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. More...
	AzimuthalPeriodicBoundary (const AzimuthalPeriodicBoundary &o, TransformationType t=FORWARD)
	Copy constructor, with option for the copy to represent an inverse transformation. More...
virtual	~AzimuthalPeriodicBoundary ()
	Destructor. More...
DenseMatrix< Real >	get_rotation_matrix () const
	Get the rotation matrix for this transformation. More...
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. More...
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. More...
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. More...
void	set_transformation_matrix (const DenseMatrix< Real > &matrix)
	Set the transformation matrix. More...
const std::set< unsigned int > &	get_variables () const
	Get the set of variables for this periodic boundary condition. More...

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

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

Private Attributes
Point	_center
Point	_axis
Real	_theta

Detailed Description

Definition at line 75 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 81 of file systems_of_equations_ex9.C.

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

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 100 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_transformation_matrix(get_rotation_matrix());
  }

References swap().

~AzimuthalPeriodicBoundary()

virtual AzimuthalPeriodicBoundary::~AzimuthalPeriodicBoundary ( )

inlinevirtual

Destructor.

Definition at line 122 of file systems_of_equations_ex9.C.

{}

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 183 of file systems_of_equations_ex9.C.

  {
    return libmesh_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 156 of file systems_of_equations_ex9.C.

  {
    DenseVector<Real> translated_pt(3);
    for(unsigned int i=0; i<3; i++)
    {
      translated_pt(i) = pt(i) - _center(i);
    }
 
    // Note that since _theta defines the angle from "paired boundary" to
    // "my boundary", and we want the inverse of that here, we must use
    // vector_mult_transpose below.
    DenseVector<Real> rotated_pt;
    get_transformation_matrix().vector_mult_transpose(rotated_pt, translated_pt);
 
    Point corresponding_pos;
    for(unsigned int i=0; i<3; i++)
    {
      corresponding_pos(i) = rotated_pt(i) + _center(i);
    }
    return corresponding_pos;
  }

get_rotation_matrix()

DenseMatrix<Real> AzimuthalPeriodicBoundary::get_rotation_matrix ( ) const

inline

Get the rotation matrix for this transformation.

Definition at line 127 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.
    Point u = _axis.unit();
    Real u_x = u(0);
    Real u_y = u(1);
    Real u_z = u(2);
    DenseMatrix<Real> R(3,3);
    R(0,0) = cos(_theta) + u_x*u_x*(1.0 - cos(_theta));
    R(0,1) = u_x*u_y*(1.0 - cos(_theta)) - u_z*sin(_theta);
    R(0,2) = u_x*u_z*(1.0 - cos(_theta)) + u_y*sin(_theta);
    R(1,0) = u_y*u_x*(1.0 - cos(_theta)) + u_z*sin(_theta);
    R(1,1) = cos(_theta) + u_y*u_y*(1.0 - cos(_theta));
    R(1,2) = u_y*u_z*(1.0 - cos(_theta)) - u_x*sin(_theta);
    R(2,0) = u_z*u_x*(1.0 - cos(_theta)) - u_y*sin(_theta);
    R(2,1) = u_z*u_y*(1.0 - cos(_theta)) + u_x*sin(_theta);
    R(2,2) = cos(_theta) + u_z*u_z*(1.0 - cos(_theta));
 
    return R;
  }

References libMesh::Real, and libMesh::TypeVector< T >::unit().

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 83 of file periodic_boundary_base.C.

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

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

Referenced by libMesh::FEGenericBase< FEOutputType< T >::type >::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 108 of file periodic_boundary_base.C.

{
  return variables;
}

References libMesh::PeriodicBoundaryBase::variables.

Referenced by libMesh::FEGenericBase< FEOutputType< T >::type >::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 76 of file periodic_boundary_base.C.

{
  return bool(_transformation_matrix);
}

References libMesh::PeriodicBoundaryBase::_transformation_matrix.

Referenced by libMesh::FEGenericBase< FEOutputType< T >::type >::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 68 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< FEOutputType< T >::type >::compute_periodic_constraints().

merge()

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

inherited

Definition at line 61 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 95 of file periodic_boundary_base.C.

{
  // Make a deep copy of matrix
  this->_transformation_matrix = libmesh_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.

set_variable()

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

inherited

Definition at line 54 of file periodic_boundary_base.C.

{
  variables.insert(var);
}

References libMesh::PeriodicBoundaryBase::variables.

Member Data Documentation

_axis

Point AzimuthalPeriodicBoundary::_axis

private

Definition at line 194 of file systems_of_equations_ex9.C.

_center

Point AzimuthalPeriodicBoundary::_center

private

Definition at line 193 of file systems_of_equations_ex9.C.

_theta

Real AzimuthalPeriodicBoundary::_theta

private

Definition at line 195 of file systems_of_equations_ex9.C.

_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 exaple, 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::DofMap::add_periodic_boundary(), Biharmonic::JR::JR(), main(), and libMesh::PeriodicBoundary::PeriodicBoundary().

pairedboundary

boundary_id_type libMesh::PeriodicBoundaryBase::pairedboundary

inherited

Definition at line 58 of file periodic_boundary_base.h.

Referenced by libMesh::DofMap::add_periodic_boundary(), libMesh::FEGenericBase< FEOutputType< T >::type >::compute_periodic_constraints(), libMesh::FEAbstract::compute_periodic_node_constraints(), Biharmonic::JR::JR(), main(), libMesh::PeriodicBoundaries::neighbor(), and libMesh::PeriodicBoundary::PeriodicBoundary().

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