#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)

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

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

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

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

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

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

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

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	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	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_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.

Protected Attributes
real_t	q_lambda

real_t	q_mu

Coefficient *	lambda

Coefficient *	mu

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

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)

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 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 3148 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ ElasticityIntegrator() [1/2]

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

inline

Definition at line 3180 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 3184 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

void mfem::ElasticityIntegrator::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 67 of file bilininteg_elasticity_pa.cpp.

◆ AddMultTransposePA()

void mfem::ElasticityIntegrator::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 73 of file bilininteg_elasticity_pa.cpp.

◆ AssembleDiagonalPA()

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

overridevirtual

Assemble diagonal and add it to Vector diag.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 60 of file bilininteg_elasticity_pa.cpp.

◆ AssembleElementMatrix()

void mfem::ElasticityIntegrator::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 3180 of file bilininteg.cpp.

◆ AssemblePA() [1/2]

void mfem::ElasticityIntegrator::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 40 of file bilininteg_elasticity_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 52 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 )

overridevirtual

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 3262 of file bilininteg.cpp.

◆ ComputeFluxEnergy()

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

overridevirtual

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 3341 of file bilininteg.cpp.

Friends And Related Symbol Documentation

◆ ElasticityComponentIntegrator

friend class ElasticityComponentIntegrator

friend

Definition at line 3150 of file bilininteg.hpp.

Member Data Documentation

◆ lambda

Coefficient* mfem::ElasticityIntegrator::lambda

protected

Definition at line 3154 of file bilininteg.hpp.

◆ mu

Coefficient * mfem::ElasticityIntegrator::mu

protected

Definition at line 3154 of file bilininteg.hpp.

◆ q_lambda

real_t mfem::ElasticityIntegrator::q_lambda

protected

Definition at line 3153 of file bilininteg.hpp.

◆ q_mu

real_t mfem::ElasticityIntegrator::q_mu

protected

Definition at line 3153 of file bilininteg.hpp.

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

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