Class for local quadrature based computations for Lagrangian finite elements and second-order scalar elliptic BVPs. More...

#include <lf/uscalfe/uscalfe.h>

Public Types
using	Scalar
	type of returned element matrix

using	ElemMat = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Public Member Functions
	ReactionDiffusionElementMatrixProvider (std::shared_ptr< const UniformScalarFESpace< SCALAR > > fe_space, DIFF_COEFF alpha, REACTION_COEFF gamma)
	Constructor: cell-independent precomputations.

	ReactionDiffusionElementMatrixProvider (std::shared_ptr< const UniformScalarFESpace< SCALAR > > fe_space, DIFF_COEFF alpha, REACTION_COEFF gamma, quad_rule_collection_t qr_collection)
	Constructor: cell-independent precomputations and custom quadrature rule.

virtual bool	isActive (const lf::mesh::Entity &)
	All cells are considered active in the default implementation.

ElemMat	Eval (const lf::mesh::Entity &cell)
	main routine for the computation of element matrices

virtual	~ReactionDiffusionElementMatrixProvider ()=default


	ReactionDiffusionElementMatrixProvider (const ReactionDiffusionElementMatrixProvider &)=delete
	standard constructors

	ReactionDiffusionElementMatrixProvider (ReactionDiffusionElementMatrixProvider &&) noexcept=default

ReactionDiffusionElementMatrixProvider &	operator= (const ReactionDiffusionElementMatrixProvider &)=delete

ReactionDiffusionElementMatrixProvider &	operator= (ReactionDiffusionElementMatrixProvider &&)=delete

Private Attributes
std::array< PrecomputedScalarReferenceFiniteElement< SCALAR >, 5 >	fe_precomp_

functors providing coefficient functions
DIFF_COEFF	alpha_

REACTION_COEFF	gamma_

Detailed Description

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>
class lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >

Class for local quadrature based computations for Lagrangian finite elements and second-order scalar elliptic BVPs.

Template Parameters

SCALAR	scalar type of the UniformScalarFESpace. Must be a field type such as `double` or `std::complex<double>`
DIFF_COEFF	a MeshFunction that defines the diffusion coefficient \( \mathbf{\alpha} \). It should be either scalar- or matrix-valued.
REACTION_COEFF	a MeshFunction that defines the reaction coefficient \( \mathbf{\gamma} \). It should be either scalar- or matrix-valued.

Note: This class complies with the type requirements for the template argument ENTITY_MATRIX_PROVIDER of the function lf::assemble::AssembleMatrixLocally().

The element matrix is corresponds to the (local) bilinear form

\[ (u,v) \mapsto\int\limits_{K}\boldsymbol{\alpha}(\mathbf{x})\mathbf{grad}\,u \cdot\mathbf{grad}\,v + \gamma(\mathbf{x})u\,\overline{v}\,\mathrm{d}\mathbf{x} \;, \]

with diffusion coefficient \(\mathbf{\alpha}\) and reaction coefficient \(\gamma\), see also Example 2.8.3.29

Template parameter requirement

SCALAR must be a type like double
DIFF_COEFF must provide an evaluation operator operator (const Entity &,ref_coord_t) that returns either a scalar or a matrix type that is compatible with Eigen's matrices. Usually it will be an Eigen::Matrix either of variable of fixed size.

Note: The constructors of this class want an object of type UniformScalarFESpace, which holds a pointer to a mesh. However, for local builder classes global information about the mesh is irrelevant, and, therefore this object is used only to obtain information about the local shape functions. A revised implementation should directly pass this information to the constructor.

Logger

This class logs additional information to ReactionDiffusionElementMatrixProviderLogger(). See Loggers and Debug output for more information.

Definition at line 87 of file loc_comp_ellbvp.h.

Member Typedef Documentation

◆ ElemMat

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

using lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ElemMat = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Definition at line 97 of file loc_comp_ellbvp.h.

◆ Scalar

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

using lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::Scalar

Initial value:

 
      typename decltype(mesh::utils::MeshFunctionReturnType<DIFF_COEFF>() *
                            Eigen::Matrix<SCALAR, Eigen::Dynamic, 1>() +
                        mesh::utils::MeshFunctionReturnType<REACTION_COEFF>() *
                            Eigen::Matrix<SCALAR, Eigen::Dynamic, 1>())::Scalar

type of returned element matrix

Definition at line 92 of file loc_comp_ellbvp.h.

Constructor & Destructor Documentation

◆ ReactionDiffusionElementMatrixProvider() [1/4]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider ( const ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF > & )

delete

standard constructors

◆ ReactionDiffusionElementMatrixProvider() [2/4]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider ( ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF > && )

defaultnoexcept

◆ ReactionDiffusionElementMatrixProvider() [3/4]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider	(	std::shared_ptr< const UniformScalarFESpace< SCALAR > >	fe_space,
		DIFF_COEFF	alpha,
		REACTION_COEFF	gamma )

Constructor: cell-independent precomputations.

Parameters

fe_space	collection of specifications for scalar-valued parametric reference elements
alpha	mesh function for the (possibly matrix-valued) diffusion coefficient
gamma	mesh function providing scalar-valued diffusion coefficient

See also: LocCompLagrFEPreprocessor::LocCompLagrFEPreprocessor()

This constructor uses local quadature rules with double the degree of exactness as the polynomial degree of the finite element space.

Definition at line 212 of file loc_comp_ellbvp.h.

References lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::fe_precomp_, lf::base::RefEl::kQuad(), lf::base::RefEl::kTria(), and lf::quad::make_QuadRule().

◆ ReactionDiffusionElementMatrixProvider() [4/4]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider	(	std::shared_ptr< const UniformScalarFESpace< SCALAR > >	fe_space,
		DIFF_COEFF	alpha,
		REACTION_COEFF	gamma,
		quad_rule_collection_t	qr_collection )

Constructor: cell-independent precomputations and custom quadrature rule.

Parameters

fe_space	collection of specifications for scalar-valued parametric reference elements
alpha	mesh function for the (possibly matrix-valued) diffusion coefficient
gamma	mesh function providing scalar-valued diffusion coefficient
qr_collection	collection of quadrature rules. A quadrature rule is required for every cell type for which the finite element space provides local shape functions. If a quadrature rule is not specified for a cell type and the Eval() method is called for such a cell, exception will be thrown.

See also: LocCompLagrFEPreprocessor::LocCompLagrFEPreprocessor()

Definition at line 236 of file loc_comp_ellbvp.h.

References lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::fe_precomp_, lf::base::RefEl::kQuad(), lf::base::RefEl::kTria(), and lf::quad::QuadRule::RefEl().

◆ ~ReactionDiffusionElementMatrixProvider()

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

virtual lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::~ReactionDiffusionElementMatrixProvider ( )

virtualdefault

Virtual destructor

Member Function Documentation

◆ Eval()

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ElemMat lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::Eval ( const lf::mesh::Entity & cell )

main routine for the computation of element matrices

Parameters

cell	reference to the (triangular or quadrilateral) cell for which the element matrix should be computed.

Returns: a small dense, containing the element matrix.

Actual computation of the element matrix based on numerical quadrature and mapping techniques. The order of the quadrature rule is tied to the polynomial degree of the underlying Lagrangian finite element spaces: for polynomial degree p a quadrature rule is chosen that is exact for polynomials o degree 2p.

Exceptions

base::LfException in case the finite element specification is missing for the type of the cell or if there is no quadrature rule specified for the given cell type.

Definition at line 271 of file loc_comp_ellbvp.h.

References lf::geometry::Geometry::DimGlobal(), lf::geometry::Geometry::DimLocal(), lf::mesh::Entity::Geometry(), lf::geometry::Geometry::Global(), lf::geometry::Geometry::IntegrationElement(), lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >::isInitialized(), lf::geometry::Geometry::JacobianInverseGramian(), lf::quad::QuadRule::NumPoints(), lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >::NumRefShapeFunctions(), lf::quad::QuadRule::Points(), lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >::PrecompGradientsReferenceShapeFunctions(), lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >::PrecompReferenceShapeFunctions(), lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >::Qr(), lf::uscalfe::ReactionDiffusionElementMatrixProviderLogger(), lf::mesh::Entity::RefEl(), and lf::quad::QuadRule::Weights().

◆ isActive()

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

virtual bool lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::isActive ( const lf::mesh::Entity & )

inlinevirtual

All cells are considered active in the default implementation.

This method is meant to be overloaded if assembly should be restricted to a subset of cells.

Definition at line 155 of file loc_comp_ellbvp.h.

◆ operator=() [1/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

ReactionDiffusionElementMatrixProvider & lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::operator= ( const ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF > & )

delete

◆ operator=() [2/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

ReactionDiffusionElementMatrixProvider & lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::operator= ( ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF > && )

delete

Member Data Documentation

◆ alpha_

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

DIFF_COEFF lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::alpha_

private

Diffusion coefficient

Definition at line 182 of file loc_comp_ellbvp.h.

◆ fe_precomp_

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

std::array<PrecomputedScalarReferenceFiniteElement<SCALAR>, 5> lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::fe_precomp_

private

Definition at line 188 of file loc_comp_ellbvp.h.

Referenced by lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider(), and lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider().

◆ gamma_

template<base::Scalar SCALAR, mesh::utils::MeshFunction DIFF_COEFF, mesh::utils::MeshFunction REACTION_COEFF>

REACTION_COEFF lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::gamma_

private

Reaction coefficient

Definition at line 184 of file loc_comp_ellbvp.h.

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

/__w/lehrfempp/lehrfempp/lib/lf/uscalfe/loc_comp_ellbvp.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

Template parameter requirement

Logger

Member Typedef Documentation

◆ ElemMat

◆ Scalar

Constructor & Destructor Documentation

◆ ReactionDiffusionElementMatrixProvider() [1/4]

◆ ReactionDiffusionElementMatrixProvider() [2/4]

◆ ReactionDiffusionElementMatrixProvider() [3/4]

◆ ReactionDiffusionElementMatrixProvider() [4/4]

◆ ~ReactionDiffusionElementMatrixProvider()

Member Function Documentation

◆ Eval()

◆ isActive()

◆ operator=() [1/2]

◆ operator=() [2/2]

Member Data Documentation

◆ alpha_

◆ fe_precomp_

◆ gamma_