fe_h1.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_H1
#define MFEM_FE_H1

#include "fe_base.hpp"

namespace mfem
{

/// Arbitrary order H1 elements in 1D
class H1_SegmentElement : public NodalTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, dshape_x, d2shape_x;
#endif

public:
   /// Construct the H1_SegmentElement of order @a p and BasisType @a btype
   H1_SegmentElement(const int p, const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 2D on a square
class H1_QuadrilateralElement : public NodalTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
#endif

public:
   /// Construct the H1_QuadrilateralElement of order @a p and BasisType @a btype
   H1_QuadrilateralElement(const int p,
                           const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 3D on a cube
class H1_HexahedronElement : public NodalTensorFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z,
           d2shape_x, d2shape_y, d2shape_z;
#endif

public:
   /// Construct the H1_HexahedronElement of order @a p and BasisType @a btype
   H1_HexahedronElement(const int p, const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
};


/// Arbitrary order H1 elements in 2D on a triangle
class H1_TriangleElement : public NodalFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
   mutable Vector ddshape_x, ddshape_y, ddshape_l;
   mutable DenseMatrix du, ddu;
#endif
   DenseMatrixInverse Ti;

public:
   /// Construct the H1_TriangleElement of order @a p and BasisType @a btype
   H1_TriangleElement(const int p, const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &ddshape) const;
};


/// Arbitrary order H1 elements in 3D  on a tetrahedron
class H1_TetrahedronElement : public NodalFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector shape_x, shape_y, shape_z, shape_l;
   mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
   mutable Vector ddshape_x, ddshape_y, ddshape_z, ddshape_l;
   mutable DenseMatrix du, ddu;
#endif
   DenseMatrixInverse Ti;

public:
   /// Construct the H1_TetrahedronElement of order @a p and BasisType @a btype
   H1_TetrahedronElement(const int p,
                         const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
   virtual void CalcHessian(const IntegrationPoint &ip,
                            DenseMatrix &ddshape) const;
};



/// Arbitrary order H1 elements in 3D on a wedge
class H1_WedgeElement : public NodalFiniteElement
{
private:
#ifndef MFEM_THREAD_SAFE
   mutable Vector t_shape, s_shape;
   mutable DenseMatrix t_dshape, s_dshape;
#endif
   Array<int> t_dof, s_dof;

   H1_TriangleElement TriangleFE;
   H1_SegmentElement  SegmentFE;

public:
   /// Construct the H1_WedgeElement of order @a p and BasisType @a btype
   H1_WedgeElement(const int p,
                   const int btype = BasisType::GaussLobatto);
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
};

} // namespace mfem

#endif