fe_pos.hpp

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// Copyright (c) 2010-2023, 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_POS
#define MFEM_FE_POS

#include "fe_base.hpp"

namespace mfem
{

/** @brief Class for finite elements utilizing the
    always positive Bernstein basis. */
class PositiveFiniteElement : public ScalarFiniteElement
{
public:
   /** @brief Construct PositiveFiniteElement with given
       @param D    Reference space dimension
       @param G    Geometry type (of type Geometry::Type)
       @param Do   Number of degrees of freedom in the FiniteElement
       @param O    Order/degree of the FiniteElement
       @param F    FunctionSpace type of the FiniteElement
   */
   PositiveFiniteElement(int D, Geometry::Type G, int Do, int O,
                         int F = FunctionSpace::Pk) :
      ScalarFiniteElement(D, G, Do, O, F)
   { }

   virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                      DenseMatrix &I) const
   { ScalarLocalInterpolation(Trans, I, *this); }

   virtual void GetLocalRestriction(ElementTransformation &Trans,
                                    DenseMatrix &R) const
   { ScalarLocalL2Restriction(Trans, R, *this); }

   virtual void GetTransferMatrix(const FiniteElement &fe,
                                  ElementTransformation &Trans,
                                  DenseMatrix &I) const
   { CheckScalarFE(fe).ScalarLocalInterpolation(Trans, I, *this); }

   using FiniteElement::Project;

   // Low-order monotone "projection" (actually it is not a projection): the
   // dofs are set to be the Coefficient values at the nodes.
   virtual void Project(Coefficient &coeff,
                        ElementTransformation &Trans, Vector &dofs) const;

   virtual void Project (VectorCoefficient &vc,
                         ElementTransformation &Trans, Vector &dofs) const;

   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
                        DenseMatrix &I) const;
};


class PositiveTensorFiniteElement : public PositiveFiniteElement,
   public TensorBasisElement
{
public:
   PositiveTensorFiniteElement(const int dims, const int p,
                               const DofMapType dmtype);

   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
                                 DofToQuad::Mode mode) const override
   {
      return (mode == DofToQuad::FULL) ?
             FiniteElement::GetDofToQuad(ir, mode) :
             GetTensorDofToQuad(*this, ir, mode, basis1d, true, dof2quad_array);
   }

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


/// A 2D positive bi-quadratic element on a square utilizing the 2nd order
/// Bernstein basis
class BiQuadPos2DFiniteElement : public PositiveFiniteElement
{
public:
   /// Construct the BiQuadPos2DFiniteElement
   BiQuadPos2DFiniteElement();
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                      DenseMatrix &I) const;
   using FiniteElement::Project;
   virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
                        Vector &dofs) const;
   virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
                        Vector &dofs) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const
   { dofs = 0.; dofs(vertex) = 1.; }
};


/// A 1D quadratic positive element utilizing the 2nd order Bernstein basis
class QuadPos1DFiniteElement : public PositiveFiniteElement
{
public:
   /// Construct the QuadPos1DFiniteElement
   QuadPos1DFiniteElement();
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};


/// Arbitrary order H1 elements in 1D utilizing the Bernstein basis
class H1Pos_SegmentElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   // This is to share scratch space between invocations, which helps speed
   // things up, but with OpenMP, we need one copy per thread. Right now, we
   // solve this by allocating this space within each function call every time
   // we call it. Alternatively, we should do some sort thread private thing.
   // Brunner, Jan 2014
   mutable Vector shape_x, dshape_x;
#endif

public:
   /// Construct the H1Pos_SegmentElement of order @a p
   H1Pos_SegmentElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 2D utilizing the Bernstein basis on a square
class H1Pos_QuadrilateralElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   // See comment in H1Pos_SegmentElement
   mutable Vector shape_x, shape_y, dshape_x, dshape_y;
#endif

public:
   /// Construct the H1Pos_QuadrilateralElement of order @a p
   H1Pos_QuadrilateralElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 3D utilizing the Bernstein basis on a cube
class H1Pos_HexahedronElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   // See comment in H1Pos_SegmentElement.
   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
#endif

public:
   /// Construct the H1Pos_HexahedronElement of order @a p
   H1Pos_HexahedronElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 2D utilizing the Bernstein basis on a triangle
class H1Pos_TriangleElement : public PositiveFiniteElement
{
protected:
#ifndef MFEM_THREAD_SAFE
   mutable Vector m_shape, dshape_1d;
   mutable DenseMatrix m_dshape;
#endif
   Array<int> dof_map;

public:
   /// Construct the H1Pos_TriangleElement of order @a p
   H1Pos_TriangleElement(const int p);

   // The size of shape is (p+1)(p+2)/2 (dof).
   static void CalcShape(const int p, const double x, const double y,
                         double *shape);

   // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
   static void CalcDShape(const int p, const double x, const double y,
                          double *dshape_1d, double *dshape);

   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};


/// Arbitrary order H1 elements in 3D utilizing the Bernstein basis on a
/// tetrahedron
class H1Pos_TetrahedronElement : public PositiveFiniteElement
{
protected:
#ifndef MFEM_THREAD_SAFE
   mutable Vector m_shape, dshape_1d;
   mutable DenseMatrix m_dshape;
#endif
   Array<int> dof_map;

public:
   /// Construct the H1Pos_TetrahedronElement of order @a p
   H1Pos_TetrahedronElement(const int p);

   // The size of shape is (p+1)(p+2)(p+3)/6 (dof).
   static void CalcShape(const int p, const double x, const double y,
                         const double z, double *shape);

   // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
   static void CalcDShape(const int p, const double x, const double y,
                          const double z, double *dshape_1d, double *dshape);

   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};


/// Arbitrary order H1 elements in 3D utilizing the Bernstein basis on a wedge
class H1Pos_WedgeElement : public PositiveFiniteElement
{
protected:
#ifndef MFEM_THREAD_SAFE
   mutable Vector t_shape, s_shape;
   mutable DenseMatrix t_dshape, s_dshape;
#endif
   Array<int> t_dof, s_dof;

   H1Pos_TriangleElement TriangleFE;
   H1Pos_SegmentElement  SegmentFE;

public:
   /// Construct the H1Pos_WedgeElement of order @a p
   H1Pos_WedgeElement(const int p);

   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};


/// Arbitrary order L2 elements in 1D utilizing the Bernstein basis on a segment
class L2Pos_SegmentElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, dshape_x;
#endif

public:
   /// Construct the L2Pos_SegmentElement of order @a p
   L2Pos_SegmentElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order L2 elements in 2D utilizing the Bernstein basis on a square
class L2Pos_QuadrilateralElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, dshape_x, dshape_y;
#endif

public:
   /// Construct the L2Pos_QuadrilateralElement of order @a p
   L2Pos_QuadrilateralElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order L2 elements in 3D utilizing the Bernstein basis on a cube
class L2Pos_HexahedronElement : public PositiveTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
#endif

public:
   /// Construct the L2Pos_HexahedronElement of order @a p
   L2Pos_HexahedronElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order L2 elements in 2D utilizing the Bernstein basis on a triangle
class L2Pos_TriangleElement : public PositiveFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector dshape_1d;
#endif

public:
   /// Construct the L2Pos_TriangleElement of order @a p
   L2Pos_TriangleElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order L2 elements in 3D utilizing the Bernstein basis on a
/// tetrahedron
class L2Pos_TetrahedronElement : public PositiveFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector dshape_1d;
#endif

public:
   /// Construct the L2Pos_TetrahedronElement of order @a p
   L2Pos_TetrahedronElement(const int p);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order L2 elements in 3D utilizing the Bernstein basis on a wedge
class L2Pos_WedgeElement : public PositiveFiniteElement
{
protected:
#ifndef MFEM_THREAD_SAFE
   mutable Vector t_shape, s_shape;
   mutable DenseMatrix t_dshape, s_dshape;
#endif
   Array<int> t_dof, s_dof;

   L2Pos_TriangleElement TriangleFE;
   L2Pos_SegmentElement  SegmentFE;

public:
   /// Construct the L2Pos_WedgeElement of order @a p
   L2Pos_WedgeElement(const int p);

   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};

} // namespace mfem

#endif