#include <bilininteg.hpp>

Inheritance diagram for mfem::ElasticityIntegrator:

Collaboration diagram for mfem::ElasticityIntegrator:

Public Member Functions
	ElasticityIntegrator (Coefficient &l, Coefficient &m)

	ElasticityIntegrator (Coefficient &m, real_t q_l, real_t q_m)

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

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

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

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

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

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

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

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	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	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	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
real_t	q_lambda

real_t	q_mu

Coefficient *	lambda

Coefficient *	mu

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

Mode	integrationMode = Mode::ELEMENTWISE

NURBSMeshRules *	patchRules = nullptr

ceed::Operator *	ceedOp

MemoryType	pa_mt = MemoryType::DEFAULT

Friends
class	ElasticityComponentIntegrator

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 linear elasticity form:

\[ a(u,v) = (\lambda \mathrm{div}(u), \mathrm{div}(v)) + (2 \mu \varepsilon(u), \varepsilon(v)), \]

where \(\varepsilon(v) = \frac{1}{2} (\mathrm{grad}(v) + \mathrm{grad}(v)^{\mathrm{T}})\). This is a 'Vector' integrator, i.e. defined for FE spaces using multiple copies of a scalar FE space.

Definition at line 3016 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ ElasticityIntegrator() [1/2]

mfem::ElasticityIntegrator::ElasticityIntegrator	(	Coefficient &	l,
		Coefficient &	m )

inline

Definition at line 3048 of file bilininteg.hpp.

◆ ElasticityIntegrator() [2/2]

mfem::ElasticityIntegrator::ElasticityIntegrator	(	Coefficient &	m,
		real_t	q_l,
		real_t	q_m )

inline

With this constructor \(\lambda = q_l m\) and \(\mu = q_m m\) if \(dim q_l + 2 q_m = 0\) then \(tr(\sigma) = 0\).

Definition at line 3052 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

virtual void mfem::ElasticityIntegrator::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::ElasticityIntegrator::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.

◆ AssembleDiagonalPA()

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

virtual

Assemble diagonal and add it to Vector diag.

Reimplemented from mfem::BilinearFormIntegrator.

◆ AssembleElementMatrix()

void mfem::ElasticityIntegrator::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 3033 of file bilininteg.cpp.

◆ AssemblePA() [1/2]

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

virtual

Compute the stress corresponding to the local displacement \(u\) and interpolate it at the nodes of the given fluxelem. Only the symmetric part of the stress is stored, so that the size of flux is equal to the number of DOFs in fluxelem times dim*(dim+1)/2. In 2D, the order of the stress components is: \(s_xx, s_yy, s_xy\). In 3D, it is: \(s_xx, s_yy, s_zz, s_xy, s_xz, s_yz\). In other words, flux is the local vector for a FE space with dim*(dim+1)/2 vector components, based on the finite element fluxelem. The integration rule is taken from fluxelem. ir exists to specific an alternative integration rule.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3115 of file bilininteg.cpp.

◆ ComputeFluxEnergy()

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

virtual

Compute the element energy (integral of the strain energy density) corresponding to the stress represented by flux which is a vector of coefficients multiplying the basis functions defined by fluxelem. In other words, flux is the local vector for a FE space with dim*(dim+1)/2 vector components, based on the finite element fluxelem. The number of components, dim*(dim+1)/2 is such that it represents the symmetric part of the (symmetric) stress tensor. The order of the components is: \(s_xx, s_yy, s_xy\) in 2D, and \(s_xx, s_yy, s_zz, s_xy, s_xz, s_yz\) in 3D.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3194 of file bilininteg.cpp.

Friends And Related Symbol Documentation

◆ ElasticityComponentIntegrator

friend class ElasticityComponentIntegrator

friend

Definition at line 3018 of file bilininteg.hpp.

Member Data Documentation

◆ lambda

Coefficient* mfem::ElasticityIntegrator::lambda

protected

Definition at line 3022 of file bilininteg.hpp.

◆ mu

Coefficient * mfem::ElasticityIntegrator::mu

protected

Definition at line 3022 of file bilininteg.hpp.

◆ q_lambda

real_t mfem::ElasticityIntegrator::q_lambda

protected

Definition at line 3021 of file bilininteg.hpp.

◆ q_mu

real_t mfem::ElasticityIntegrator::q_mu

protected

Definition at line 3021 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

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ElasticityIntegrator() [1/2]

◆ ElasticityIntegrator() [2/2]

Member Function Documentation

◆ AddMultPA()

◆ AddMultTransposePA()

◆ AssembleDiagonalPA()

◆ AssembleElementMatrix()

◆ AssemblePA() [1/2]

◆ AssemblePA() [2/2]

◆ ComputeElementFlux()

◆ ComputeFluxEnergy()

Friends And Related Symbol Documentation

◆ ElasticityComponentIntegrator

Member Data Documentation

◆ lambda

◆ mu

◆ q_lambda

◆ q_mu