Handles the construction and management of a reference inclusion geometry and its basis. More...

#include <reference_cross_section.h>

Public Member Functions
	ReferenceCrossSection (const ReferenceCrossSectionParameters< dim, spacedim, n_components > &par)
	Constructs the ReferenceCrossSection from parameters.

const Quadrature< spacedim > &	get_global_quadrature () const
	Returns the global quadrature object in the embedding space.

const std::vector< Vector< double > > &	get_basis_functions () const
	Returns the list of selected basis functions.

const double &	shape_value (const unsigned int i, const unsigned int q, const unsigned int comp) const

const SparseMatrix< double > &	get_mass_matrix () const
	Returns the mass matrix corresponding to selected basis functions.

unsigned int	n_selected_basis () const
	Returns the number of selected basis functions.

unsigned int	max_n_basis () const
	Returns the total number of available basis functions.

Quadrature< spacedim >	get_transformed_quadrature (const Point< spacedim > &new_origin, const Tensor< 1, spacedim > &new_vertical, const double scale) const

unsigned int	n_quadrature_points () const

void	initialize ()
	Initializes the reference inclusion domain.

double	measure (const double scale=1.0) const

Private Member Functions
void	make_grid ()
	Builds the mesh for the reference inclusion domain.

void	setup_dofs ()
	Initializes the degrees of freedom and finite element space.

void	compute_basis ()
	Computes and stores all basis functions.

Private Attributes
const ReferenceCrossSectionParameters< dim, spacedim, n_components > &	par
	Reference to parameter configuration.

PolynomialsP< spacedim >	polynomials
	Polynomial space used for modal basis generation.

Triangulation< dim, spacedim >	triangulation
	Triangulation of the reference inclusion domain.

QGauss< dim >	quadrature_formula
	Quadrature formula for integration on the reference domain.

FESystem< dim, spacedim >	fe
	Finite element space for the inclusion.

MappingQ< dim, spacedim >	mapping

DoFHandler< dim, spacedim >	dof_handler
	Degree of freedom handler for the inclusion.

std::vector< Vector< double > >	basis_functions
	List of all computed basis functions.

std::vector< Vector< double > >	selected_basis_functions
	Subset of selected basis functions.

SparsityPattern	sparsity_pattern
	Sparsity pattern used for assembling the mass matrix.

SparseMatrix< double >	mass_matrix
	Mass matrix associated with the selected basis functions.

Quadrature< spacedim >	global_quadrature
	Quadrature rule in the embedding space.

double	reference_measure
	Reference measure for the inclusion.

FullMatrix< double >	basis_functions_on_qpoints
	The basis functions computed on the quadrature points.

Detailed Description

template<int dim, int spacedim = dim, int n_components = 1>
class ReferenceCrossSection< dim, spacedim, n_components >

Handles the construction and management of a reference inclusion geometry and its basis.

Used in reduced basis immersed boundary methods, this class initializes and stores a full finite element space, computes basis functions, and provides access to quadrature rules and mass matrices.

Template Parameters

dim	The intrinsic dimension of the inclusion.
spacedim	The embedding dimension.
n_components	Number of components per field variable.

Definition at line 92 of file reference_cross_section.h.

Constructor & Destructor Documentation

◆ ReferenceCrossSection()

template<int dim, int spacedim, int n_components>

ReferenceCrossSection< dim, spacedim, n_components >::ReferenceCrossSection ( const ReferenceCrossSectionParameters< dim, spacedim, n_components > & par )

Constructs the ReferenceCrossSection from parameters.

Definition at line 41 of file reference_cross_section.cc.

References dof_handler, fe, initialize(), mapping, par, polynomials, quadrature_formula, and triangulation.

Member Function Documentation

◆ compute_basis()

template<int dim, int spacedim, int n_components>

void ReferenceCrossSection< dim, spacedim, n_components >::compute_basis ( )

private

Computes and stores all basis functions.

Definition at line 131 of file reference_cross_section.cc.

Referenced by initialize().

◆ get_basis_functions()

template<int dim, int spacedim, int n_components>

auto ReferenceCrossSection< dim, spacedim, n_components >::get_basis_functions ( ) const

Returns the list of selected basis functions.

Definition at line 262 of file reference_cross_section.cc.

References selected_basis_functions.

◆ get_global_quadrature()

template<int dim, int spacedim, int n_components>

auto ReferenceCrossSection< dim, spacedim, n_components >::get_global_quadrature ( ) const

Returns the global quadrature object in the embedding space.

Definition at line 252 of file reference_cross_section.cc.

References global_quadrature.

◆ get_mass_matrix()

template<int dim, int spacedim, int n_components>

auto ReferenceCrossSection< dim, spacedim, n_components >::get_mass_matrix ( ) const

Returns the mass matrix corresponding to selected basis functions.

Definition at line 290 of file reference_cross_section.cc.

References mass_matrix.

◆ get_transformed_quadrature()

template<int dim, int spacedim, int n_components>

Quadrature< spacedim > ReferenceCrossSection< dim, spacedim, n_components >::get_transformed_quadrature	(	const Point< spacedim > &	new_origin,
		const Tensor< 1, spacedim > &	new_vertical,
		const double	scale ) const

Definition at line 337 of file reference_cross_section.cc.

References Physics::VectorRelations::angle(), global_quadrature, Tensor< int rank_, int dim, typename Number >::norm(), std::pow(), Physics::Transformations::Rotations::rotation_matrix_2d(), Physics::Transformations::Rotations::rotation_matrix_3d(), and Physics::VectorRelations::signed_angle().

◆ initialize()

template<int dim, int spacedim, int n_components>

void ReferenceCrossSection< dim, spacedim, n_components >::initialize ( )

Initializes the reference inclusion domain.

Definition at line 407 of file reference_cross_section.cc.

References compute_basis(), dof_handler, make_grid(), setup_dofs(), and triangulation.

Referenced by ReferenceCrossSection().

◆ make_grid()

template<int dim, int spacedim, int n_components>

void ReferenceCrossSection< dim, spacedim, n_components >::make_grid ( )

private

Builds the mesh for the reference inclusion domain.

Definition at line 56 of file reference_cross_section.cc.

References par.

Referenced by initialize().

◆ max_n_basis()

template<int dim, int spacedim, int n_components>

unsigned int ReferenceCrossSection< dim, spacedim, n_components >::max_n_basis ( ) const

Returns the total number of available basis functions.

Definition at line 310 of file reference_cross_section.cc.

References basis_functions.

◆ measure()

template<int dim, int spacedim, int n_components>

double ReferenceCrossSection< dim, spacedim, n_components >::measure ( const double scale = 1.0 ) const

Compute the cross section measure for the inclusion. The returned value is exact w.r.t. to the used quadrature formula, i.e., it is the integral of one on the cross section. If a scale is provided, the measure is multiplied by the scale^dim.

Parameters

scale The scaling factor for the measure.

Definition at line 242 of file reference_cross_section.cc.

References std::pow(), and reference_measure.

◆ n_quadrature_points()

template<int dim, int spacedim, int n_components>

unsigned int ReferenceCrossSection< dim, spacedim, n_components >::n_quadrature_points ( ) const

Definition at line 400 of file reference_cross_section.cc.

References global_quadrature.

◆ n_selected_basis()

template<int dim, int spacedim, int n_components>

auto ReferenceCrossSection< dim, spacedim, n_components >::n_selected_basis ( ) const

Returns the number of selected basis functions.

Definition at line 300 of file reference_cross_section.cc.

References selected_basis_functions.

◆ setup_dofs()

template<int dim, int spacedim, int n_components>

void ReferenceCrossSection< dim, spacedim, n_components >::setup_dofs ( )

private

Initializes the degrees of freedom and finite element space.

Definition at line 89 of file reference_cross_section.cc.

References dof_handler, fe, DoFTools::make_sparsity_pattern(), and sparsity_pattern.

Referenced by initialize().

◆ shape_value()

template<int dim, int spacedim, int n_components>

const double & ReferenceCrossSection< dim, spacedim, n_components >::shape_value	(	const unsigned int	i,
		const unsigned int	q,
		const unsigned int	comp ) const

the component comp of the ith selected reference basis function, at the quadrature point index q,

Definition at line 270 of file reference_cross_section.cc.

References basis_functions_on_qpoints, global_quadrature, and selected_basis_functions.

Member Data Documentation

◆ basis_functions

template<int dim, int spacedim = dim, int n_components = 1>

std::vector<Vector<double> > ReferenceCrossSection< dim, spacedim, n_components >::basis_functions

private

List of all computed basis functions.

Definition at line 183 of file reference_cross_section.h.

Referenced by max_n_basis().

◆ basis_functions_on_qpoints

template<int dim, int spacedim = dim, int n_components = 1>

FullMatrix<double> ReferenceCrossSection< dim, spacedim, n_components >::basis_functions_on_qpoints

private

The basis functions computed on the quadrature points.

Definition at line 201 of file reference_cross_section.h.

Referenced by shape_value().

◆ dof_handler

template<int dim, int spacedim = dim, int n_components = 1>

DoFHandler<dim, spacedim> ReferenceCrossSection< dim, spacedim, n_components >::dof_handler

private

Degree of freedom handler for the inclusion.

Definition at line 180 of file reference_cross_section.h.

Referenced by initialize(), ReferenceCrossSection(), and setup_dofs().

◆ fe

template<int dim, int spacedim = dim, int n_components = 1>

FESystem<dim, spacedim> ReferenceCrossSection< dim, spacedim, n_components >::fe

private

Finite element space for the inclusion.

Definition at line 174 of file reference_cross_section.h.

Referenced by ReferenceCrossSection(), and setup_dofs().

◆ global_quadrature

template<int dim, int spacedim = dim, int n_components = 1>

Quadrature<spacedim> ReferenceCrossSection< dim, spacedim, n_components >::global_quadrature

private

Quadrature rule in the embedding space.

Definition at line 195 of file reference_cross_section.h.

Referenced by get_global_quadrature(), get_transformed_quadrature(), n_quadrature_points(), and shape_value().

◆ mapping

template<int dim, int spacedim = dim, int n_components = 1>

MappingQ<dim, spacedim> ReferenceCrossSection< dim, spacedim, n_components >::mapping

private

Definition at line 177 of file reference_cross_section.h.

Referenced by ReferenceCrossSection().

◆ mass_matrix

template<int dim, int spacedim = dim, int n_components = 1>

SparseMatrix<double> ReferenceCrossSection< dim, spacedim, n_components >::mass_matrix

private

Mass matrix associated with the selected basis functions.

Definition at line 192 of file reference_cross_section.h.

Referenced by get_mass_matrix().

◆ par

template<int dim, int spacedim = dim, int n_components = 1>

const ReferenceCrossSectionParameters<dim, spacedim, n_components>& ReferenceCrossSection< dim, spacedim, n_components >::par

private

Reference to parameter configuration.

Definition at line 162 of file reference_cross_section.h.

Referenced by make_grid(), and ReferenceCrossSection().

◆ polynomials

template<int dim, int spacedim = dim, int n_components = 1>

PolynomialsP<spacedim> ReferenceCrossSection< dim, spacedim, n_components >::polynomials

private

Polynomial space used for modal basis generation.

Definition at line 165 of file reference_cross_section.h.

Referenced by ReferenceCrossSection().

◆ quadrature_formula

template<int dim, int spacedim = dim, int n_components = 1>

QGauss<dim> ReferenceCrossSection< dim, spacedim, n_components >::quadrature_formula

private

Quadrature formula for integration on the reference domain.

Definition at line 171 of file reference_cross_section.h.

Referenced by ReferenceCrossSection().

◆ reference_measure

template<int dim, int spacedim = dim, int n_components = 1>

double ReferenceCrossSection< dim, spacedim, n_components >::reference_measure

private

Reference measure for the inclusion.

Definition at line 198 of file reference_cross_section.h.

Referenced by measure().

◆ selected_basis_functions

template<int dim, int spacedim = dim, int n_components = 1>

std::vector<Vector<double> > ReferenceCrossSection< dim, spacedim, n_components >::selected_basis_functions

private

Subset of selected basis functions.

Definition at line 186 of file reference_cross_section.h.

Referenced by get_basis_functions(), n_selected_basis(), and shape_value().

◆ sparsity_pattern

template<int dim, int spacedim = dim, int n_components = 1>

SparsityPattern ReferenceCrossSection< dim, spacedim, n_components >::sparsity_pattern

private

Sparsity pattern used for assembling the mass matrix.

Definition at line 189 of file reference_cross_section.h.

Referenced by setup_dofs().

◆ triangulation

template<int dim, int spacedim = dim, int n_components = 1>

Triangulation<dim, spacedim> ReferenceCrossSection< dim, spacedim, n_components >::triangulation

private

Triangulation of the reference inclusion domain.

Definition at line 168 of file reference_cross_section.h.

Referenced by initialize(), and ReferenceCrossSection().

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

/github/workspace/include/reference_cross_section.h
/github/workspace/source/reference_cross_section.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ReferenceCrossSection()

Member Function Documentation

◆ compute_basis()

◆ get_basis_functions()

◆ get_global_quadrature()

◆ get_mass_matrix()

◆ get_transformed_quadrature()

◆ initialize()

◆ make_grid()

◆ max_n_basis()

◆ measure()

◆ n_quadrature_points()

◆ n_selected_basis()

◆ setup_dofs()

◆ shape_value()

Member Data Documentation

◆ basis_functions

◆ basis_functions_on_qpoints

◆ dof_handler

◆ fe

◆ global_quadrature

◆ mapping

◆ mass_matrix

◆ par

◆ polynomials

◆ quadrature_formula

◆ reference_measure

◆ selected_basis_functions

◆ sparsity_pattern

◆ triangulation