Abstract base class BilinearFormIntegrator. More...

#include <bilininteg.hpp>

Inheritance diagram for mfem::BilinearFormIntegrator:

Collaboration diagram for mfem::BilinearFormIntegrator:

Public Member Functions
virtual void	AssemblePA (const FiniteElementSpace &fes)
	Method defining partial assembly. More...

virtual void	AssemblePA (const FiniteElementSpace &trial_fes, const FiniteElementSpace &test_fes)

virtual void	AssemblePAInteriorFaces (const FiniteElementSpace &fes)

virtual void	AssemblePABoundaryFaces (const FiniteElementSpace &fes)

virtual void	AssembleDiagonalPA (Vector &diag)
	Assemble diagonal and add it to Vector diag. More...

virtual void	AssembleDiagonalPA_ADAt (const Vector &D, Vector &diag)
	Assemble diagonal of ADA^T (A is this integrator) and add it to diag. More...

virtual void	AddMultPA (const Vector &x, Vector &y) const
	Method for partially assembled action. More...

virtual void	AddMultTransposePA (const Vector &x, Vector &y) const
	Method for partially assembled transposed action. More...

virtual void	AssembleEA (const FiniteElementSpace &fes, Vector &emat, const bool add=true)
	Method defining element assembly. More...

virtual void	AssembleMF (const FiniteElementSpace &fes)
	Method defining matrix-free assembly. More...

virtual void	AddMultMF (const Vector &x, Vector &y) const

virtual void	AddMultTransposeMF (const Vector &x, Vector &y) const

virtual void	AssembleDiagonalMF (Vector &diag)
	Assemble diagonal and add it to Vector diag. More...

virtual void	AssembleEAInteriorFaces (const FiniteElementSpace &fes, Vector &ea_data_int, Vector &ea_data_ext, const bool add=true)

virtual void	AssembleEABoundaryFaces (const FiniteElementSpace &fes, Vector &ea_data_bdr, const bool add=true)

virtual void	AssembleElementMatrix (const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
	Given a particular Finite Element computes the element matrix elmat. More...

virtual void	AssembleElementMatrix2 (const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)

virtual void	AssembleFaceMatrix (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)

virtual void	AssembleFaceMatrix (const FiniteElement &trial_face_fe, const FiniteElement &test_fe1, const FiniteElement &test_fe2, FaceElementTransformations &Trans, DenseMatrix &elmat)

virtual void	AssembleElementVector (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, Vector &elvect)
	Perform the local action of the BilinearFormIntegrator. Note that the default implementation in the base class is general but not efficient. More...

virtual void	AssembleFaceVector (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, Vector &elvect)
	Perform the local action of the BilinearFormIntegrator resulting from a face integral term. Note that the default implementation in the base class is general but not efficient. More...

virtual void	AssembleElementGrad (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, DenseMatrix &elmat)
	Assemble the local gradient matrix. More...

virtual void	AssembleFaceGrad (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, DenseMatrix &elmat)
	Assemble the local action of the gradient of the NonlinearFormIntegrator resulting from a face integral term. More...

virtual void	ComputeElementFlux (const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, bool with_coef=true)
	Virtual method required for Zienkiewicz-Zhu type error estimators. More...

virtual double	ComputeFluxEnergy (const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL)
	Virtual method required for Zienkiewicz-Zhu type error estimators. More...

virtual	~BilinearFormIntegrator ()

Public Member Functions inherited from mfem::NonlinearFormIntegrator
void	SetIntRule (const IntegrationRule *ir)
	Prescribe a fixed IntegrationRule to use (when ir != NULL) or let the integrator choose (when ir == NULL). More...

void	SetIntegrationRule (const IntegrationRule &irule)
	Prescribe a fixed IntegrationRule to use. More...

virtual double	GetElementEnergy (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun)
	Compute the local energy. More...

virtual	~NonlinearFormIntegrator ()

Protected Member Functions
	BilinearFormIntegrator (const IntegrationRule *ir=NULL)

Protected Member Functions inherited from mfem::NonlinearFormIntegrator
	NonlinearFormIntegrator (const IntegrationRule *ir=NULL)

Additional Inherited Members
Protected Attributes inherited from mfem::NonlinearFormIntegrator
const IntegrationRule *	IntRule

Detailed Description

Abstract base class BilinearFormIntegrator.

Definition at line 31 of file bilininteg.hpp.

Constructor & Destructor Documentation

mfem::BilinearFormIntegrator::BilinearFormIntegrator ( const IntegrationRule * ir = NULL )

inlineprotected

Definition at line 34 of file bilininteg.hpp.

virtual mfem::BilinearFormIntegrator::~BilinearFormIntegrator ( )

inlinevirtual

Definition at line 244 of file bilininteg.hpp.

Member Function Documentation

void mfem::BilinearFormIntegrator::AddMultMF	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Perform the action of integrator on the input x and add the result to the output y. Both x and y are E-vectors, i.e. they represent the element-wise discontinuous version of the FE space.

This method can be called only after the method AssembleMF() has been called.

Reimplemented in mfem::VectorDiffusionIntegrator, mfem::VectorMassIntegrator, mfem::MassIntegrator, and mfem::DiffusionIntegrator.

Definition at line 105 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AddMultPA	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Method for partially assembled action.

Perform the action of integrator on the input x and add the result to the output y. Both x and y are E-vectors, i.e. they represent the element-wise discontinuous version of the FE space.

This method can be called only after the method AssemblePA() has been called.

Reimplemented from mfem::NonlinearFormIntegrator.

Reimplemented in mfem::DGTraceIntegrator, mfem::VectorDiffusionIntegrator, mfem::DivDivIntegrator, mfem::VectorDivergenceIntegrator, mfem::VectorFEMassIntegrator, mfem::CurlCurlIntegrator, mfem::VectorFEDivergenceIntegrator, mfem::VectorMassIntegrator, mfem::ConvectionIntegrator, mfem::MassIntegrator, mfem::DiffusionIntegrator, mfem::GradientIntegrator, mfem::MixedVectorWeakCurlIntegrator, mfem::MixedVectorCurlIntegrator, mfem::MixedVectorGradientIntegrator, and mfem::TransposeIntegrator.

Definition at line 87 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AddMultTransposeMF	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Perform the transpose action of integrator on the input x and add the result to the output y. Both x and y are E-vectors, i.e. they represent the element-wise discontinuous version of the FE space.

This method can be called only after the method AssemblePA() has been called.

Definition at line 111 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AddMultTransposePA	(	const Vector &	x,
		Vector &	y
	)		const

virtual

Method for partially assembled transposed action.

Perform the transpose action of integrator on the input x and add the result to the output y. Both x and y are E-vectors, i.e. they represent the element-wise discontinuous version of the FE space.

This method can be called only after the method AssemblePA() has been called.

Reimplemented in mfem::DGTraceIntegrator, mfem::VectorDivergenceIntegrator, mfem::VectorFEDivergenceIntegrator, mfem::GradientIntegrator, and mfem::TransposeIntegrator.

Definition at line 93 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleDiagonalMF ( Vector & diag )

virtual

Assemble diagonal and add it to Vector diag.

Reimplemented in mfem::VectorDiffusionIntegrator, mfem::VectorMassIntegrator, mfem::MassIntegrator, and mfem::DiffusionIntegrator.

Definition at line 117 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleDiagonalPA ( Vector & diag )

virtual

Assemble diagonal and add it to Vector diag.

Reimplemented in mfem::VectorDiffusionIntegrator, mfem::DivDivIntegrator, mfem::VectorFEMassIntegrator, mfem::CurlCurlIntegrator, mfem::VectorMassIntegrator, mfem::MassIntegrator, and mfem::DiffusionIntegrator.

Definition at line 48 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleDiagonalPA_ADAt	(	const Vector &	D,
		Vector &	diag
	)

virtual

Assemble diagonal of ADA^T (A is this integrator) and add it to diag.

Reimplemented in mfem::VectorFEDivergenceIntegrator.

Definition at line 81 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleEA	(	const FiniteElementSpace &	fes,
		Vector &	emat,
		const bool	add = `true`
	)

virtual

Method defining element assembly.

The result of the element assembly is added to the emat Vector if add is true. Otherwise, if add is false, we set emat.

Reimplemented in mfem::ConvectionIntegrator, mfem::MassIntegrator, mfem::DiffusionIntegrator, and mfem::TransposeIntegrator.

Definition at line 54 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleEABoundaryFaces	(	const FiniteElementSpace &	fes,
		Vector &	ea_data_bdr,
		const bool	add = `true`
	)

virtual

Reimplemented in mfem::DGTraceIntegrator, and mfem::TransposeIntegrator.

Definition at line 72 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleEAInteriorFaces	(	const FiniteElementSpace &	fes,
		Vector &	ea_data_int,
		Vector &	ea_data_ext,
		const bool	add = `true`
	)

virtual

Reimplemented in mfem::DGTraceIntegrator, and mfem::TransposeIntegrator.

Definition at line 62 of file bilininteg.cpp.

virtual void mfem::BilinearFormIntegrator::AssembleElementGrad	(	const FiniteElement &	el,
		ElementTransformation &	Tr,
		const Vector &	elfun,
		DenseMatrix &	elmat
	)

inlinevirtual

Assemble the local gradient matrix.

Reimplemented from mfem::NonlinearFormIntegrator.

Definition at line 174 of file bilininteg.hpp.

void mfem::BilinearFormIntegrator::AssembleElementMatrix	(	const FiniteElement &	el,
		ElementTransformation &	Trans,
		DenseMatrix &	elmat
	)

virtual

Given a particular Finite Element computes the element matrix elmat.

Reimplemented in mfem::ElasticityIntegrator, mfem::VectorDiffusionIntegrator, mfem::DivDivIntegrator, mfem::VectorFEMassIntegrator, mfem::VectorCurlCurlIntegrator, mfem::CurlCurlIntegrator, mfem::DerivativeIntegrator, mfem::VectorFECurlIntegrator, mfem::VectorFEWeakDivergenceIntegrator, mfem::VectorFEDivergenceIntegrator, mfem::VectorMassIntegrator, mfem::GroupConvectionIntegrator, mfem::ConvectionIntegrator, mfem::MassIntegrator, mfem::DiffusionIntegrator, mfem::MixedScalarVectorIntegrator, mfem::MixedVectorIntegrator, mfem::MixedScalarIntegrator, mfem::SumIntegrator, mfem::InverseIntegrator, mfem::LumpedIntegrator, and mfem::TransposeIntegrator.

Definition at line 123 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleElementMatrix2	(	const FiniteElement &	trial_fe,
		const FiniteElement &	test_fe,
		ElementTransformation &	Trans,
		DenseMatrix &	elmat
	)

virtual

Compute the local matrix representation of a bilinear form a(u,v) defined on different trial (given by u) and test (given by v) spaces. The rows in the local matrix correspond to the test dofs and the columns – to the trial dofs.

Reimplemented in mfem::VectorInnerProductInterpolator, mfem::VectorCrossProductInterpolator, mfem::VectorScalarProductInterpolator, mfem::ScalarVectorProductInterpolator, mfem::ScalarProductInterpolator, mfem::NormalInterpolator, mfem::DivergenceInterpolator, mfem::CurlInterpolator, mfem::IdentityInterpolator, mfem::GradientInterpolator, mfem::VectorDivergenceIntegrator, mfem::VectorFEMassIntegrator, mfem::DerivativeIntegrator, mfem::VectorFECurlIntegrator, mfem::VectorFEWeakDivergenceIntegrator, mfem::VectorFEDivergenceIntegrator, mfem::VectorMassIntegrator, mfem::MassIntegrator, mfem::DiffusionIntegrator, mfem::GradientIntegrator, mfem::MixedScalarVectorIntegrator, mfem::MixedVectorIntegrator, mfem::MixedScalarIntegrator, mfem::TransposeIntegrator, and DomainIntegrator.

Definition at line 131 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleElementVector	(	const FiniteElement &	el,
		ElementTransformation &	Tr,
		const Vector &	elfun,
		Vector &	elvect
	)

virtual

Perform the local action of the BilinearFormIntegrator. Note that the default implementation in the base class is general but not efficient.

Reimplemented from mfem::NonlinearFormIntegrator.

Reimplemented in mfem::VectorDiffusionIntegrator, and mfem::DiffusionIntegrator.

Definition at line 156 of file bilininteg.cpp.

virtual void mfem::BilinearFormIntegrator::AssembleFaceGrad	(	const FiniteElement &	el1,
		const FiniteElement &	el2,
		FaceElementTransformations &	Tr,
		const Vector &	elfun,
		DenseMatrix &	elmat
	)

inlinevirtual

Assemble the local action of the gradient of the NonlinearFormIntegrator resulting from a face integral term.

Reimplemented from mfem::NonlinearFormIntegrator.

Definition at line 179 of file bilininteg.hpp.

void mfem::BilinearFormIntegrator::AssembleFaceMatrix	(	const FiniteElement &	el1,
		const FiniteElement &	el2,
		FaceElementTransformations &	Trans,
		DenseMatrix &	elmat
	)

virtual

Reimplemented in mfem::DGElasticityIntegrator, mfem::DGDiffusionIntegrator, mfem::DGTraceIntegrator, mfem::BoundaryMassIntegrator, and mfem::TransposeIntegrator.

Definition at line 139 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleFaceMatrix	(	const FiniteElement &	trial_face_fe,
		const FiniteElement &	test_fe1,
		const FiniteElement &	test_fe2,
		FaceElementTransformations &	Trans,
		DenseMatrix &	elmat
	)

virtual

Abstract method used for assembling TraceFaceIntegrators in a MixedBilinearForm.

Reimplemented in mfem::NormalTraceJumpIntegrator, and mfem::TraceJumpIntegrator.

Definition at line 147 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleFaceVector	(	const FiniteElement &	el1,
		const FiniteElement &	el2,
		FaceElementTransformations &	Tr,
		const Vector &	elfun,
		Vector &	elvect
	)

virtual

Perform the local action of the BilinearFormIntegrator resulting from a face integral term. Note that the default implementation in the base class is general but not efficient.

Reimplemented from mfem::NonlinearFormIntegrator.

Definition at line 167 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssembleMF ( const FiniteElementSpace & fes )

virtual

Method defining matrix-free assembly.

Used with BilinearFormIntegrators that have different spaces.The result of fully matrix-free assembly is stored internally so that it can be used later in the methods AddMultMF() and AddMultTransposeMF().

Reimplemented in mfem::VectorDiffusionIntegrator, mfem::VectorMassIntegrator, mfem::MassIntegrator, and mfem::DiffusionIntegrator.

Definition at line 99 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssemblePA ( const FiniteElementSpace & fes )

virtual

Method defining partial assembly.

The result of the partial assembly is stored internally so that it can be used later in the methods AddMultPA() and AddMultTransposePA().

Reimplemented from mfem::NonlinearFormIntegrator.

Reimplemented in mfem::VectorDiffusionIntegrator, mfem::DivDivIntegrator, mfem::VectorFEMassIntegrator, mfem::CurlCurlIntegrator, mfem::VectorMassIntegrator, mfem::ConvectionIntegrator, mfem::MassIntegrator, mfem::DiffusionIntegrator, and mfem::TransposeIntegrator.

Definition at line 23 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssemblePA	(	const FiniteElementSpace &	trial_fes,
		const FiniteElementSpace &	test_fes
	)

virtual

Used with BilinearFormIntegrators that have different spaces.

Reimplemented from mfem::NonlinearFormIntegrator.

Reimplemented in mfem::VectorDivergenceIntegrator, mfem::VectorFEMassIntegrator, mfem::VectorFEDivergenceIntegrator, mfem::GradientIntegrator, mfem::MixedVectorWeakCurlIntegrator, mfem::MixedVectorCurlIntegrator, and mfem::MixedVectorGradientIntegrator.

Definition at line 29 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssemblePABoundaryFaces ( const FiniteElementSpace & fes )

virtual

Reimplemented in mfem::DGTraceIntegrator, and mfem::TransposeIntegrator.

Definition at line 42 of file bilininteg.cpp.

void mfem::BilinearFormIntegrator::AssemblePAInteriorFaces ( const FiniteElementSpace & fes )

virtual

Reimplemented in mfem::DGTraceIntegrator, and mfem::TransposeIntegrator.

Definition at line 36 of file bilininteg.cpp.

virtual void mfem::BilinearFormIntegrator::ComputeElementFlux	(	const FiniteElement &	el,
		ElementTransformation &	Trans,
		Vector &	u,
		const FiniteElement &	fluxelem,
		Vector &	flux,
		bool	with_coef = `true`
	)

inlinevirtual

Virtual method required for Zienkiewicz-Zhu type error estimators.

The purpose of the method is to compute a local "flux" finite element function given a local finite element solution. The "flux" function has to be computed in terms of its coefficients (represented by the Vector flux) which multiply the basis functions defined by the FiniteElement fluxelem. Typically, the "flux" function will have more than one component and consequently flux should be store the coefficients of all components: first all coefficient for component 0, then all coefficients for component 1, etc. What the "flux" function represents depends on the specific integrator. For example, in the case of DiffusionIntegrator, the flux is the gradient of the solution multiplied by the diffusion coefficient.

Parameters

[in]	el	FiniteElement of the solution.
[in]	Trans	The ElementTransformation describing the physical position of the mesh element.
[in]	u	Solution coefficients representing the expansion of the solution function in the basis of el.
[in]	fluxelem	FiniteElement of the "flux".
[out]	flux	"Flux" coefficients representing the expansion of the "flux" function in the basis of fluxelem. The size of flux as a Vector has to be set by this method, e.g. using Vector::SetSize().
[in]	with_coef	If zero (the default value is 1) the implementation of the method may choose not to scale the "flux" function by any coefficients describing the integrator.

Reimplemented in mfem::ElasticityIntegrator, mfem::CurlCurlIntegrator, and mfem::DiffusionIntegrator.

Definition at line 214 of file bilininteg.hpp.

virtual double mfem::BilinearFormIntegrator::ComputeFluxEnergy	(	const FiniteElement &	fluxelem,
		ElementTransformation &	Trans,
		Vector &	flux,
		Vector *	d_energy = `NULL`
	)

inlinevirtual

Virtual method required for Zienkiewicz-Zhu type error estimators.

The purpose of this method is to compute a local number that measures the energy of a given "flux" function (see ComputeElementFlux() for a description of the "flux" function). Typically, the energy of a "flux" function should be equal to a_local(u,u), if the "flux" is defined from a solution u; here a_local(.,.) denotes the element-local bilinear form represented by the integrator.

Parameters

[in]	fluxelem	FiniteElement of the "flux".
[in]	Trans	The ElementTransformation describing the physical position of the mesh element.
[in]	flux	"Flux" coefficients representing the expansion of the "flux" function in the basis of fluxelem.
[out]	d_energy	If not NULL, the given Vector should be set to represent directional energy split that can be used for anisotropic error estimation.

Returns: The computed energy.

Reimplemented in mfem::ElasticityIntegrator, mfem::CurlCurlIntegrator, and mfem::DiffusionIntegrator.

Definition at line 239 of file bilininteg.hpp.

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

fem/bilininteg.hpp
fem/bilininteg.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation