nedelec.h

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/*
 * Copyright (c) 2013-2015:  G-CSC, Goethe University Frankfurt
 * Author: Dmitry Logashenko
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
/*
 * This file contains implementations of the local shape function set for
 * the so-called Nedelec (or Whitney-1) elements.
 */
#ifndef __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__NEDELEC__NEDELEC__
#define __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__NEDELEC__NEDELEC__
 
#include "common/util/provider.h"
#include "../local_dof_set.h"
#include "lib_disc/common/multi_index.h"
 
namespace ug{
 
// Nedelec Set
 
template <typename TRefElem>
class NedelecLDS
{
  protected:
    static const int refDim = TRefElem::dim;
 
  public:
    NedelecLDS()
    {
      if(refDim < 2)
      {
      //  No dofs if the dimension is less than 2:
        nsh = 0;
        m_vLocalDoF.clear();
        return;
      }
 
      const TRefElem& rRefElem = Provider<TRefElem>::get();
 
      nsh = rRefElem.num(1); // number of the edges
    //  set local DoFs (all located at the edges)
      m_vLocalDoF.resize(nsh);
      for(size_t i = 0; i < nsh; ++i)
        m_vLocalDoF[i] = LocalDoF(1, i, 0);
    }
    NedelecLDS() {…}
 
    ReferenceObjectID roid() const {return TRefElem::REFERENCE_OBJECT_ID;}
 
    size_t num_dof() const {return nsh;};
 
    size_t num_dof(ReferenceObjectID type) const
    {
      if(ReferenceElementDimension(type) == 1) return 1;
      else return 0;
    }
    size_t num_dof(ReferenceObjectID type) const {…}
 
    const LocalDoF& local_dof(size_t dof) const {return m_vLocalDoF[dof];}
 
    bool exact_position_available() const {return true;};
 
  protected:
    size_t nsh;
 
    std::vector<LocalDoF> m_vLocalDoF;
};
class NedelecLDS {…};
 
template <typename TRefElement>
class NedelecLSFS;
 
template <>
class NedelecLSFS<ReferenceTriangle>
: public NedelecLDS<ReferenceTriangle>,
  public
  BaseLSFS
    <
      NedelecLSFS<ReferenceTriangle>,
      ReferenceTriangle::dim, 
      MathVector<ReferenceTriangle::dim>, 
      MathMatrix<ReferenceTriangle::dim, ReferenceTriangle::dim> 
    >
{
  public:
    typedef ReferenceTriangle reference_element_type;
 
    static const size_t order = 1;
 
    static const int dim = reference_element_type::dim;
 
  private:
    typedef BaseLSFS<NedelecLSFS<reference_element_type>, dim, MathVector<dim>,  MathMatrix<dim,dim> > base_type;
 
  public:
    typedef base_type::shape_type shape_type;
 
    typedef base_type::grad_type grad_type;
 
  protected:
    static const size_t nsh = reference_element_type::numEdges;
 
  public:
    NedelecLSFS() {};
 
    inline bool continuous() const {return false;}
 
    inline size_t num_sh() const {return nsh;}
 
    inline bool position(size_t i, MathVector<dim>& pos) const
    {
      switch(i)
      {
        case 0: pos[0] = 0.5;
            pos[1] = 0.0;
            return true;
        case 1: pos[0] = 0.5;
            pos[1] = 0.5;
            return true;
        case 2: pos[0] = 0.0;
            pos[1] = 0.5;
            return true;
        default: UG_THROW("NedelecLSFS: shape function "<<i<<
                  " not found. Only "<<nsh<<" shapes present.");
      }
    }
    inline bool position(size_t i, MathVector<dim>& pos) const {…}
 
    inline MathVector<dim> shape(const size_t i, const MathVector<dim>& x) const
    {
      UG_THROW ("NedelecLSFS: Nedelec shapes cannot be computed in the reference space.");
    }
    inline MathVector<dim> shape(const size_t i, const MathVector<dim>& x) const {…}
 
    inline void grad(MathMatrix<dim,dim>& g, const size_t i, const MathVector<dim>& x) const
    {
      UG_THROW ("NedelecLSFS: Gradients of the Nedelec shapes cannot be computed in the reference space.");
    }
    inline void grad(MathMatrix<dim,dim>& g, const size_t i, const MathVector<dim>& x) const {…}
};
class NedelecLSFS<ReferenceTriangle> {…};
 
template <>
class NedelecLSFS<ReferenceTetrahedron>
: public NedelecLDS<ReferenceTetrahedron>,
  public
  BaseLSFS
    <
      NedelecLSFS<ReferenceTetrahedron>,
      ReferenceTetrahedron::dim, 
      MathVector<ReferenceTetrahedron::dim>, 
      MathMatrix<ReferenceTetrahedron::dim, ReferenceTetrahedron::dim> 
    >
{
  public:
    typedef ReferenceTetrahedron reference_element_type;
 
    static const size_t order = 1;
 
    static const int dim = reference_element_type::dim;
 
  private:
    typedef BaseLSFS<NedelecLSFS<reference_element_type>, dim, MathVector<dim>,  MathMatrix<dim,dim> > base_type;
 
  public:
    typedef base_type::shape_type shape_type;
 
    typedef base_type::grad_type grad_type;
 
  protected:
    static const size_t nsh = reference_element_type::numEdges;
 
  public:
    NedelecLSFS() {};
 
    inline bool continuous() const {return false;}
 
    inline size_t num_sh() const {return nsh;}
 
    inline bool position(size_t i, MathVector<dim>& pos) const
    {
      switch(i)
      {
        case 0: pos[0] = 0.5;
            pos[1] = 0.0;
            pos[2] = 0.0;
            return true;
        case 1: pos[0] = 0.5;
            pos[1] = 0.5;
            pos[2] = 0.0;
            return true;
        case 2: pos[0] = 0.0;
            pos[1] = 0.5;
            pos[2] = 0.0;
            return true;
        case 3: pos[0] = 0.0;
            pos[1] = 0.0;
            pos[2] = 0.5;
            return true;
        case 4: pos[0] = 0.5;
            pos[1] = 0.0;
            pos[2] = 0.5;
            return true;
        case 5: pos[0] = 0.0;
            pos[1] = 0.5;
            pos[2] = 0.5;
            return true;
        default: UG_THROW("NedelecLSFS: shape function "<<i<<
                  " not found. Only "<<nsh<<" shapes present.");
      }
    }
    inline bool position(size_t i, MathVector<dim>& pos) const {…}
 
    inline MathVector<dim> shape(const size_t i, const MathVector<dim>& x) const
    {
      UG_THROW ("NedelecLSFS: Nedelec shapes cannot be computed in the reference space.");
    }
    inline MathVector<dim> shape(const size_t i, const MathVector<dim>& x) const {…}
 
    inline void grad(MathMatrix<dim,dim>& g, const size_t i, const MathVector<dim>& x) const
    {
      UG_THROW ("NedelecLSFS: Gradients of the Nedelec shapes cannot be computed in the reference space.");
    }
    inline void grad(MathMatrix<dim,dim>& g, const size_t i, const MathVector<dim>& x) const {…}
};
class NedelecLSFS<ReferenceTetrahedron> {…};
 
} // namespace ug
 
#endif // __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__NEDELEC__NEDELEC__
 
/* End of File */