inf_fe.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2018 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.

// This library 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.

// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



#ifndef LIBMESH_INF_FE_H
#define LIBMESH_INF_FE_H

#include "libmesh/libmesh_config.h"

#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS

// Local includes
#include "libmesh/fe_base.h"

// C++ includes
#include <cstddef>

namespace libMesh
{


// forward declarations
class Elem;
class FEComputeData;



template <unsigned int Dim, FEFamily T_radial, InfMapType T_map>
class InfFE : public FEBase
{

  /*
   * Protect the nested class
   */
protected:

  class Radial
  {
  private:

    Radial() {}

  public:

    static Real decay (const Real v);

    static Real decay_deriv (const Real) { return -.5; }

    static Real D (const Real v) { return (1.-v)*(1.-v)/4.; }

    static Real D_deriv (const Real v) { return (v-1.)/2.; }

    static Order mapping_order() { return FIRST; }

    static unsigned int n_dofs (const Order o_radial)
    { return static_cast<unsigned int>(o_radial)+1; }

    static unsigned int n_dofs_at_node (const Order o_radial,
                                        const unsigned int n_onion);

    static unsigned int n_dofs_per_elem (const Order o_radial)
    { return static_cast<unsigned int>(o_radial)+1; }

  };



  class Base
  {
  private:

    Base() {}

  public:

    static Elem * build_elem (const Elem * inf_elem);

    static ElemType get_elem_type (const ElemType type);

    static unsigned int n_base_mapping_sf (const ElemType base_elem_type,
                                           const Order base_mapping_order);

  };







public:

  // InfFE continued

  explicit
  InfFE(const FEType & fet);
  ~InfFE() {}

  // The static public members for access from FEInterface etc

  static Real shape(const FEType & fet,
                    const ElemType t,
                    const unsigned int i,
                    const Point & p);

  static Real shape(const FEType & fet,
                    const Elem * elem,
                    const unsigned int i,
                    const Point & p);

  static void compute_data(const FEType & fe_t,
                           const Elem * inf_elem,
                           FEComputeData & data);

  static unsigned int n_shape_functions (const FEType & fet,
                                         const ElemType t)
  { return n_dofs(fet, t); }

  static unsigned int n_dofs(const FEType & fet,
                             const ElemType inf_elem_type);

  static unsigned int n_dofs_at_node(const FEType & fet,
                                     const ElemType inf_elem_type,
                                     const unsigned int n);

  static unsigned int n_dofs_per_elem(const FEType & fet,
                                      const ElemType inf_elem_type);

  virtual FEContinuity get_continuity() const override
  { return C_ZERO; }  // FIXME - is this true??

  virtual bool is_hierarchic() const override
  { return false; }  // FIXME - Inf FEs don't handle p elevation yet

  static void nodal_soln(const FEType & fet,
                         const Elem * elem,
                         const std::vector<Number> & elem_soln,
                         std::vector<Number> & nodal_soln);

  static Point map (const Elem * inf_elem,
                    const Point & reference_point);

  static Point inverse_map (const Elem * elem,
                            const Point & p,
                            const Real tolerance = TOLERANCE,
                            const bool secure = true);


  static void inverse_map (const Elem * elem,
                           const std::vector<Point> & physical_points,
                           std::vector<Point> &       reference_points,
                           const Real tolerance = TOLERANCE,
                           const bool secure = true);


  // The workhorses of InfFE. These are often used during matrix assembly.

  virtual void reinit (const Elem * elem,
                       const std::vector<Point> * const pts = nullptr,
                       const std::vector<Real> * const weights = nullptr) override;

  virtual void reinit (const Elem * elem,
                       const unsigned int side,
                       const Real tolerance = TOLERANCE,
                       const std::vector<Point> * const pts = nullptr,
                       const std::vector<Real> * const weights = nullptr) override;

  virtual void edge_reinit (const Elem * elem,
                            const unsigned int edge,
                            const Real tolerance = TOLERANCE,
                            const std::vector<Point> * const pts = nullptr,
                            const std::vector<Real> * const weights = nullptr) override;

  virtual void side_map (const Elem * /* elem */,
                         const Elem * /* side */,
                         const unsigned int /* s */,
                         const std::vector<Point> & /* reference_side_points */,
                         std::vector<Point> & /* reference_points */) override
  {
    libmesh_not_implemented();
  }

  virtual void attach_quadrature_rule (QBase * q) override;

  virtual unsigned int n_shape_functions () const override
  { return _n_total_approx_sf; }

  virtual unsigned int n_quadrature_points () const override
  { libmesh_assert(radial_qrule); return _n_total_qp; }


protected:

  // static members used by the workhorses

  static Real eval(Real v,
                   Order o_radial,
                   unsigned int i);

  static Real eval_deriv(Real v,
                         Order o_radial,
                         unsigned int i);



  // Non-static members used by the workhorses

  void update_base_elem (const Elem * inf_elem);

  virtual void init_base_shape_functions(const std::vector<Point> &,
                                         const Elem *) override
  { libmesh_not_implemented(); }

  void init_radial_shape_functions(const Elem * inf_elem,
                                   const std::vector<Point> * radial_pts = nullptr);

  void init_shape_functions(const std::vector<Point> & radial_qp,
                            const std::vector<Point> & base_qp,
                            const Elem * inf_elem);

  void init_face_shape_functions (const std::vector<Point> & qp,
                                  const Elem * side);

  void combine_base_radial(const Elem * inf_elem);

  virtual void compute_shape_functions(const Elem *, const std::vector<Point> &) override;



  // Miscellaneous static members

  static void compute_node_indices (const ElemType inf_elem_type,
                                    const unsigned int outer_node_index,
                                    unsigned int & base_node,
                                    unsigned int & radial_node);

  static void compute_node_indices_fast (const ElemType inf_elem_type,
                                         const unsigned int outer_node_index,
                                         unsigned int & base_node,
                                         unsigned int & radial_node);

  static void compute_shape_indices (const FEType & fet,
                                     const ElemType inf_elem_type,
                                     const unsigned int i,
                                     unsigned int & base_shape,
                                     unsigned int & radial_shape);

  std::vector<Real> dist;

  std::vector<Real> dweightdv;

  std::vector<Real> som;
  std::vector<Real> dsomdv;

  std::vector<std::vector<Real>> mode;

  std::vector<std::vector<Real>> dmodedv;

  std::vector<std::vector<Real>> radial_map;


  std::vector<std::vector<Real>> dradialdv_map;

  std::vector<Real> dphasedxi;

  std::vector<Real> dphasedeta;

  std::vector<Real> dphasedzeta;




  // numbering scheme maps

  std::vector<unsigned int> _radial_node_index;

  std::vector<unsigned int> _base_node_index;

  std::vector<unsigned int> _radial_shape_index;

  std::vector<unsigned int> _base_shape_index;




  // some more protected members

  unsigned int _n_total_approx_sf;

  unsigned int _n_total_qp;

  std::vector<Real> _total_qrule_weights;

  std::unique_ptr<QBase> base_qrule;

  std::unique_ptr<QBase> radial_qrule;

  std::unique_ptr<Elem> base_elem;

  std::unique_ptr<FEBase> base_fe;

  FEType current_fe_type;


private:

  virtual bool shapes_need_reinit() const override;

  static ElemType _compute_node_indices_fast_current_elem_type;


#ifdef DEBUG

  static bool _warned_for_nodal_soln;
  static bool _warned_for_shape;

#endif

  template <unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
  friend class InfFE;

};



// InfFE::Radial class inline members
template <unsigned int Dim, FEFamily T_radial, InfMapType T_map>
inline
Real InfFE<Dim,T_radial,T_map>::Radial::decay(const Real v)
{
  switch (Dim)
    //TODO:[DD] What decay do i have in 2D and 1D?
    {
    case 3:
      return (1.-v)/2.;

    case 2:
      return 0.;

    case 1:
      return 0.;

    default:
      libmesh_error_msg("Invalid Dim = " << Dim);
    }
}

} // namespace libMesh


#endif // ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS


#endif // LIBMESH_INF_FE_H