Integrator for \((\mathrm{curl}(u), \mathrm{curl}(v))\) for Nedelec elements. More...

#include <bilininteg.hpp>

Inheritance diagram for mfem::CurlCurlIntegrator:

Collaboration diagram for mfem::CurlCurlIntegrator:

Public Member Functions
	CurlCurlIntegrator ()

	CurlCurlIntegrator (Coefficient &q, const IntegrationRule *ir=NULL)
	Construct a bilinear form integrator for Nedelec elements.

	CurlCurlIntegrator (DiagonalMatrixCoefficient &dq, const IntegrationRule *ir=NULL)

	CurlCurlIntegrator (MatrixCoefficient &mq, const IntegrationRule *ir=NULL)

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

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

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

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

virtual void	AssemblePA (const FiniteElementSpace &fes)
	Method defining partial assembly.

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

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

const Coefficient *	GetCoefficient () const

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

Public Member Functions inherited from mfem::BilinearFormIntegrator
virtual void	AssembleNURBSPA (const FiniteElementSpace &fes)
	Method defining partial assembly on NURBS patches.

virtual void	AssemblePABoundary (const FiniteElementSpace &fes)

virtual void	AssemblePAInteriorFaces (const FiniteElementSpace &fes)

virtual void	AssemblePABoundaryFaces (const FiniteElementSpace &fes)

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

virtual void	AddMultNURBSPA (const Vector &x, Vector &y) const
	Method for partially assembled action on NURBS patches.

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

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

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

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.

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	AssemblePatchMatrix (const int patch, const FiniteElementSpace &fes, SparseMatrix *&smat)

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	AssembleTraceFaceMatrix (int elem, const FiniteElement &trial_face_fe, const FiniteElement &test_fe, 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.

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.

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

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.

virtual bool	RequiresFaceNormalDerivatives () const
	For bilinear forms on element faces, specifies if the normal derivatives are needed on the faces or just the face restriction.

virtual void	AddMultPAFaceNormalDerivatives (const Vector &x, const Vector &dxdn, Vector &y, Vector &dydn) const
	Method for partially assembled action.

virtual	~BilinearFormIntegrator ()

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

void	SetIntegrationMode (Mode m)

void	SetNURBSPatchIntRule (NURBSMeshRules *pr)
	For patchwise integration, SetNURBSPatchIntRule must be called.

bool	HasNURBSPatchIntRule () const

bool	Patchwise () const

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

void	SetPAMemoryType (MemoryType mt)

const IntegrationRule *	GetIntegrationRule () const
	Get the integration rule of the integrator (possibly NULL).

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

virtual void	AssembleGradPA (const Vector &x, const FiniteElementSpace &fes)
	Prepare the integrator for partial assembly (PA) gradient evaluations on the given FE space fes at the state x.

virtual real_t	GetLocalStateEnergyPA (const Vector &x) const
	Compute the local (to the MPI rank) energy with partial assembly.

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

virtual void	AssembleGradDiagonalPA (Vector &diag) const
	Method for computing the diagonal of the gradient with partial assembly.

virtual bool	SupportsCeed () const
	Indicates whether this integrator can use a Ceed backend.

ceed::Operator &	GetCeedOp ()

virtual	~NonlinearFormIntegrator ()

Protected Attributes
Coefficient *	Q

DiagonalMatrixCoefficient *	DQ

MatrixCoefficient *	MQ

Vector	pa_data

const DofToQuad *	mapsO
	Not owned. DOF-to-quad map, open.

const DofToQuad *	mapsC
	Not owned. DOF-to-quad map, closed.

const GeometricFactors *	geom
	Not owned.

int	dim

int	ne

int	nq

int	dofs1D

int	quad1D

bool	symmetric = true
	False if using a nonsymmetric matrix coefficient.

Protected Attributes inherited from mfem::NonlinearFormIntegrator
const IntegrationRule *	IntRule

Mode	integrationMode = Mode::ELEMENTWISE

NURBSMeshRules *	patchRules = nullptr

ceed::Operator *	ceedOp

MemoryType	pa_mt = MemoryType::DEFAULT

Additional Inherited Members
Public Types inherited from mfem::NonlinearFormIntegrator
enum	Mode { ELEMENTWISE = 0 , PATCHWISE = 1 , PATCHWISE_REDUCED = 2 }

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

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

Detailed Description

Integrator for \((\mathrm{curl}(u), \mathrm{curl}(v))\) for Nedelec elements.

Definition at line 2639 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ CurlCurlIntegrator() [1/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( )

inline

Definition at line 2664 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [2/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator	(	Coefficient &	q,
		const IntegrationRule *	ir = NULL )

inline

Construct a bilinear form integrator for Nedelec elements.

Definition at line 2666 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [3/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator	(	DiagonalMatrixCoefficient &	dq,
		const IntegrationRule *	ir = NULL )

inline

Definition at line 2668 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [4/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator	(	MatrixCoefficient &	mq,
		const IntegrationRule *	ir = NULL )

inline

Definition at line 2671 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

virtual void mfem::CurlCurlIntegrator::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::BilinearFormIntegrator.

◆ AssembleDiagonalPA()

virtual void mfem::CurlCurlIntegrator::AssembleDiagonalPA ( Vector & diag )

virtual

Assemble diagonal and add it to Vector diag.

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssembleElementMatrix()

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

virtual

Given a particular Finite Element computes the element matrix elmat.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 1996 of file bilininteg.cpp.

◆ AssembleElementMatrix2()

void mfem::CurlCurlIntegrator::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 from mfem::BilinearFormIntegrator.

Definition at line 2067 of file bilininteg.cpp.

◆ AssemblePA() [1/2]

virtual void mfem::CurlCurlIntegrator::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::BilinearFormIntegrator.

◆ AssemblePA() [2/2]

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

virtual

Used with BilinearFormIntegrators that have different spaces.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 50 of file bilininteg.cpp.

◆ ComputeElementFlux()

void mfem::CurlCurlIntegrator::ComputeElementFlux	(	const FiniteElement &	el,
		ElementTransformation &	Trans,
		Vector &	u,
		const FiniteElement &	fluxelem,
		Vector &	flux,
		bool	with_coef,
		const IntegrationRule *	ir = NULL )

virtual

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.
[in]	ir	If passed (the default value is NULL), the implementation of the method will ignore the integration rule provided by the fluxelem parameter and, instead, compute the discrete flux at the points specified by the integration rule ir.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 2144 of file bilininteg.cpp.

◆ ComputeFluxEnergy()

real_t mfem::CurlCurlIntegrator::ComputeFluxEnergy	(	const FiniteElement &	fluxelem,
		ElementTransformation &	Trans,
		Vector &	flux,
		Vector *	d_energy = NULL )

virtual

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 from mfem::BilinearFormIntegrator.

Definition at line 2163 of file bilininteg.cpp.

◆ GetCoefficient()

const Coefficient * mfem::CurlCurlIntegrator::GetCoefficient ( ) const

inline

Definition at line 2700 of file bilininteg.hpp.

Member Data Documentation

◆ dim

int mfem::CurlCurlIntegrator::dim

protected

Definition at line 2660 of file bilininteg.hpp.

◆ dofs1D

int mfem::CurlCurlIntegrator::dofs1D

protected

Definition at line 2660 of file bilininteg.hpp.

◆ DQ

DiagonalMatrixCoefficient* mfem::CurlCurlIntegrator::DQ

protected

Definition at line 2652 of file bilininteg.hpp.

◆ geom

const GeometricFactors* mfem::CurlCurlIntegrator::geom

protected

Not owned.

Definition at line 2659 of file bilininteg.hpp.

◆ mapsC

const DofToQuad* mfem::CurlCurlIntegrator::mapsC

protected

Not owned. DOF-to-quad map, closed.

Definition at line 2658 of file bilininteg.hpp.

◆ mapsO

const DofToQuad* mfem::CurlCurlIntegrator::mapsO

protected

Not owned. DOF-to-quad map, open.

Definition at line 2657 of file bilininteg.hpp.

◆ MQ

MatrixCoefficient* mfem::CurlCurlIntegrator::MQ

protected

Definition at line 2653 of file bilininteg.hpp.

◆ ne

int mfem::CurlCurlIntegrator::ne

protected

Definition at line 2660 of file bilininteg.hpp.

◆ nq

int mfem::CurlCurlIntegrator::nq

protected

Definition at line 2660 of file bilininteg.hpp.

◆ pa_data

Vector mfem::CurlCurlIntegrator::pa_data

protected

Definition at line 2656 of file bilininteg.hpp.

◆ Q

Coefficient* mfem::CurlCurlIntegrator::Q

protected

Definition at line 2651 of file bilininteg.hpp.

◆ quad1D

int mfem::CurlCurlIntegrator::quad1D

protected

Definition at line 2660 of file bilininteg.hpp.

◆ symmetric

bool mfem::CurlCurlIntegrator::symmetric = true

protected

False if using a nonsymmetric matrix coefficient.

Definition at line 2661 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 Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CurlCurlIntegrator() [1/4]

◆ CurlCurlIntegrator() [2/4]

◆ CurlCurlIntegrator() [3/4]

◆ CurlCurlIntegrator() [4/4]

Member Function Documentation

◆ AddMultPA()

◆ AssembleDiagonalPA()

◆ AssembleElementMatrix()

◆ AssembleElementMatrix2()

◆ AssemblePA() [1/2]

◆ AssemblePA() [2/2]

◆ ComputeElementFlux()

◆ ComputeFluxEnergy()

◆ GetCoefficient()

Member Data Documentation

◆ dim

◆ dofs1D

◆ DQ

◆ geom

◆ mapsC

◆ mapsO

◆ MQ

◆ ne

◆ nq

◆ pa_data

◆ Q

◆ quad1D

◆ symmetric