html/fe__rt_8hpp_source.html

// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced

// at the Lawrence Livermore National Laboratory. All Rights reserved. See files

// LICENSE and NOTICE for details. LLNL-CODE-806117.

//

// This file is part of the MFEM library. For more information and source code

// availability visit https://mfem.org.

//

// MFEM is free software; you can redistribute it and/or modify it under the

// terms of the BSD-3 license. We welcome feedback and contributions, see file

// CONTRIBUTING.md for details.


#ifndef MFEM_FE_RT

#define MFEM_FE_RT


#include "fe_base.hpp"

#include "fe_h1.hpp"

#include "fe_l2.hpp"

#include "fe_pyramid.hpp"


namespace mfem

{


/// Arbitrary order Raviart-Thomas elements in 2D on a square


class RT_QuadrilateralElement : public VectorTensorFiniteElement

{

private:

   static const real_t nk[8];


#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;

   mutable Vector dshape_cx, dshape_cy;

#endif

   Array<int> dof2nk;

   const real_t *cp;


public:

   /** @brief Construct the RT_QuadrilateralElement of order @a p and closed and

       open BasisType @a cb_type and @a ob_type */

   RT_QuadrilateralElement(const int p,

                           const int cb_type = BasisType::GaussLobatto,

                           const int ob_type = BasisType::GaussLegendre);

   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override

   { CalcVShape_RT(Trans, shape); }


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override

   {

      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }

      else { Project_RT(nk, dof2nk, vc, Trans, dofs); }

   }


   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,

                         Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectMatrixCoefficient(MatrixCoefficient &mc,

                                 ElementTransformation &T,

                                 Vector &dofs) const override

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   // Gradient + rotation = Curl: H1 -> H(div)


   void ProjectGrad(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &grad) const override

   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }


   // Curl = Gradient + rotation: H1 -> H(div)


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override

   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }


   void GetFaceMap(const int face_id, Array<int> &face_map) const override;


protected:

   void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans,

                          Vector &dofs) const;

};


/// Arbitrary order Raviart-Thomas elements in 3D on a cube


class RT_HexahedronElement : public VectorTensorFiniteElement

{

   static const real_t nk[18];


#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;

   mutable Vector dshape_cx, dshape_cy, dshape_cz;

#endif

   Array<int> dof2nk;

   const real_t *cp;


public:

   /** @brief Construct the RT_HexahedronElement of order @a p and closed and

       open BasisType @a cb_type and @a ob_type */

   RT_HexahedronElement(const int p,

                        const int cb_type = BasisType::GaussLobatto,

                        const int ob_type = BasisType::GaussLegendre);


   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override

   { CalcVShape_RT(Trans, shape); }


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override

   {

      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }

      else { Project_RT(nk, dof2nk, vc, Trans, dofs); }

   }


   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,

                         Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectMatrixCoefficient(MatrixCoefficient &mc,

                                 ElementTransformation &T,

                                 Vector &dofs) const override

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override

   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }


   /// @brief Return the mapping from lexicographically ordered face DOFs to

   /// lexicographically ordered element DOFs corresponding to local face

   /// @a face_id.

   void GetFaceMap(const int face_id, Array<int> &face_map) const override;


protected:

   void ProjectIntegrated(VectorCoefficient &vc,

                          ElementTransformation &Trans,

                          Vector &dofs) const;

};


/// Arbitrary order Raviart-Thomas elements in 2D on a triangle


class RT_TriangleElement : public VectorFiniteElement

{

   static const real_t nk[6], c;


#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_x, shape_y, shape_l;

   mutable Vector dshape_x, dshape_y, dshape_l;

   mutable DenseMatrix u;

   mutable Vector divu;

#endif

   Array<int> dof2nk;

   DenseMatrixInverse Ti;


public:

   /// Construct the RT_TriangleElement of order @a p

   RT_TriangleElement(const int p);

   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override

   { CalcVShape_RT(Trans, shape); }


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,

                         Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectMatrixCoefficient(MatrixCoefficient &mc,

                                 ElementTransformation &T,

                                 Vector &dofs) const override

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   // Gradient + rotation = Curl: H1 -> H(div)


   void ProjectGrad(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &grad) const override

   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }


   // Curl = Gradient + rotation: H1 -> H(div)


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override

   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }


};


/// Arbitrary order Raviart-Thomas elements in 3D on a tetrahedron


class RT_TetrahedronElement : public VectorFiniteElement

{

   static const real_t nk[12], c;


#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_x, shape_y, shape_z, shape_l;

   mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;

   mutable DenseMatrix u;

   mutable Vector divu;

#endif

   Array<int> dof2nk;

   DenseMatrixInverse Ti;


public:

   /// Construct the RT_TetrahedronElement of order @a p

   RT_TetrahedronElement(const int p);

   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override

   { CalcVShape_RT(Trans, shape); }


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,

                         Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectMatrixCoefficient(MatrixCoefficient &mc,

                                 ElementTransformation &T,

                                 Vector &dofs) const override

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override

   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }


};


class RT_WedgeElement : public VectorFiniteElement

{

   static const real_t nk[15];


#ifndef MFEM_THREAD_SAFE

   mutable Vector      tl2_shape;

   mutable Vector      sh1_shape;

   mutable DenseMatrix trt_shape;

   mutable Vector      sl2_shape;

   mutable DenseMatrix sh1_dshape;

   mutable Vector      trt_dshape;

#endif

   Array<int> dof2nk, t_dof, s_dof;


   // The RT_Wedge is implemented as the sum of tensor products of

   // lower dimensional basis funcgtions.

   // Specifically: L2TriangleFE x H1SegmentFE + RTTriangle x L2SegmentFE

   L2_TriangleElement L2TriangleFE;

   RT_TriangleElement RTTriangleFE;

   H1_SegmentElement  H1SegmentFE;

   L2_SegmentElement  L2SegmentFE;


public:

   RT_WedgeElement(const int p);

   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override

   { CalcVShape_RT(Trans, shape); }


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   void ProjectMatrixCoefficient(MatrixCoefficient &mc,

                                 ElementTransformation &T,

                                 Vector &dofs) const override

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override

   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }


};


/** Arbitrary order H(Div) basis functions defined on pyramid-shaped elements


  This implementation is closely based on the finite elements

  described in section 9.3 of the paper "Orientation embedded high

  order shape functions for the exact sequence elements of all shapes"

  by Federico Fuentes, Brendan Keith, Leszek Demkowicz, and Sriram

  Nagaraj, see https://doi.org/10.1016/j.camwa.2015.04.027.

 */


class RT_FuentesPyramidElement

   : public VectorFiniteElement, public FuentesPyramid

{

private:

   static const real_t nk[24];


   mutable real_t zmax;


#ifndef MFEM_THREAD_SAFE

   mutable Vector      tmp1_i;

   mutable DenseMatrix tmp1_ij;

   mutable DenseMatrix tmp2_ij;

   mutable DenseMatrix tmp3_ij;

   mutable DenseMatrix tmp4_ij;

   mutable DenseTensor tmp1_ijk;

   mutable DenseTensor tmp2_ijk;

   mutable DenseTensor tmp3_ijk;

   mutable DenseTensor tmp4_ijk;

   mutable DenseTensor tmp5_ijk;

   mutable DenseTensor tmp6_ijk;

   mutable DenseTensor tmp7_ijk;

   mutable DenseMatrix u;

   mutable Vector      divu;

#endif

   Array<int> dof2nk;

   DenseMatrixInverse Ti;


   void calcBasis(const int p, const IntegrationPoint &ip,

                  Vector &phi_k,

                  DenseMatrix &phi_ij,

                  DenseMatrix &dphi_k,

                  DenseTensor &VQ_ijk,

                  DenseTensor &VT_ijk,

                  DenseTensor &VTT_ijk,

                  DenseTensor &E_ijk, DenseTensor &dE_ijk,

                  DenseTensor &dphi_ijk,

                  DenseTensor &VL_ijk,

                  DenseMatrix &VR_ij,

                  DenseMatrix &F) const;


   void calcDivBasis(const int p, const IntegrationPoint &ip,

                     Vector &phi_k,

                     DenseMatrix &phi_ij,

                     DenseMatrix &dphi_k,

                     DenseTensor &VQ_ijk,

                     DenseTensor &VT_ijk,

                     DenseTensor &VTT_ijk, DenseMatrix &dVTT_ij,

                     DenseTensor &E_ijk, DenseTensor &dE_ijk,

                     DenseTensor &dphi_ijk,

                     DenseTensor &VL_ijk,

                     DenseMatrix &VR_ij,

                     Vector &dF) const;


public:

   RT_FuentesPyramidElement(const int p);

   virtual void CalcVShape(const IntegrationPoint &ip,

                           DenseMatrix &shape) const;


   virtual void CalcVShape(ElementTransformation &Trans,

                           DenseMatrix &shape) const

   { CalcVShape_RT(Trans, shape); }


   virtual void CalcDivShape(const IntegrationPoint &ip,

                             Vector &divshape) const;


   virtual void GetLocalInterpolation(ElementTransformation &Trans,

                                      DenseMatrix &I) const

   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }


   virtual void GetLocalRestriction(ElementTransformation &Trans,

                                    DenseMatrix &R) const

   { LocalRestriction_RT(nk, dof2nk, Trans, R); }


   virtual void GetTransferMatrix(const FiniteElement &fe,

                                  ElementTransformation &Trans,

                                  DenseMatrix &I) const

   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }


   using FiniteElement::Project;


   virtual void Project(VectorCoefficient &vc,

                        ElementTransformation &Trans, Vector &dofs) const

   { Project_RT(nk, dof2nk, vc, Trans, dofs); }


   virtual void ProjectMatrixCoefficient(

      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const

   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }


   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,

                        DenseMatrix &I) const

   { Project_RT(nk, dof2nk, fe, Trans, I); }


   virtual void ProjectCurl(const FiniteElement &fe,

                            ElementTransformation &Trans,

                            DenseMatrix &curl) const

   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }


   void CalcRawVShape(const IntegrationPoint &ip,

                      DenseMatrix &shape) const;


   void CalcRawDivShape(const IntegrationPoint &ip,

                        Vector &dshape) const;


   real_t GetZetaMax() const { return zmax; }

};


/// Arbitrary order, three component, Raviart-Thomas elements in 1D on a segment

/** RT_R1D_SegmentElement provides a representation of a three component

    Raviart-Thomas basis where the vector components vary along only one

    dimension.

*/


class RT_R1D_SegmentElement : public VectorFiniteElement

{

   static const real_t nk[9];

#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_cx, shape_ox;

   mutable Vector dshape_cx;

#endif

   Array<int> dof_map, dof2nk;


   Poly_1D::Basis &cbasis1d, &obasis1d;


public:

   /** @brief Construct the RT_R1D_SegmentElement of order @a p and closed and

       open BasisType @a cb_type and @a ob_type */

   RT_R1D_SegmentElement(const int p,

                         const int cb_type = BasisType::GaussLobatto,

                         const int ob_type = BasisType::GaussLegendre);


   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override;


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override;


   void Project(const FiniteElement &fe,

                ElementTransformation &Trans,

                DenseMatrix &I) const override;


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override;

};


/** RT_R2D_SegmentElement provides a representation of a 3D Raviart-Thomas

    basis where the vector field is assumed constant in the third dimension.

*/


class RT_R2D_SegmentElement : public VectorFiniteElement

{

   static const real_t nk[2];

#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_ox;

#endif

   Array<int> dof_map, dof2nk;


   Poly_1D::Basis &obasis1d;


private:

   void LocalInterpolation(const VectorFiniteElement &cfe,

                           ElementTransformation &Trans,

                           DenseMatrix &I) const;


public:

   /** @brief Construct the RT_R2D_SegmentElement of order @a p and open

       BasisType @a ob_type */

   RT_R2D_SegmentElement(const int p,

                         const int ob_type = BasisType::GaussLegendre);


   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override;


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &div_shape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation(*this, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override

   { MFEM_ABORT("method is not overloaded"); }


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }


};


class RT_R2D_FiniteElement : public VectorFiniteElement

{

protected:

   const real_t *nk;

   Array<int> dof_map, dof2nk;


   RT_R2D_FiniteElement(int p, Geometry::Type G, int Do, const real_t *nk_fe);


private:

   void LocalInterpolation(const VectorFiniteElement &cfe,

                           ElementTransformation &Trans,

                           DenseMatrix &I) const;


public:

   using FiniteElement::CalcVShape;


   void CalcVShape(ElementTransformation &Trans,

                   DenseMatrix &shape) const override;


   void GetLocalInterpolation(ElementTransformation &Trans,

                              DenseMatrix &I) const override

   { LocalInterpolation(*this, Trans, I); }


   void GetLocalRestriction(ElementTransformation &Trans,

                            DenseMatrix &R) const override;


   void GetTransferMatrix(const FiniteElement &fe,

                          ElementTransformation &Trans,

                          DenseMatrix &I) const override

   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }


   using FiniteElement::Project;


   void Project(VectorCoefficient &vc,

                ElementTransformation &Trans, Vector &dofs) const override;


   void Project(const FiniteElement &fe, ElementTransformation &Trans,

                DenseMatrix &I) const override;


   void ProjectCurl(const FiniteElement &fe,

                    ElementTransformation &Trans,

                    DenseMatrix &curl) const override;

};


/// Arbitrary order Raviart-Thomas 3D elements in 2D on a triangle


class RT_R2D_TriangleElement : public RT_R2D_FiniteElement

{

private:

   static const real_t nk_t[12];


#ifndef MFEM_THREAD_SAFE

   mutable DenseMatrix rt_shape;

   mutable Vector      l2_shape;

   mutable Vector      rt_dshape;

#endif


   RT_TriangleElement RT_FE;

   L2_TriangleElement L2_FE;


public:

   /** @brief Construct the RT_R2D_TriangleElement of order @a p */

   RT_R2D_TriangleElement(const int p);


   using RT_R2D_FiniteElement::CalcVShape;


   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;


   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;

};


/// Arbitrary order Raviart-Thomas 3D elements in 2D on a square


class RT_R2D_QuadrilateralElement : public RT_R2D_FiniteElement

{

private:

   static const real_t nk_q[15];


#ifndef MFEM_THREAD_SAFE

   mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;

   mutable Vector dshape_cx, dshape_cy;

#endif


   Poly_1D::Basis &cbasis1d, &obasis1d;


public:

   /** @brief Construct the RT_QuadrilateralElement of order @a p and closed and

       open BasisType @a cb_type and @a ob_type */

   RT_R2D_QuadrilateralElement(const int p,

                               const int cb_type = BasisType::GaussLobatto,

                               const int ob_type = BasisType::GaussLegendre);


   using RT_R2D_FiniteElement::CalcVShape;


   void CalcVShape(const IntegrationPoint &ip,

                   DenseMatrix &shape) const override;

   void CalcDivShape(const IntegrationPoint &ip,

                     Vector &divshape) const override;

};


} // namespace mfem


#endif

mfem::Array
Definition array.hpp:47

mfem::BasisType::GaussLobatto
@ GaussLobatto
Closed type.
Definition fe_base.hpp:36

mfem::BasisType::GaussLegendre
@ GaussLegendre
Open type.
Definition fe_base.hpp:35

mfem::DenseMatrixInverse
Definition densemat.hpp:838

mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition densemat.hpp:24

mfem::DenseTensor
Rank 3 tensor (array of matrices)
Definition densemat.hpp:1112

mfem::ElementTransformation
Definition eltrans.hpp:28

mfem::FiniteElement
Abstract class for all finite elements.
Definition fe_base.hpp:244

mfem::FiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_base.cpp:40

mfem::FiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Given a coefficient and a transformation, compute its projection (approximation) in the local finite ...
Definition fe_base.cpp:126

mfem::FuentesPyramid
Definition fe_pyramid.hpp:39

mfem::Geometry::Type
Type
Definition geom.hpp:40

mfem::H1_SegmentElement
Arbitrary order H1 elements in 1D.
Definition fe_h1.hpp:23

mfem::IntegrationPoint
Class for integration point with weight.
Definition intrules.hpp:35

mfem::L2_SegmentElement
Arbitrary order L2 elements in 1D on a segment.
Definition fe_l2.hpp:23

mfem::L2_TriangleElement
Arbitrary order L2 elements in 2D on a triangle.
Definition fe_l2.hpp:110

mfem::MatrixCoefficient
Base class for Matrix Coefficients that optionally depend on time and space.
Definition coefficient.hpp:1047

mfem::Poly_1D::Basis
Class for evaluating 1D nodal, positive (Bernstein), or integrated (Gerritsma) bases.
Definition fe_base.hpp:1003

mfem::Poly_1D::Basis::IsIntegratedType
bool IsIntegratedType() const
Returns true if the basis is "integrated", false otherwise.
Definition fe_base.hpp:1047

mfem::RT_FuentesPyramidElement
Definition fe_rt.hpp:348

mfem::RT_FuentesPyramidElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:1398

mfem::RT_FuentesPyramidElement::RT_FuentesPyramidElement
RT_FuentesPyramidElement(const int p)
Definition fe_rt.cpp:1273

mfem::RT_FuentesPyramidElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:403

mfem::RT_FuentesPyramidElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:419

mfem::RT_FuentesPyramidElement::GetZetaMax
real_t GetZetaMax() const
Definition fe_rt.hpp:439

mfem::RT_FuentesPyramidElement::CalcRawDivShape
void CalcRawDivShape(const IntegrationPoint &ip, Vector &dshape) const
Definition fe_rt.cpp:1478

mfem::RT_FuentesPyramidElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:425

mfem::RT_FuentesPyramidElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:428

mfem::RT_FuentesPyramidElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:411

mfem::RT_FuentesPyramidElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:408

mfem::RT_FuentesPyramidElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:1449

mfem::RT_FuentesPyramidElement::CalcRawVShape
void CalcRawVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition fe_rt.cpp:1425

mfem::RT_FuentesPyramidElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:422

mfem::RT_FuentesPyramidElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:414

mfem::RT_HexahedronElement
Arbitrary order Raviart-Thomas elements in 3D on a cube.
Definition fe_rt.hpp:97

mfem::RT_HexahedronElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:492

mfem::RT_HexahedronElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:127

mfem::RT_HexahedronElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:121

mfem::RT_HexahedronElement::ProjectIntegrated
void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition fe_rt.cpp:661

mfem::RT_HexahedronElement::Project
void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:145

mfem::RT_HexahedronElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:116

mfem::RT_HexahedronElement::GetFaceMap
void GetFaceMap(const int face_id, Array< int > &face_map) const override
Return the mapping from lexicographically ordered face DOFs to lexicographically ordered element DOFs...
Definition fe_rt.cpp:711

mfem::RT_HexahedronElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:582

mfem::RT_HexahedronElement::RT_HexahedronElement
RT_HexahedronElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the RT_HexahedronElement of order p and closed and open BasisType cb_type and ob_type.
Definition fe_rt.cpp:326

mfem::RT_HexahedronElement::ProjectFromNodes
void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition fe_rt.hpp:138

mfem::RT_HexahedronElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:148

mfem::RT_HexahedronElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:132

mfem::RT_HexahedronElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:124

mfem::RT_HexahedronElement::ProjectMatrixCoefficient
void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:141

mfem::RT_QuadrilateralElement
Arbitrary order Raviart-Thomas elements in 2D on a square.
Definition fe_rt.hpp:25

mfem::RT_QuadrilateralElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:82

mfem::RT_QuadrilateralElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:55

mfem::RT_QuadrilateralElement::ProjectIntegrated
void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition fe_rt.cpp:258

mfem::RT_QuadrilateralElement::ProjectGrad
void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const override
Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:77

mfem::RT_QuadrilateralElement::ProjectMatrixCoefficient
void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:69

mfem::RT_QuadrilateralElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:203

mfem::RT_QuadrilateralElement::GetFaceMap
void GetFaceMap(const int face_id, Array< int > &face_map) const override
Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local fac...
Definition fe_rt.cpp:301

mfem::RT_QuadrilateralElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:52

mfem::RT_QuadrilateralElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:142

mfem::RT_QuadrilateralElement::ProjectFromNodes
void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition fe_rt.hpp:66

mfem::RT_QuadrilateralElement::Project
void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:73

mfem::RT_QuadrilateralElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:49

mfem::RT_QuadrilateralElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:60

mfem::RT_QuadrilateralElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:44

mfem::RT_QuadrilateralElement::RT_QuadrilateralElement
RT_QuadrilateralElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the RT_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_type.
Definition fe_rt.cpp:26

mfem::RT_R1D_SegmentElement
Arbitrary order, three component, Raviart-Thomas elements in 1D on a segment.
Definition fe_rt.hpp:448

mfem::RT_R1D_SegmentElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.cpp:2146

mfem::RT_R1D_SegmentElement::RT_R1D_SegmentElement
RT_R1D_SegmentElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the RT_R1D_SegmentElement of order p and closed and open BasisType cb_type and ob_type.
Definition fe_rt.cpp:2005

mfem::RT_R1D_SegmentElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:2059

mfem::RT_R1D_SegmentElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.cpp:2258

mfem::RT_R1D_SegmentElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:2113

mfem::RT_R2D_FiniteElement
Definition fe_rt.hpp:537

mfem::RT_R2D_FiniteElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:555

mfem::RT_R2D_FiniteElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.cpp:2463

mfem::RT_R2D_FiniteElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.cpp:2511

mfem::RT_R2D_FiniteElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:562

mfem::RT_R2D_FiniteElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.cpp:2623

mfem::RT_R2D_FiniteElement::dof_map
Array< int > dof_map
Definition fe_rt.hpp:540

mfem::RT_R2D_FiniteElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.cpp:2404

mfem::RT_R2D_FiniteElement::dof2nk
Array< int > dof2nk
Definition fe_rt.hpp:540

mfem::RT_R2D_FiniteElement::nk
const real_t * nk
Definition fe_rt.hpp:539

mfem::RT_R2D_FiniteElement::RT_R2D_FiniteElement
RT_R2D_FiniteElement(int p, Geometry::Type G, int Do, const real_t *nk_fe)
Definition fe_rt.cpp:2392

mfem::RT_R2D_QuadrilateralElement
Arbitrary order Raviart-Thomas 3D elements in 2D on a square.
Definition fe_rt.hpp:610

mfem::RT_R2D_QuadrilateralElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:2896

mfem::RT_R2D_QuadrilateralElement::RT_R2D_QuadrilateralElement
RT_R2D_QuadrilateralElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the RT_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_type.
Definition fe_rt.cpp:2770

mfem::RT_R2D_QuadrilateralElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:2953

mfem::RT_R2D_SegmentElement
Definition fe_rt.hpp:493

mfem::RT_R2D_SegmentElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:530

mfem::RT_R2D_SegmentElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &div_shape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:2345

mfem::RT_R2D_SegmentElement::RT_R2D_SegmentElement
RT_R2D_SegmentElement(const int p, const int ob_type=BasisType::GaussLegendre)
Construct the RT_R2D_SegmentElement of order p and open BasisType ob_type.
Definition fe_rt.cpp:2281

mfem::RT_R2D_SegmentElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:522

mfem::RT_R2D_SegmentElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:2309

mfem::RT_R2D_SegmentElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:526

mfem::RT_R2D_TriangleElement
Arbitrary order Raviart-Thomas 3D elements in 2D on a triangle.
Definition fe_rt.hpp:582

mfem::RT_R2D_TriangleElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:2715

mfem::RT_R2D_TriangleElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:2744

mfem::RT_R2D_TriangleElement::RT_R2D_TriangleElement
RT_R2D_TriangleElement(const int p)
Construct the RT_R2D_TriangleElement of order p.
Definition fe_rt.cpp:2647

mfem::RT_TetrahedronElement
Arbitrary order Raviart-Thomas elements in 3D on a tetrahedron.
Definition fe_rt.hpp:228

mfem::RT_TetrahedronElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:1037

mfem::RT_TetrahedronElement::RT_TetrahedronElement
RT_TetrahedronElement(const int p)
Construct the RT_TetrahedronElement of order p.
Definition fe_rt.cpp:899

mfem::RT_TetrahedronElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:256

mfem::RT_TetrahedronElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:250

mfem::RT_TetrahedronElement::Project
void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:271

mfem::RT_TetrahedronElement::ProjectMatrixCoefficient
void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:267

mfem::RT_TetrahedronElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:1001

mfem::RT_TetrahedronElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:253

mfem::RT_TetrahedronElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:274

mfem::RT_TetrahedronElement::ProjectFromNodes
void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition fe_rt.hpp:264

mfem::RT_TetrahedronElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:261

mfem::RT_TetrahedronElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:245

mfem::RT_TriangleElement
Arbitrary order Raviart-Thomas elements in 2D on a triangle.
Definition fe_rt.hpp:167

mfem::RT_TriangleElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:200

mfem::RT_TriangleElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:195

mfem::RT_TriangleElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:219

mfem::RT_TriangleElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:824

mfem::RT_TriangleElement::ProjectMatrixCoefficient
void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:206

mfem::RT_TriangleElement::RT_TriangleElement
RT_TriangleElement(const int p)
Construct the RT_TriangleElement of order p.
Definition fe_rt.cpp:746

mfem::RT_TriangleElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:184

mfem::RT_TriangleElement::Project
void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:210

mfem::RT_TriangleElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:857

mfem::RT_TriangleElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:192

mfem::RT_TriangleElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:189

mfem::RT_TriangleElement::ProjectGrad
void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const override
Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:214

mfem::RT_TriangleElement::ProjectFromNodes
void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition fe_rt.hpp:203

mfem::RT_WedgeElement
Definition fe_rt.hpp:281

mfem::RT_WedgeElement::CalcDivShape
void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const override
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition fe_rt.cpp:1235

mfem::RT_WedgeElement::Project
void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:329

mfem::RT_WedgeElement::GetTransferMatrix
void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const override
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition fe_rt.hpp:317

mfem::RT_WedgeElement::RT_WedgeElement
RT_WedgeElement(const int p)
Definition fe_rt.cpp:1082

mfem::RT_WedgeElement::GetLocalRestriction
void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const override
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
Definition fe_rt.hpp:314

mfem::RT_WedgeElement::ProjectCurl
void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const override
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement....
Definition fe_rt.hpp:332

mfem::RT_WedgeElement::CalcVShape
void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition fe_rt.cpp:1200

mfem::RT_WedgeElement::Project
void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const override
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition fe_rt.hpp:322

mfem::RT_WedgeElement::ProjectMatrixCoefficient
void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local...
Definition fe_rt.hpp:325

mfem::RT_WedgeElement::GetLocalInterpolation
void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const override
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition fe_rt.hpp:311

mfem::RT_WedgeElement::CalcVShape
void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const override
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition fe_rt.hpp:306

mfem::VectorCoefficient
Base class for vector Coefficients that optionally depend on time and space.
Definition coefficient.hpp:567

mfem::VectorFiniteElement
Intermediate class for finite elements whose basis functions return vector values.
Definition fe_base.hpp:813

mfem::VectorFiniteElement::ProjectGrad_RT
void ProjectGrad_RT(const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition fe_base.cpp:1222

mfem::VectorFiniteElement::LocalRestriction_RT
void LocalRestriction_RT(const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &R) const
Definition fe_base.cpp:1628

mfem::VectorFiniteElement::Project_RT
void Project_RT(const real_t *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Project a vector coefficient onto the RT basis functions.
Definition fe_base.cpp:1082

mfem::VectorFiniteElement::LocalInterpolation_RT
void LocalInterpolation_RT(const VectorFiniteElement &cfe, const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const
Definition fe_base.cpp:1502

mfem::VectorFiniteElement::CalcVShape_RT
void CalcVShape_RT(ElementTransformation &Trans, DenseMatrix &shape) const
Definition fe_base.cpp:1059

mfem::VectorFiniteElement::ProjectCurl_RT
void ProjectCurl_RT(const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition fe_base.cpp:1287

mfem::VectorFiniteElement::CheckVectorFE
static const VectorFiniteElement & CheckVectorFE(const FiniteElement &fe)
Definition fe_base.hpp:973

mfem::VectorFiniteElement::ProjectMatrixCoefficient_RT
void ProjectMatrixCoefficient_RT(const real_t *nk, const Array< int > &d2n, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Project the rows of the matrix coefficient in an RT space.
Definition fe_base.cpp:1119

mfem::VectorTensorFiniteElement
Definition fe_base.hpp:1337

mfem::VectorTensorFiniteElement::obasis1d
Poly_1D::Basis & obasis1d
Definition fe_base.hpp:1342

mfem::Vector
Vector data type.
Definition vector.hpp:82

fe_base.hpp

fe_h1.hpp

fe_l2.hpp

fe_pyramid.hpp

mfem
Definition CodeDocumentation.dox:1

mfem::real_t
float real_t
Definition config.hpp:43

p
real_t p(const Vector &x, real_t t)
Definition navier_mms.cpp:53