#include <bilininteg.hpp>

Inheritance diagram for mfem::DGTraceIntegrator:

Collaboration diagram for mfem::DGTraceIntegrator:

Public Member Functions
	DGTraceIntegrator (VectorCoefficient &u_, real_t a)
	Construct integrator with \(\rho = 1\), \(\beta = \alpha/2\).

	DGTraceIntegrator (VectorCoefficient &u_, real_t a, real_t b)
	Construct integrator with \(\rho = 1\).

	DGTraceIntegrator (Coefficient &rho_, VectorCoefficient &u_, real_t a, real_t b)

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

virtual void	AssemblePAInteriorFaces (const FiniteElementSpace &fes)

virtual void	AssemblePABoundaryFaces (const FiniteElementSpace &fes)

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

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

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

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

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

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	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 ()

Static Public Member Functions
static const IntegrationRule &	GetRule (Geometry::Type geom, int order, FaceElementTransformations &T)

Protected Attributes
Coefficient *	rho

VectorCoefficient *	u

real_t	alpha

real_t	beta

Vector	pa_data

const DofToQuad *	maps
	Not owned.

const FaceGeometricFactors *	geom
	Not owned.

int	dim

int	nf

int	nq

int	dofs1D

int	quad1D

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 the DG form:

\[ \alpha \langle \rho_u (u \cdot n) \{v\},[w] \rangle + \beta \langle \rho_u |u \cdot n| [v],[w] \rangle, \]

where \(v\) and \(w\) are the trial and test variables, respectively, and \(\rho\)/ \(u\) are given scalar/vector coefficients. \(\{v\}\) represents the average value of \(v\) on the face and \([v]\) is the jump such that \(\{v\}=(v_1+v_2)/2\) and \([v]=(v_1-v_2)\) for the face between elements \(1\) and \(2\). For boundary elements, \(v2=0\). The vector coefficient, \(u\), is assumed to be continuous across the faces and when given the scalar coefficient, \(\rho\), is assumed to be discontinuous. The integrator uses the upwind value of \(\rho\), denoted by \(\rho_u\), which is value from the side into which the vector coefficient, \(u\), points.

One use case for this integrator is to discretize the operator \(-u \cdot \nabla v\) with a DG formulation. The resulting formulation uses the ConvectionIntegrator (with coefficient \(u\), and parameter \(\alpha = -1\)) and the transpose of the DGTraceIntegrator (with coefficient \(u\), and parameters \(\alpha = 1\), \(\beta = -1/2\) to use the upwind face flux, see also NonconservativeDGTraceIntegrator). This discretization and the handling of the inflow and outflow boundaries is illustrated in Example 9/9p.

Another use case for this integrator is to discretize the operator \(-\mathrm{div}(u v)\) with a DG formulation. The resulting formulation is conservative and consists of the ConservativeConvectionIntegrator (with coefficient \(u\), and parameter \(\alpha = -1\)) plus the DGTraceIntegrator (with coefficient \(u\), and parameters \(\alpha = -1\), \(\beta = -1/2\) to use the upwind face flux).

Definition at line 3157 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ DGTraceIntegrator() [1/3]

mfem::DGTraceIntegrator::DGTraceIntegrator	(	VectorCoefficient &	u_,
		real_t	a )

inline

Construct integrator with \(\rho = 1\), \(\beta = \alpha/2\).

Definition at line 3174 of file bilininteg.hpp.

◆ DGTraceIntegrator() [2/3]

mfem::DGTraceIntegrator::DGTraceIntegrator	(	VectorCoefficient &	u_,
		real_t	a,
		real_t	b )

inline

Construct integrator with \(\rho = 1\).

Definition at line 3178 of file bilininteg.hpp.

◆ DGTraceIntegrator() [3/3]

mfem::DGTraceIntegrator::DGTraceIntegrator	(	Coefficient &	rho_,
		VectorCoefficient &	u_,
		real_t	a,
		real_t	b )

inline

Definition at line 3181 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

virtual void mfem::DGTraceIntegrator::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.

◆ AddMultTransposePA()

virtual void mfem::DGTraceIntegrator::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 from mfem::BilinearFormIntegrator.

◆ AssembleEABoundaryFaces()

virtual void mfem::DGTraceIntegrator::AssembleEABoundaryFaces	(	const FiniteElementSpace &	fes,
		Vector &	ea_data_bdr,
		const bool	add )

virtual

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssembleEAInteriorFaces()

virtual void mfem::DGTraceIntegrator::AssembleEAInteriorFaces	(	const FiniteElementSpace &	fes,
		Vector &	ea_data_int,
		Vector &	ea_data_ext,
		const bool	add )

virtual

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssembleFaceMatrix() [1/2]

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

virtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3287 of file bilininteg.cpp.

◆ 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.

◆ AssemblePABoundaryFaces()

virtual void mfem::DGTraceIntegrator::AssemblePABoundaryFaces ( const FiniteElementSpace & fes )

virtual

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssemblePAInteriorFaces()

virtual void mfem::DGTraceIntegrator::AssemblePAInteriorFaces ( const FiniteElementSpace & fes )

virtual

Reimplemented from mfem::BilinearFormIntegrator.

◆ GetRule()

const IntegrationRule & mfem::DGTraceIntegrator::GetRule	(	Geometry::Type	geom,
		int	order,
		FaceElementTransformations &	T )

static

Definition at line 3421 of file bilininteg.cpp.

Member Data Documentation

◆ alpha

real_t mfem::DGTraceIntegrator::alpha

protected

Definition at line 3162 of file bilininteg.hpp.

◆ beta

real_t mfem::DGTraceIntegrator::beta

protected

Definition at line 3162 of file bilininteg.hpp.

◆ dim

int mfem::DGTraceIntegrator::dim

protected

Definition at line 3167 of file bilininteg.hpp.

◆ dofs1D

int mfem::DGTraceIntegrator::dofs1D

protected

Definition at line 3167 of file bilininteg.hpp.

◆ geom

const FaceGeometricFactors* mfem::DGTraceIntegrator::geom

protected

Not owned.

Definition at line 3166 of file bilininteg.hpp.

◆ maps

const DofToQuad* mfem::DGTraceIntegrator::maps

protected

Not owned.

Definition at line 3165 of file bilininteg.hpp.

◆ nf

int mfem::DGTraceIntegrator::nf

protected

Definition at line 3167 of file bilininteg.hpp.

◆ nq

int mfem::DGTraceIntegrator::nq

protected

Definition at line 3167 of file bilininteg.hpp.

◆ pa_data

Vector mfem::DGTraceIntegrator::pa_data

protected

Definition at line 3164 of file bilininteg.hpp.

◆ quad1D

int mfem::DGTraceIntegrator::quad1D

protected

Definition at line 3167 of file bilininteg.hpp.

◆ rho

Coefficient* mfem::DGTraceIntegrator::rho

protected

Definition at line 3160 of file bilininteg.hpp.

◆ u

VectorCoefficient* mfem::DGTraceIntegrator::u

protected

Definition at line 3161 of file bilininteg.hpp.

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

fem/bilininteg.hpp
fem/bilininteg.cpp

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DGTraceIntegrator() [1/3]

◆ DGTraceIntegrator() [2/3]

◆ DGTraceIntegrator() [3/3]

Member Function Documentation

◆ AddMultPA()

◆ AddMultTransposePA()

◆ AssembleEABoundaryFaces()

◆ AssembleEAInteriorFaces()

◆ AssembleFaceMatrix() [1/2]

◆ AssembleFaceMatrix() [2/2]

◆ AssemblePABoundaryFaces()

◆ AssemblePAInteriorFaces()

◆ GetRule()

Member Data Documentation

◆ alpha

◆ beta

◆ dim

◆ dofs1D

◆ geom

◆ maps

◆ nf

◆ nq

◆ pa_data

◆ quad1D

◆ rho

◆ u