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:

Classes
struct	Kernels

Public Types
using	ApplyKernelType

using	DiagonalKernelType
	arguments: d1d, q1d, symmetric, ne, Bo, Bc, Go, Gc, pa_data, diag

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

Public Member Functions
	CurlCurlIntegrator ()

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

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

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

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

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

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

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

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

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

void	AddAbsMultPA (const Vector &x, Vector &y) const override

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

const Coefficient *	GetCoefficient () const

	MFEM_REGISTER_KERNELS (ApplyPAKernels, ApplyKernelType,(int, int, int))
	parameters: dim, d1d, q1d

	MFEM_REGISTER_KERNELS (DiagonalPAKernels, DiagonalKernelType,(int, int, int))
	parameters: dim, d1d, q1d

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

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	AddAbsMultTransposePA (const Vector &x, Vector &y) const

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

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

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

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

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

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

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

virtual void	AssembleEAInteriorFaces (const FiniteElementSpace &trial_fes, const FiniteElementSpace &test_fes, Vector &emat, const bool add=true)
	Method defining element assembly for mixed trace integrators.

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_fe1, const FiniteElement &test_fe1, const FiniteElement &trial_fe2, const FiniteElement &test_fe2, 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)

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

void	AssembleFaceVector (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, Vector &elvect) override
	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.

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

void	AssembleFaceGrad (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, DenseMatrix &elmat) override
	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
void	SetIntegrationMode (Mode m)

bool	Patchwise () const

void	SetPAMemoryType (MemoryType mt)

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 ()

Public Member Functions inherited from mfem::Integrator
	Integrator (const IntegrationRule *ir=NULL)
	Create a new Integrator, optionally providing a prescribed quadrature rule to use in assembly.

virtual void	SetIntRule (const IntegrationRule *ir)
	Prescribe a fixed IntegrationRule to use, or set to null to let the integrator choose an appropriate rule.

void	SetIntegrationRule (const IntegrationRule &ir)
	Prescribe a fixed IntegrationRule to use. Sets the NURBS patch integration rule to null.

void	SetNURBSPatchIntRule (NURBSMeshRules *pr)
	Sets an integration rule for use on NURBS patches.

bool	HasNURBSPatchIntRule () const
	Check if a NURBS patch integration rule has been set.

const IntegrationRule *	GetIntRule () const
	Directly return the IntRule pointer (possibly null) without checking for NURBS patch rules or falling back on a default.

const IntegrationRule *	GetIntegrationRule () const
	Equivalent to GetIntRule, but retained for backward compatibility with applications.

Static Public Member Functions
template<int DIM, int D1D, int Q1D>
static void	AddSpecialization ()

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
Mode	integrationMode = Mode::ELEMENTWISE

ceed::Operator *	ceedOp

MemoryType	pa_mt = MemoryType::DEFAULT

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

NURBSMeshRules *	patchRules = nullptr

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

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

Protected Member Functions inherited from mfem::Integrator
const IntegrationRule *	GetIntegrationRule (const FiniteElement &trial_fe, const FiniteElement &test_fe, const ElementTransformation &trans) const
	Returns an integration rule based on the arguments and internal state of the Integrator object.

const IntegrationRule *	GetIntegrationRule (const FiniteElement &el, const ElementTransformation &trans) const
	Returns an integration rule based on the arguments and internal state. (Version for identical trial_fe and test_fe)

virtual const IntegrationRule *	GetDefaultIntegrationRule (const FiniteElement &trial_fe, const FiniteElement &test_fe, const ElementTransformation &trans) const
	Subclasses should override to choose a default integration rule.

Detailed Description

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

Definition at line 2808 of file bilininteg.hpp.

Member Typedef Documentation

◆ ApplyKernelType

using mfem::CurlCurlIntegrator::ApplyKernelType

Initial value:

 void (*)(
                              const int, const int, const bool, const int, const Array<real_t> &,
                              const Array<real_t> &, const Array<real_t> &, const Array<real_t> &,
                              const Array<real_t> &, const Array<real_t> &, const Vector &,
                              const Vector &, Vector &, const bool)

arguments: d1d, q1d, symmetric, NE, bo, bc, bot, bct, gc, gct, pa_data, x, y, useAbs

Definition at line 2872 of file bilininteg.hpp.

◆ DiagonalKernelType

using mfem::CurlCurlIntegrator::DiagonalKernelType

Initial value:

 void (*)(const int, const int, const bool,
                                       const int, const Array<real_t> &,
                                       const Array<real_t> &,
                                       const Array<real_t> &,
                                       const Array<real_t> &, const Vector &,
                                       Vector &)

arguments: d1d, q1d, symmetric, ne, Bo, Bc, Go, Gc, pa_data, diag

Definition at line 2879 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ CurlCurlIntegrator() [1/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( )

Definition at line 18 of file bilininteg_curlcurl_pa.cpp.

◆ CurlCurlIntegrator() [2/4]

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

Construct a bilinear form integrator for Nedelec elements.

Definition at line 23 of file bilininteg_curlcurl_pa.cpp.

◆ CurlCurlIntegrator() [3/4]

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

Definition at line 30 of file bilininteg_curlcurl_pa.cpp.

◆ CurlCurlIntegrator() [4/4]

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

Definition at line 37 of file bilininteg_curlcurl_pa.cpp.

Member Function Documentation

◆ AddAbsMultPA()

void mfem::CurlCurlIntegrator::AddAbsMultPA	(	const Vector &	x,
		Vector &	y ) const

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 172 of file bilininteg_curlcurl_pa.cpp.

◆ AddMultPA()

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

overridevirtual

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.

Definition at line 165 of file bilininteg_curlcurl_pa.cpp.

◆ AddSpecialization()

template<int DIM, int D1D, int Q1D>

static void mfem::CurlCurlIntegrator::AddSpecialization ( )

inlinestatic

Definition at line 2892 of file bilininteg.hpp.

◆ AssembleDiagonalPA()

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

overridevirtual

Assemble diagonal and add it to Vector diag.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 158 of file bilininteg_curlcurl_pa.cpp.

◆ AssembleElementMatrix()

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

overridevirtual

Given a particular Finite Element computes the element matrix elmat.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 2164 of file bilininteg.cpp.

◆ AssembleElementMatrix2()

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

overridevirtual

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 2235 of file bilininteg.cpp.

◆ AssemblePA() [1/2]

DO_NOT_DOCUMENT void mfem::CurlCurlIntegrator::AssemblePA ( const FiniteElementSpace & fes )

overridevirtual

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.

Definition at line 98 of file bilininteg_curlcurl_pa.cpp.

◆ AssemblePA() [2/2]

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

overridevirtual

Used with BilinearFormIntegrators that have different spaces.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 54 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 )

overridevirtual

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 2313 of file bilininteg.cpp.

◆ ComputeFluxEnergy()

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

overridevirtual

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 2332 of file bilininteg.cpp.

◆ GetCoefficient()

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

inline

Definition at line 2868 of file bilininteg.hpp.

◆ MFEM_REGISTER_KERNELS() [1/2]

mfem::CurlCurlIntegrator::MFEM_REGISTER_KERNELS	(	ApplyPAKernels	,
		ApplyKernelType	,
		(int, int, int)	)

parameters: dim, d1d, q1d

◆ MFEM_REGISTER_KERNELS() [2/2]

mfem::CurlCurlIntegrator::MFEM_REGISTER_KERNELS	(	DiagonalPAKernels	,
		DiagonalKernelType	,
		(int, int, int)	)

parameters: dim, d1d, q1d

Member Data Documentation

◆ dim

int mfem::CurlCurlIntegrator::dim

protected

Definition at line 2829 of file bilininteg.hpp.

◆ dofs1D

int mfem::CurlCurlIntegrator::dofs1D

protected

Definition at line 2829 of file bilininteg.hpp.

◆ DQ

DiagonalMatrixCoefficient* mfem::CurlCurlIntegrator::DQ

protected

Definition at line 2821 of file bilininteg.hpp.

◆ geom

const GeometricFactors* mfem::CurlCurlIntegrator::geom

protected

Not owned.

Definition at line 2828 of file bilininteg.hpp.

◆ mapsC

const DofToQuad* mfem::CurlCurlIntegrator::mapsC

protected

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

Definition at line 2827 of file bilininteg.hpp.

◆ mapsO

const DofToQuad* mfem::CurlCurlIntegrator::mapsO

protected

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

Definition at line 2826 of file bilininteg.hpp.

◆ MQ

MatrixCoefficient* mfem::CurlCurlIntegrator::MQ

protected

Definition at line 2822 of file bilininteg.hpp.

◆ ne

int mfem::CurlCurlIntegrator::ne

protected

Definition at line 2829 of file bilininteg.hpp.

◆ nq

int mfem::CurlCurlIntegrator::nq

protected

Definition at line 2829 of file bilininteg.hpp.

◆ pa_data

Vector mfem::CurlCurlIntegrator::pa_data

protected

Definition at line 2825 of file bilininteg.hpp.

◆ Q

Coefficient* mfem::CurlCurlIntegrator::Q

protected

Definition at line 2820 of file bilininteg.hpp.

◆ quad1D

int mfem::CurlCurlIntegrator::quad1D

protected

Definition at line 2829 of file bilininteg.hpp.

◆ symmetric

bool mfem::CurlCurlIntegrator::symmetric = true

protected

False if using a nonsymmetric matrix coefficient.

Definition at line 2830 of file bilininteg.hpp.

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ApplyKernelType

◆ DiagonalKernelType

Constructor & Destructor Documentation

◆ CurlCurlIntegrator() [1/4]

◆ CurlCurlIntegrator() [2/4]

◆ CurlCurlIntegrator() [3/4]

◆ CurlCurlIntegrator() [4/4]

Member Function Documentation

◆ AddAbsMultPA()

◆ AddMultPA()

◆ AddSpecialization()

◆ AssembleDiagonalPA()

◆ AssembleElementMatrix()

◆ AssembleElementMatrix2()

◆ AssemblePA() [1/2]

◆ AssemblePA() [2/2]

◆ ComputeElementFlux()

◆ ComputeFluxEnergy()

◆ GetCoefficient()

◆ MFEM_REGISTER_KERNELS() [1/2]

◆ MFEM_REGISTER_KERNELS() [2/2]

Member Data Documentation

◆ dim

◆ dofs1D

◆ DQ

◆ geom

◆ mapsC

◆ mapsO

◆ MQ

◆ ne

◆ nq

◆ pa_data

◆ Q

◆ quad1D

◆ symmetric