MFEM v4.8.0
Finite element discretization library
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mfem::CurlCurlIntegrator Class Reference

Integrator for \((\mathrm{curl}(u), \mathrm{curl}(v))\) for Nedelec elements. More...

#include <bilininteg.hpp>

Inheritance diagram for mfem::CurlCurlIntegrator:
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Collaboration diagram for mfem::CurlCurlIntegrator:
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Public Member Functions

 CurlCurlIntegrator ()
 
 CurlCurlIntegrator (Coefficient &q, const IntegrationRule *ir=NULL)
 Construct a bilinear form integrator for Nedelec elements.
 
 CurlCurlIntegrator (DiagonalMatrixCoefficient &dq, const IntegrationRule *ir=NULL)
 
 CurlCurlIntegrator (MatrixCoefficient &mq, const IntegrationRule *ir=NULL)
 
void AssembleElementMatrix (const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat) override
 Given a particular Finite Element computes the element matrix elmat.
 
void AssembleElementMatrix2 (const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat) override
 
void ComputeElementFlux (const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, bool with_coef, const IntegrationRule *ir=NULL) override
 Virtual method required for Zienkiewicz-Zhu type error estimators.
 
real_t ComputeFluxEnergy (const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL) override
 Virtual method required for Zienkiewicz-Zhu type error estimators.
 
void AssemblePA (const FiniteElementSpace &fes) override
 Method defining partial assembly.
 
void AddMultPA (const Vector &x, Vector &y) const override
 Method for partially assembled action.
 
void AssembleDiagonalPA (Vector &diag) override
 Assemble diagonal and add it to Vector diag.
 
const CoefficientGetCoefficient () const
 
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 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.
 
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 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::OperatorGetCeedOp ()
 
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 IntegrationRuleGetIntRule () const
 Directly return the IntRule pointer (possibly null) without checking for NURBS patch rules or falling back on a default.
 
const IntegrationRuleGetIntegrationRule () const
 Equivalent to GetIntRule, but retained for backward compatibility with applications.
 

Protected Attributes

CoefficientQ
 
DiagonalMatrixCoefficientDQ
 
MatrixCoefficientMQ
 
Vector pa_data
 
const DofToQuadmapsO
 Not owned. DOF-to-quad map, open.
 
const DofToQuadmapsC
 Not owned. DOF-to-quad map, closed.
 
const GeometricFactorsgeom
 Not owned.
 
int dim
 
int ne
 
int nq
 
int dofs1D
 
int quad1D
 
bool symmetric = true
 False if using a nonsymmetric matrix coefficient.
 
- Protected Attributes inherited from mfem::NonlinearFormIntegrator
Mode integrationMode = Mode::ELEMENTWISE
 
ceed::OperatorceedOp
 
MemoryType pa_mt = MemoryType::DEFAULT
 
- Protected Attributes inherited from mfem::Integrator
const IntegrationRuleIntRule
 
NURBSMeshRulespatchRules = 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 IntegrationRuleGetIntegrationRule (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 IntegrationRuleGetIntegrationRule (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 IntegrationRuleGetDefaultIntegrationRule (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 \((\mathrm{curl}(u), \mathrm{curl}(v))\) for Nedelec elements.

Definition at line 2760 of file bilininteg.hpp.

Constructor & Destructor Documentation

◆ CurlCurlIntegrator() [1/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( )
inline

Definition at line 2785 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [2/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( Coefficient & q,
const IntegrationRule * ir = NULL )
inline

Construct a bilinear form integrator for Nedelec elements.

Definition at line 2787 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [3/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( DiagonalMatrixCoefficient & dq,
const IntegrationRule * ir = NULL )
inline

Definition at line 2789 of file bilininteg.hpp.

◆ CurlCurlIntegrator() [4/4]

mfem::CurlCurlIntegrator::CurlCurlIntegrator ( MatrixCoefficient & mq,
const IntegrationRule * ir = NULL )
inline

Definition at line 2792 of file bilininteg.hpp.

Member Function Documentation

◆ AddMultPA()

void mfem::CurlCurlIntegrator::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 147 of file bilininteg_curlcurl_pa.cpp.

◆ AssembleDiagonalPA()

void mfem::CurlCurlIntegrator::AssembleDiagonalPA ( Vector & diag)
overridevirtual

Assemble diagonal and add it to Vector diag.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 78 of file bilininteg_curlcurl_pa.cpp.

◆ AssembleElementMatrix()

void mfem::CurlCurlIntegrator::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 2135 of file bilininteg.cpp.

◆ AssembleElementMatrix2()

void mfem::CurlCurlIntegrator::AssembleElementMatrix2 ( const FiniteElement & trial_fe,
const FiniteElement & test_fe,
ElementTransformation & Trans,
DenseMatrix & elmat )
overridevirtual

Compute the local matrix representation of a bilinear form \(a(u,v)\) defined on different trial (given by \(u\)) and test (given by \(v\)) spaces. The rows in the local matrix correspond to the test dofs and the columns – to the trial dofs.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 2206 of file bilininteg.cpp.

◆ AssemblePA() [1/2]

void mfem::CurlCurlIntegrator::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 18 of file bilininteg_curlcurl_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::CurlCurlIntegrator::ComputeElementFlux ( const FiniteElement & el,
ElementTransformation & Trans,
Vector & u,
const FiniteElement & fluxelem,
Vector & flux,
bool with_coef,
const IntegrationRule * ir = NULL )
overridevirtual

Virtual method required for Zienkiewicz-Zhu type error estimators.

The purpose of the method is to compute a local "flux" finite element function given a local finite element solution. The "flux" function has to be computed in terms of its coefficients (represented by the Vector flux) which multiply the basis functions defined by the FiniteElement fluxelem. Typically, the "flux" function will have more than one component and consequently flux should be store the coefficients of all components: first all coefficient for component 0, then all coefficients for component 1, etc. What the "flux" function represents depends on the specific integrator. For example, in the case of DiffusionIntegrator, the flux is the gradient of the solution multiplied by the diffusion coefficient.

Parameters
[in]elFiniteElement of the solution.
[in]TransThe ElementTransformation describing the physical position of the mesh element.
[in]uSolution coefficients representing the expansion of the solution function in the basis of el.
[in]fluxelemFiniteElement of the "flux".
[out]flux"Flux" coefficients representing the expansion of the "flux" function in the basis of fluxelem. The size of flux as a Vector has to be set by this method, e.g. using Vector::SetSize().
[in]with_coefIf zero (the default value is 1) the implementation of the method may choose not to scale the "flux" function by any coefficients describing the integrator.
[in]irIf passed (the default value is NULL), the implementation of the method will ignore the integration rule provided by the fluxelem parameter and, instead, compute the discrete flux at the points specified by the integration rule ir.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 2284 of file bilininteg.cpp.

◆ ComputeFluxEnergy()

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

Virtual method required for Zienkiewicz-Zhu type error estimators.

The purpose of this method is to compute a local number that measures the energy of a given "flux" function (see ComputeElementFlux() for a description of the "flux" function). Typically, the energy of a "flux" function should be equal to a_local(u,u), if the "flux" is defined from a solution u; here a_local(.,.) denotes the element-local bilinear form represented by the integrator.

Parameters
[in]fluxelemFiniteElement of the "flux".
[in]TransThe ElementTransformation describing the physical position of the mesh element.
[in]flux"Flux" coefficients representing the expansion of the "flux" function in the basis of fluxelem.
[out]d_energyIf not NULL, the given Vector should be set to represent directional energy split that can be used for anisotropic error estimation.
Returns
The computed energy.

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 2303 of file bilininteg.cpp.

◆ GetCoefficient()

const Coefficient * mfem::CurlCurlIntegrator::GetCoefficient ( ) const
inline

Definition at line 2821 of file bilininteg.hpp.

Member Data Documentation

◆ dim

int mfem::CurlCurlIntegrator::dim
protected

Definition at line 2781 of file bilininteg.hpp.

◆ dofs1D

int mfem::CurlCurlIntegrator::dofs1D
protected

Definition at line 2781 of file bilininteg.hpp.

◆ DQ

DiagonalMatrixCoefficient* mfem::CurlCurlIntegrator::DQ
protected

Definition at line 2773 of file bilininteg.hpp.

◆ geom

const GeometricFactors* mfem::CurlCurlIntegrator::geom
protected

Not owned.

Definition at line 2780 of file bilininteg.hpp.

◆ mapsC

const DofToQuad* mfem::CurlCurlIntegrator::mapsC
protected

Not owned. DOF-to-quad map, closed.

Definition at line 2779 of file bilininteg.hpp.

◆ mapsO

const DofToQuad* mfem::CurlCurlIntegrator::mapsO
protected

Not owned. DOF-to-quad map, open.

Definition at line 2778 of file bilininteg.hpp.

◆ MQ

MatrixCoefficient* mfem::CurlCurlIntegrator::MQ
protected

Definition at line 2774 of file bilininteg.hpp.

◆ ne

int mfem::CurlCurlIntegrator::ne
protected

Definition at line 2781 of file bilininteg.hpp.

◆ nq

int mfem::CurlCurlIntegrator::nq
protected

Definition at line 2781 of file bilininteg.hpp.

◆ pa_data

Vector mfem::CurlCurlIntegrator::pa_data
protected

Definition at line 2777 of file bilininteg.hpp.

◆ Q

Coefficient* mfem::CurlCurlIntegrator::Q
protected

Definition at line 2772 of file bilininteg.hpp.

◆ quad1D

int mfem::CurlCurlIntegrator::quad1D
protected

Definition at line 2781 of file bilininteg.hpp.

◆ symmetric

bool mfem::CurlCurlIntegrator::symmetric = true
protected

False if using a nonsymmetric matrix coefficient.

Definition at line 2782 of file bilininteg.hpp.


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