#include <bilininteg.hpp>

Inheritance diagram for mfem::DGDiffusionBR2Integrator:

Collaboration diagram for mfem::DGDiffusionBR2Integrator:

Public Member Functions
	DGDiffusionBR2Integrator (class FiniteElementSpace &fes, real_t e=1.0)

	DGDiffusionBR2Integrator (class FiniteElementSpace &fes, Coefficient &Q_, real_t e=1.0)

MFEM_DEPRECATED	DGDiffusionBR2Integrator (class FiniteElementSpace *fes, real_t e=1.0)

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)

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

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

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

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

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

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 void	ComputeElementFlux (const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, bool with_coef=true, 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 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 Member Functions
void	PrecomputeMassInverse (class FiniteElementSpace &fes)
	Precomputes the inverses (LU factorizations) of the local mass matrices.

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 Attributes
real_t	eta

Array< real_t >	Minv

Array< int >	ipiv

Array< int >	ipiv_offsets

Array< int >	Minv_offsets

Coefficient *	Q

Vector	shape1

Vector	shape2

DenseMatrix	R11

DenseMatrix	R12

DenseMatrix	R21

DenseMatrix	R22

DenseMatrix	MinvR11

DenseMatrix	MinvR12

DenseMatrix	MinvR21

DenseMatrix	MinvR22

DenseMatrix	Re

DenseMatrix	MinvRe

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 }

Detailed Description

Integrator for the "BR2" diffusion stabilization term

\[ \sum_e \eta (r_e([u]), r_e([v])) \]

where \(r_e\) is the lifting operator defined on each edge \(e\) (potentially weighted by a coefficient \(Q\)). The parameter eta can be chosen to be one to obtain a stable discretization. The constructor for this integrator requires the finite element space because the lifting operator depends on the element-wise inverse mass matrix.

BR2 stands for the second method of Bassi and Rebay:

F. Bassi and S. Rebay. A high order discontinuous Galerkin method for compressible turbulent flows. In B. Cockburn, G. E. Karniadakis, and C.-W. Shu, editors, Discontinuous Galerkin Methods, pages 77-88. Springer Berlin Heidelberg, 2000.
D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis, 39(5):1749-1779, 2002.

Definition at line 3322 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ DGDiffusionBR2Integrator() [1/3]

mfem::DGDiffusionBR2Integrator::DGDiffusionBR2Integrator	(	class FiniteElementSpace &	fes,
		real_t	e = 1.0 )

◆ DGDiffusionBR2Integrator() [2/3]

mfem::DGDiffusionBR2Integrator::DGDiffusionBR2Integrator	(	class FiniteElementSpace &	fes,
		Coefficient &	Q_,
		real_t	e = 1.0 )

◆ DGDiffusionBR2Integrator() [3/3]

MFEM_DEPRECATED mfem::DGDiffusionBR2Integrator::DGDiffusionBR2Integrator	(	class FiniteElementSpace *	fes,
		real_t	e = 1.0 )

Member Function Documentation

◆ AssembleFaceMatrix() [1/2]

virtual void mfem::DGDiffusionBR2Integrator::AssembleFaceMatrix	(	const FiniteElement &	el1,
		const FiniteElement &	el2,
		FaceElementTransformations &	Trans,
		DenseMatrix &	elmat )

virtual

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssembleFaceMatrix() [2/2]

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 from mfem::BilinearFormIntegrator.

Definition at line 162 of file bilininteg.cpp.

◆ PrecomputeMassInverse()

void mfem::DGDiffusionBR2Integrator::PrecomputeMassInverse ( class FiniteElementSpace & fes )

protected

Precomputes the inverses (LU factorizations) of the local mass matrices.

fes must be a DG space, so the mass matrix is block diagonal, and its inverse can be computed locally. This is required for the computation of the lifting operators r_e.

Member Data Documentation

◆ eta

real_t mfem::DGDiffusionBR2Integrator::eta

protected

Definition at line 3325 of file bilininteg.hpp.

◆ ipiv

Array<int> mfem::DGDiffusionBR2Integrator::ipiv

protected

Definition at line 3330 of file bilininteg.hpp.

◆ ipiv_offsets

Array<int> mfem::DGDiffusionBR2Integrator::ipiv_offsets

protected

Definition at line 3331 of file bilininteg.hpp.

◆ Minv

Array<real_t> mfem::DGDiffusionBR2Integrator::Minv

protected

Definition at line 3329 of file bilininteg.hpp.

◆ Minv_offsets

Array<int> mfem::DGDiffusionBR2Integrator::Minv_offsets

protected

Definition at line 3331 of file bilininteg.hpp.

◆ MinvR11

DenseMatrix mfem::DGDiffusionBR2Integrator::MinvR11

protected

Definition at line 3338 of file bilininteg.hpp.

◆ MinvR12

DenseMatrix mfem::DGDiffusionBR2Integrator::MinvR12

protected

Definition at line 3338 of file bilininteg.hpp.

◆ MinvR21

DenseMatrix mfem::DGDiffusionBR2Integrator::MinvR21

protected

Definition at line 3338 of file bilininteg.hpp.

◆ MinvR22

DenseMatrix mfem::DGDiffusionBR2Integrator::MinvR22

protected

Definition at line 3338 of file bilininteg.hpp.

◆ MinvRe

DenseMatrix mfem::DGDiffusionBR2Integrator::MinvRe

protected

Definition at line 3339 of file bilininteg.hpp.

◆ Q

Coefficient* mfem::DGDiffusionBR2Integrator::Q

protected

Definition at line 3333 of file bilininteg.hpp.

◆ R11

DenseMatrix mfem::DGDiffusionBR2Integrator::R11

protected

Definition at line 3337 of file bilininteg.hpp.

◆ R12

DenseMatrix mfem::DGDiffusionBR2Integrator::R12

protected

Definition at line 3337 of file bilininteg.hpp.

◆ R21

DenseMatrix mfem::DGDiffusionBR2Integrator::R21

protected

Definition at line 3337 of file bilininteg.hpp.

◆ R22

DenseMatrix mfem::DGDiffusionBR2Integrator::R22

protected

Definition at line 3337 of file bilininteg.hpp.

◆ Re

DenseMatrix mfem::DGDiffusionBR2Integrator::Re

protected

Definition at line 3339 of file bilininteg.hpp.

◆ shape1

Vector mfem::DGDiffusionBR2Integrator::shape1

protected

Definition at line 3335 of file bilininteg.hpp.

◆ shape2

Vector mfem::DGDiffusionBR2Integrator::shape2

protected

Definition at line 3335 of file bilininteg.hpp.

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

fem/bilininteg.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DGDiffusionBR2Integrator() [1/3]

◆ DGDiffusionBR2Integrator() [2/3]

◆ DGDiffusionBR2Integrator() [3/3]

Member Function Documentation

◆ AssembleFaceMatrix() [1/2]

◆ AssembleFaceMatrix() [2/2]

◆ PrecomputeMassInverse()

Member Data Documentation

◆ eta

◆ ipiv

◆ ipiv_offsets

◆ Minv

◆ Minv_offsets

◆ MinvR11

◆ MinvR12

◆ MinvR21

◆ MinvR22

◆ MinvRe

◆ Q

◆ R11

◆ R12

◆ R21

◆ R22

◆ Re

◆ shape1

◆ shape2