling_group_variablesName of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon). Vector entries correspond to each nonlinear system.
C++ Type:std::vector<std::vector<std::vector<std::string, std::allocator<std::string>>>>
Controllable:No
Description:Name of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon). Vector entries correspond to each nonlinear system.

Solver Variable Scaling Parameters

contact_line_search_allowed_lambda_cuts2The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
Default:2
C++ Type:unsigned int
Controllable:No
Description:The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
contact_line_search_ltolThe linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
line_searchdefaultSpecifies the line search type (Note: none = basic)
Default:default
C++ Type:MooseEnum
Options:basic, bt, contact, cp, default, l2, none, project, shell
Controllable:No
Description:Specifies the line search type (Note: none = basic)
line_search_packagepetscThe solver package to use to conduct the line-search
Default:petsc
C++ Type:MooseEnum
Options:petsc, moose
Controllable:No
Description:The solver package to use to conduct the line-search

Solver Line Search Parameters

l_abs_tol1e-50Linear Absolute Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Absolute Tolerance
l_max_its10000Max Linear Iterations
Default:10000
C++ Type:unsigned int
Controllable:No
Description:Max Linear Iterations
l_tol0.01Linear Relative Tolerance
Default:0.01
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Relative Tolerance
reuse_preconditionerFalseIf true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
Default:False
C++ Type:bool
Controllable:No
Description:If true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
reuse_preconditioner_max_linear_its25Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number
Default:25
C++ Type:unsigned int
Controllable:No
Description:Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number

Linear Solver Parameters

linear_convergenceName of the Convergence object(s) to use to assess convergence of the linear system(s) solve. If not provided, the linear solver tolerance parameters are used
C++ Type:std::vector<ConvergenceName>
Controllable:No
Description:Name of the Convergence object(s) to use to assess convergence of the linear system(s) solve. If not provided, the linear solver tolerance parameters are used
n_max_nonlinear_pingpong100The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut for transient simulations
Default:100
C++ Type:unsigned int
Controllable:No
Description:The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut for transient simulations
nl_abs_div_tol1e+50Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
Default:1e+50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
nl_abs_step_tol0Nonlinear Absolute step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute step Tolerance
nl_abs_tol1e-06Nonlinear Absolute Tolerance
Default:1e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Tolerance
nl_div_tol1e+10Nonlinear Relative Divergence Tolerance. A negative value disables this check.
Default:1e+10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Divergence Tolerance. A negative value disables this check.
nl_forced_its0The Number of Forced Nonlinear Iterations
Default:0
C++ Type:unsigned int
Controllable:No
Description:The Number of Forced Nonlinear Iterations
nl_max_funcs10000Max Nonlinear solver function evaluations
Default:10000
C++ Type:unsigned int
Controllable:No
Description:Max Nonlinear solver function evaluations
nl_max_its50Max Nonlinear Iterations
Default:50
C++ Type:unsigned int
Controllable:No
Description:Max Nonlinear Iterations
nl_rel_step_tol0Nonlinear Relative step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative step Tolerance
nl_rel_tol1e-50Nonlinear Relative Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Tolerance
nonlinear_convergenceName of the Convergence object(s) to use to assess convergence of the nonlinear system(s) solve. If not provided, the default Convergence associated with the Problem will be constructed internally.
C++ Type:std::vector<ConvergenceName>
Controllable:No
Description:Name of the Convergence object(s) to use to assess convergence of the nonlinear system(s) solve. If not provided, the default Convergence associated with the Problem will be constructed internally.
num_grids1The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
Default:1
C++ Type:unsigned int
Controllable:No
Description:The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
residual_and_jacobian_together0 Whether to compute the residual and Jacobian together. Vector entries correspond to each nonlinear system.
Default:0
C++ Type:std::vector<bool>
Controllable:No
Description:Whether to compute the residual and Jacobian together. Vector entries correspond to each nonlinear system.
snesmf_reuse_baseTrueSpecifies whether or not to reuse the base vector for matrix-free calculation
Default:True
C++ Type:bool
Controllable:No
Description:Specifies whether or not to reuse the base vector for matrix-free calculation
solve_typePJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
C++ Type:MooseEnum
Options:PJFNK, JFNK, NEWTON, FD, LINEAR
Controllable:No
Description:PJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
use_pre_SMO_residualFalseCompute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.
Default:False
C++ Type:bool
Controllable:No
Description:Compute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.

Nonlinear Solver Parameters

max_xfem_update4294967295Maximum number of times to update XFEM crack topology in a step due to evolving cracks
Default:4294967295
C++ Type:unsigned int
Controllable:No
Description:Maximum number of times to update XFEM crack topology in a step due to evolving cracks
update_xfem_at_timestep_beginFalseShould XFEM update the mesh at the beginning of the timestep
Default:False
C++ Type:bool
Controllable:No
Description:Should XFEM update the mesh at the beginning of the timestep

Xfem Fixed Point Iterations Parameters

mffd_typewpSpecifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
Default:wp
C++ Type:MooseEnum
Options:wp, ds
Controllable:No
Description:Specifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
petsc_optionsSingleton PETSc options
C++ Type:MultiMooseEnum
Options:-dm_moose_print_embedding, -dm_view, -KSP_CONVERGED_REASON, -KSP_GMRES_MODIFIEDGRAMSCHMIDT, -KSP_MONITOR, -KSP_MONITOR_SNES_LG, -SNES_KSP_EW, -KSP_SNES_EW, -SNES_CONVERGED_REASON, -SNES_KSP, -SNES_LINESEARCH_MONITOR, -SNES_MF, -SNES_MF_OPERATOR, -SNES_MONITOR, -SNES_TEST_DISPLAY, -SNES_VIEW, -SNES_MONITOR_CANCEL
Controllable:No
Description:Singleton PETSc options
petsc_options_inameNames of PETSc name/value pairs
C++ Type:MultiMooseEnum
Options:-mat_fd_coloring_err, -mat_fd_type, -mat_mffd_type, -pc_asm_overlap, -pc_factor_levels, -pc_factor_mat_ordering_type, -pc_hypre_boomeramg_grid_sweeps_all, -pc_hypre_boomeramg_max_iter, -pc_hypre_boomeramg_strong_threshold, -pc_hypre_type, -pc_type, -sub_pc_type, -KSP_ATOL, -KSP_GMRES_RESTART, -KSP_MAX_IT, -KSP_PC_SIDE, -KSP_RTOL, -KSP_TYPE, -SUB_KSP_TYPE, -SNES_ATOL, -SNES_LINESEARCH_TYPE, -SNES_LS, -SNES_MAX_IT, -SNES_RTOL, -SNES_DIVERGENCE_TOLERANCE, -SNES_TYPE
Controllable:No
Description:Names of PETSc name/value pairs
petsc_options_valueValues of PETSc name/value pairs (must correspond with "petsc_options_iname"
C++ Type:std::vector<std::string>
Controllable:No
Description:Values of PETSc name/value pairs (must correspond with "petsc_options_iname"

Petsc Parameters

multi_system_fixed_pointFalseWhether to perform fixed point (Picard) iterations between the nonlinear systems.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to perform fixed point (Picard) iterations between the nonlinear systems.
multi_system_fixed_point_convergenceConvergence object to determine the convergence of the multi-system fixed point iteration. If unspecified, defaults to checking that every system is converged (based on their own convergence criterion)
C++ Type:ConvergenceName
Controllable:No
Description:Convergence object to determine the convergence of the multi-system fixed point iteration. If unspecified, defaults to checking that every system is converged (based on their own convergence criterion)
system_namesNames of the solver systems (both linear and nonlinear) that will be solved
C++ Type:std::vector<SolverSystemName>
Controllable:No
Description:Names of the solver systems (both linear and nonlinear) that will be solved

Multiple Solver System Parameters

normal_factorNormalize x to make |x| equal to this factor
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Normalize x to make |x| equal to this factor
normalizationTo evaluate |x| for normalization
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:To evaluate |x| for normalization
output_before_normalizationTrueTrue to output a step before normalization
Default:True
C++ Type:bool
Controllable:No
Description:True to output a step before normalization

Normalization Parameters

Restart Parameters

Overview
The nonlinear Newton method
Input Parameters