AzimuthalPeriodicBoundary Class Reference

Inheritance diagram for AzimuthalPeriodicBoundary:

Public Types
enum	TransformationType { FORWARD =0 , INVERSE =1 }

Public Member Functions
	AzimuthalPeriodicBoundary (Point center, Point axis, Real angle)
	Constructor.
	AzimuthalPeriodicBoundary (const AzimuthalPeriodicBoundary &o, TransformationType t=FORWARD)
	Copy constructor, with option for the copy to represent an inverse transformation.
virtual	~AzimuthalPeriodicBoundary ()=default
	Destructor.
void	set_up_rotation_matrix ()
	Computes and stores the rotation matrix for this transformation, and then calls the base class API to store it.
virtual Point	get_corresponding_pos (const Point &pt) const override
	This function should be overridden by derived classes to define how one finds corresponding nodes on the periodic boundary pair.
virtual std::unique_ptr< PeriodicBoundaryBase >	clone (TransformationType t=FORWARD) const override
	If we want the DofMap to be able to make copies of references and store them in the underlying map, this class must be clone'able, i.e.
void	set_variable (unsigned int var)
void	merge (const PeriodicBoundaryBase &pb)
bool	is_my_variable (unsigned int var_num) const
bool	has_transformation_matrix () const
const DenseMatrix< Real > &	get_transformation_matrix () const
	Get the transformation matrix, if it is defined.
void	set_transformation_matrix (const DenseMatrix< Real > &matrix)
	Set the transformation matrix.
const std::set< unsigned int > &	get_variables () const
	Get the set of variables for this periodic boundary condition.

Public Attributes
boundary_id_type	myboundary
	The boundary ID of this boundary and its counterpart.
boundary_id_type	pairedboundary

Protected Attributes
std::set< unsigned int >	variables
	Set of variables for this periodic boundary, empty means all variables possible.
std::unique_ptr< DenseMatrix< Real > >	_transformation_matrix
	A DenseMatrix that defines the mapping of variables on this boundary and the counterpart boundary.

Private Attributes
Point	_center
Point	_axis
Real	_theta
RealTensorValue	_R

Detailed Description

Definition at line 78 of file systems_of_equations_ex9.C.

Member Enumeration Documentation

TransformationType

enum libMesh::PeriodicBoundaryBase::TransformationType

inherited

Enumerator
FORWARD
INVERSE

Definition at line 51 of file periodic_boundary_base.h.

    { FORWARD=0,
      INVERSE=1 };

Constructor & Destructor Documentation

AzimuthalPeriodicBoundary() [1/2]

AzimuthalPeriodicBoundary::AzimuthalPeriodicBoundary ( Point  center, Point  axis, Real  angle  )

inline

Constructor.

Definition at line 84 of file systems_of_equations_ex9.C.

  :
    PeriodicBoundaryBase(),
    _center(center),
    _axis(axis),
    _theta(angle)
  {
    set_variable(0);
    set_variable(1);
    set_variable(2);
    set_up_rotation_matrix();
  }

References set_up_rotation_matrix(), and libMesh::PeriodicBoundaryBase::set_variable().

AzimuthalPeriodicBoundary() [2/2]

AzimuthalPeriodicBoundary::AzimuthalPeriodicBoundary ( const AzimuthalPeriodicBoundary &  o, TransformationType  t = FORWARD  )

inline

Copy constructor, with option for the copy to represent an inverse transformation.

Definition at line 103 of file systems_of_equations_ex9.C.

    :
    PeriodicBoundaryBase(o),
    _center(o._center),
    _axis(o._axis),
    _theta(o._theta)
  {
    if (t == INVERSE)
      {
        std::swap(myboundary, pairedboundary);
        _theta *= -1.0;
      }
 
    set_variable(0);
    set_variable(1);
    set_variable(2);
    set_up_rotation_matrix();
  }

References _theta, libMesh::PeriodicBoundaryBase::INVERSE, libMesh::PeriodicBoundaryBase::myboundary, libMesh::PeriodicBoundaryBase::pairedboundary, set_up_rotation_matrix(), and libMesh::PeriodicBoundaryBase::set_variable().

~AzimuthalPeriodicBoundary()

virtual AzimuthalPeriodicBoundary::~AzimuthalPeriodicBoundary ( )

virtualdefault

Destructor.

Member Function Documentation

clone()

virtual std::unique_ptr< PeriodicBoundaryBase > AzimuthalPeriodicBoundary::clone ( TransformationType  t = FORWARD ) const

inlineoverridevirtual

If we want the DofMap to be able to make copies of references and store them in the underlying map, this class must be clone'able, i.e.

have a kind of virtual construction mechanism.

Implements libMesh::PeriodicBoundaryBase.

Definition at line 176 of file systems_of_equations_ex9.C.

  {
    return std::make_unique<AzimuthalPeriodicBoundary>(*this, t);
  }

get_corresponding_pos()

virtual Point AzimuthalPeriodicBoundary::get_corresponding_pos ( const Point &  pt ) const

inlineoverridevirtual

This function should be overridden by derived classes to define how one finds corresponding nodes on the periodic boundary pair.

Implements libMesh::PeriodicBoundaryBase.

Definition at line 163 of file systems_of_equations_ex9.C.

  {
    // Note that since _theta defines the angle from "paired boundary" to
    // "my boundary", and we want the inverse of that here, we multiply
    // by the transpose of the transformation matrix below.
    return _R.left_multiply(pt - _center) + _center;
  }

References _center, _R, and libMesh::TypeTensor< T >::left_multiply().

get_transformation_matrix()

const DenseMatrix< Real > & libMesh::PeriodicBoundaryBase::get_transformation_matrix ( ) const

inherited

Get the transformation matrix, if it is defined.

Throw an error if it is not defined.

Definition at line 86 of file periodic_boundary_base.C.

{
  libmesh_error_msg_if(!has_transformation_matrix(),
                       "Transformation matrix is not defined");
 
  return *_transformation_matrix;
}

References libMesh::PeriodicBoundaryBase::_transformation_matrix, and libMesh::PeriodicBoundaryBase::has_transformation_matrix().

Referenced by libMesh::FEGenericBase< OutputType >::compute_periodic_constraints().

get_variables()

const std::set< unsigned int > & libMesh::PeriodicBoundaryBase::get_variables ( ) const

inherited

Get the set of variables for this periodic boundary condition.

Definition at line 109 of file periodic_boundary_base.C.

{
  return variables;
}

References libMesh::PeriodicBoundaryBase::variables.

Referenced by libMesh::DofMap::add_periodic_boundary(), and libMesh::FEGenericBase< OutputType >::compute_periodic_constraints().

has_transformation_matrix()

bool libMesh::PeriodicBoundaryBase::has_transformation_matrix ( ) const

inherited

Returns

true if _transformation_matrix is not null.

Definition at line 79 of file periodic_boundary_base.C.

{
  return bool(_transformation_matrix);
}

References libMesh::PeriodicBoundaryBase::_transformation_matrix.

Referenced by libMesh::FEGenericBase< OutputType >::compute_periodic_constraints(), and libMesh::PeriodicBoundaryBase::get_transformation_matrix().

is_my_variable()

bool libMesh::PeriodicBoundaryBase::is_my_variable ( unsigned int  var_num ) const

inherited

Definition at line 71 of file periodic_boundary_base.C.

{
  bool a = variables.empty() || (!variables.empty() && variables.find(var_num) != variables.end());
  return a;
}

References libMesh::PeriodicBoundaryBase::variables.

Referenced by libMesh::FEGenericBase< OutputType >::compute_periodic_constraints().

merge()

void libMesh::PeriodicBoundaryBase::merge ( const PeriodicBoundaryBase &  pb )

inherited

Definition at line 64 of file periodic_boundary_base.C.

{
  variables.insert(pb.variables.begin(), pb.variables.end());
}

References libMesh::PeriodicBoundaryBase::variables.

Referenced by libMesh::DofMap::add_periodic_boundary().

set_transformation_matrix()

void libMesh::PeriodicBoundaryBase::set_transformation_matrix ( const DenseMatrix< Real > &  matrix )

inherited

Set the transformation matrix.

When calling this method we require the following conditions: 1) matrix is square with size that matches this->variables.size() 2) the list of variables in this->variables set must all have the same FE type Both of these conditions are asserted in DBG mode.

Definition at line 96 of file periodic_boundary_base.C.

{
  // Make a deep copy of matrix
  this->_transformation_matrix = std::make_unique<DenseMatrix<Real>>();
  *(this->_transformation_matrix) = matrix;
 
  // if _transformation_matrix is defined then it must be the same sie as variables.
  libmesh_assert_equal_to(_transformation_matrix->m(), variables.size());
  libmesh_assert_equal_to(_transformation_matrix->n(), variables.size());
}

References libMesh::PeriodicBoundaryBase::_transformation_matrix, and libMesh::PeriodicBoundaryBase::variables.

Referenced by set_up_rotation_matrix().

set_up_rotation_matrix()

void AzimuthalPeriodicBoundary::set_up_rotation_matrix ( )

inline

Computes and stores the rotation matrix for this transformation, and then calls the base class API to store it.

This should only be done once, since the direction and angle do not change once the class is constructed.

Definition at line 133 of file systems_of_equations_ex9.C.

  {
    // Formula for rotation matrix about an axis is given on wikipedia:
    // en.wikipedia.org/wiki/Rotation_matrix
    // We rotate by angle theta about the axis defined by u, which is a
    // unit vector in the direction of _axis.
    // Note: this example already requires LIBMESH_DIM==3 so we don't
    // explicitly check for that here.
    Point u = _axis.unit();
    Real u_x = u(0);
    Real u_y = u(1);
    Real u_z = u(2);
    Real cost = std::cos(_theta);
    Real sint = std::sin(_theta);
    _R = RealTensorValue
      (cost + u_x*u_x*(1.0 - cost),     u_x*u_y*(1.0 - cost) - u_z*sint, u_x*u_z*(1.0 - cost) + u_y*sint,
       u_y*u_x*(1.0 - cost) + u_z*sint, cost + u_y*u_y*(1.0 - cost),     u_y*u_z*(1.0 - cost) - u_x*sint,
       u_z*u_x*(1.0 - cost) - u_y*sint, u_z*u_y*(1.0 - cost) + u_x*sint, cost + u_z*u_z*(1.0 - cost));
 
    // For generality, PeriodicBoundaryBase::set_transformation_matrix() takes an
    // (n_vars * n_vars) DenseMatrix which we construct on the fly.
    this->set_transformation_matrix
      (DenseMatrix<Real> (3, 3, {_R(0,0), _R(0,1), _R(0,2), _R(1,0), _R(1,1), _R(1,2), _R(2,0), _R(2,1), _R(2,2)}));
  }

References _axis, _R, _theta, libMesh::Real, libMesh::PeriodicBoundaryBase::set_transformation_matrix(), and libMesh::TypeVector< T >::unit().

Referenced by AzimuthalPeriodicBoundary(), and AzimuthalPeriodicBoundary().

set_variable()

void libMesh::PeriodicBoundaryBase::set_variable ( unsigned int  var )

inherited

Definition at line 57 of file periodic_boundary_base.C.

{
  variables.insert(var);
}

References libMesh::PeriodicBoundaryBase::variables.

Referenced by AzimuthalPeriodicBoundary(), and AzimuthalPeriodicBoundary().

Member Data Documentation

_axis

Point AzimuthalPeriodicBoundary::_axis

private

Definition at line 187 of file systems_of_equations_ex9.C.

Referenced by set_up_rotation_matrix().

_center

Point AzimuthalPeriodicBoundary::_center

private

Definition at line 186 of file systems_of_equations_ex9.C.

Referenced by get_corresponding_pos().

_R

RealTensorValue AzimuthalPeriodicBoundary::_R

private

Definition at line 189 of file systems_of_equations_ex9.C.

Referenced by get_corresponding_pos(), and set_up_rotation_matrix().

_theta

Real AzimuthalPeriodicBoundary::_theta

private

Definition at line 188 of file systems_of_equations_ex9.C.

Referenced by AzimuthalPeriodicBoundary(), and set_up_rotation_matrix().

_transformation_matrix

std::unique_ptr<DenseMatrix<Real> > libMesh::PeriodicBoundaryBase::_transformation_matrix

protectedinherited

A DenseMatrix that defines the mapping of variables on this boundary and the counterpart boundary.

This is necessary for periodic-boundaries with vector-valued quantities (e.g. velocity or displacement) on a sector of a circular domain, for example, since in that case we must map each variable to a corresponding linear combination of all the variables. We store the DenseMatrix via a unique_ptr, and an uninitialized pointer is treated as equivalent to the identity matrix.

Definition at line 146 of file periodic_boundary_base.h.

Referenced by libMesh::PeriodicBoundaryBase::get_transformation_matrix(), libMesh::PeriodicBoundaryBase::has_transformation_matrix(), libMesh::PeriodicBoundaryBase::PeriodicBoundaryBase(), and libMesh::PeriodicBoundaryBase::set_transformation_matrix().

myboundary

boundary_id_type libMesh::PeriodicBoundaryBase::myboundary

inherited

The boundary ID of this boundary and its counterpart.

Definition at line 58 of file periodic_boundary_base.h.

Referenced by libMesh::MeshBase::add_disjoint_neighbor_boundary_pairs(), libMesh::DofMap::add_periodic_boundary(), AzimuthalPeriodicBoundary(), Biharmonic::JR::JR(), main(), libMesh::PeriodicBoundary::PeriodicBoundary(), and PeriodicBCTest::testPeriodicBC().

pairedboundary

boundary_id_type libMesh::PeriodicBoundaryBase::pairedboundary

inherited

Definition at line 58 of file periodic_boundary_base.h.

Referenced by libMesh::MeshBase::add_disjoint_neighbor_boundary_pairs(), libMesh::DofMap::add_periodic_boundary(), AzimuthalPeriodicBoundary(), libMesh::FEGenericBase< OutputType >::compute_periodic_constraints(), Biharmonic::JR::JR(), main(), libMesh::PeriodicBoundary::PeriodicBoundary(), and PeriodicBCTest::testPeriodicBC().

variables

std::set<unsigned int> libMesh::PeriodicBoundaryBase::variables

protectedinherited

Set of variables for this periodic boundary, empty means all variables possible.

Definition at line 134 of file periodic_boundary_base.h.

Referenced by libMesh::PeriodicBoundaryBase::get_variables(), libMesh::PeriodicBoundaryBase::is_my_variable(), libMesh::PeriodicBoundaryBase::merge(), libMesh::PeriodicBoundaryBase::set_transformation_matrix(), and libMesh::PeriodicBoundaryBase::set_variable().

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The documentation for this class was generated from the following file:

• examples/systems_of_equations/systems_of_equations_ex9/systems_of_equations_ex9.C