#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)

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

void	AssembleFaceMatrix (const FiniteElement &trial_fe1, const FiniteElement &test_fe1, const FiniteElement &trial_fe2, const FiniteElement &test_fe2, FaceElementTransformations &Trans, DenseMatrix &elmat) override

void	AssemblePAInteriorFaces (const FiniteElementSpace &fes) override

void	AssemblePABoundaryFaces (const FiniteElementSpace &fes) override

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

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

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

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

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

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.

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

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

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.

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	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)

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

static const IntegrationRule &	GetRule (Geometry::Type geom, int order, const ElementTransformation &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
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
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)

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 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 3289 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 3307 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 3311 of file bilininteg.hpp.

◆ DGTraceIntegrator() [3/3]

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

inline

Definition at line 3314 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

void mfem::DGTraceIntegrator::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 1077 of file bilininteg_dgtrace_pa.cpp.

◆ AddMultTransposePA()

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

overridevirtual

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.

Definition at line 1084 of file bilininteg_dgtrace_pa.cpp.

◆ AssembleEABoundaryFaces()

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

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 427 of file bilininteg_dgtrace_ea.cpp.

◆ AssembleEAInteriorFaces() [1/2]

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

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 348 of file bilininteg_dgtrace_ea.cpp.

◆ AssembleEAInteriorFaces() [2/2]

void mfem::BilinearFormIntegrator::AssembleEAInteriorFaces	(	const FiniteElementSpace &	trial_fes,
		const FiniteElementSpace &	test_fes,
		Vector &	emat,
		const bool	add = true )

virtual

Method defining element assembly for mixed trace integrators.

This is the element assembly analogue of AssembleFaceMatrix(const FiniteElement&, const FiniteElement&, const FiniteElement&, FaceElementTransformations&, DenseMatrix&).

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 141 of file bilininteg.cpp.

◆ AssembleFaceMatrix() [1/3]

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

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3434 of file bilininteg.cpp.

◆ AssembleFaceMatrix() [2/3]

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 185 of file bilininteg.cpp.

◆ AssembleFaceMatrix() [3/3]

void mfem::DGTraceIntegrator::AssembleFaceMatrix	(	const FiniteElement &	trial_fe1,
		const FiniteElement &	test_fe1,
		const FiniteElement &	trial_fe2,
		const FiniteElement &	test_fe2,
		FaceElementTransformations &	Trans,
		DenseMatrix &	elmat )

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3567 of file bilininteg.cpp.

◆ AssemblePABoundaryFaces()

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

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 240 of file bilininteg_dgtrace_pa.cpp.

◆ AssemblePAInteriorFaces()

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

overridevirtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 235 of file bilininteg_dgtrace_pa.cpp.

◆ GetRule() [1/2]

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

static

Definition at line 3712 of file bilininteg.cpp.

◆ GetRule() [2/2]

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

static

Definition at line 3718 of file bilininteg.cpp.

Member Data Documentation

◆ alpha

real_t mfem::DGTraceIntegrator::alpha

protected

Definition at line 3294 of file bilininteg.hpp.

◆ beta

real_t mfem::DGTraceIntegrator::beta

protected

Definition at line 3294 of file bilininteg.hpp.

◆ dim

int mfem::DGTraceIntegrator::dim

protected

Definition at line 3299 of file bilininteg.hpp.

◆ dofs1D

int mfem::DGTraceIntegrator::dofs1D

protected

Definition at line 3299 of file bilininteg.hpp.

◆ geom

const FaceGeometricFactors* mfem::DGTraceIntegrator::geom

protected

Not owned.

Definition at line 3298 of file bilininteg.hpp.

◆ maps

const DofToQuad* mfem::DGTraceIntegrator::maps

protected

Not owned.

Definition at line 3297 of file bilininteg.hpp.

◆ nf

int mfem::DGTraceIntegrator::nf

protected

Definition at line 3299 of file bilininteg.hpp.

◆ nq

int mfem::DGTraceIntegrator::nq

protected

Definition at line 3299 of file bilininteg.hpp.

◆ pa_data

Vector mfem::DGTraceIntegrator::pa_data

protected

Definition at line 3296 of file bilininteg.hpp.

◆ quad1D

int mfem::DGTraceIntegrator::quad1D

protected

Definition at line 3299 of file bilininteg.hpp.

◆ rho

Coefficient* mfem::DGTraceIntegrator::rho

protected

Definition at line 3292 of file bilininteg.hpp.

◆ u

VectorCoefficient* mfem::DGTraceIntegrator::u

protected

Definition at line 3293 of file bilininteg.hpp.

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

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() [1/2]

◆ AssembleEAInteriorFaces() [2/2]

◆ AssembleFaceMatrix() [1/3]

◆ AssembleFaceMatrix() [2/3]

◆ AssembleFaceMatrix() [3/3]

◆ AssemblePABoundaryFaces()

◆ AssemblePAInteriorFaces()

◆ GetRule() [1/2]

◆ GetRule() [2/2]

Member Data Documentation

◆ alpha

◆ beta

◆ dim

◆ dofs1D

◆ geom

◆ maps

◆ nf

◆ nq

◆ pa_data

◆ quad1D

◆ rho

◆ u