inf_fe.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 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"
#include "libmesh/inf_fe_map.h"
 
// C++ includes
#include <cstddef>
 
namespace libMesh
{
 
 
// forward declarations
class Elem;
class FEComputeData;
 
 
class InfFERadial
{
private:
 
  InfFERadial() {}
 
public:
 
  static Real decay (const unsigned int dim, const Real v);
 
  static Real decay_deriv (const unsigned int dim, const Real);
 
  static Real D (const Real v) { return (1.-v)*(1.-v)/4.; }
 
  static Real Dxr_sq (const Real /*v*/) { return 1.; }
 
  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 InfFEBase
{
private:
 
  InfFEBase() {}
 
public:
 
  static std::unique_ptr<const Elem> build_elem (const Elem * inf_elem);
 
  static ElemType get_elem_type (const ElemType type);
 
  static unsigned int n_base_mapping_sf (const Elem & base_elem,
                                         const Order base_mapping_order);
 
};
 
 
 
template <unsigned int Dim, FEFamily T_radial, InfMapType T_map>
class InfFE : public FEBase
{
 
  /*
   * Protect the nested class
   */
protected:
 
 
public:
 
  // InfFE continued
 
  explicit
  InfFE(const FEType & fet);
  ~InfFE() = default;
 
  // 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 Real shape(const FEType fet,
                    const Elem * elem,
                    const unsigned int i,
                    const Point & p,
                    const bool add_p_level);
 
  static Real shape_deriv (const FEType & fet,
                           const Elem * inf_elem,
                           const unsigned int i,
                           const unsigned int j,
                           const Point & p);
 
  static Real shape_deriv (const FEType fet,
                           const Elem * inf_elem,
                           const unsigned int i,
                           const unsigned int j,
                           const Point & p,
                           const bool add_p_level);
 
  static Real shape_deriv (const FEType & fet,
                           const ElemType inf_elem_type,
                           const unsigned int i,
                           const unsigned int j,
                           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 Elem * inf_elem)
  { return n_dofs(fet, inf_elem); }
 
  static unsigned int n_dofs(const FEType & fet,
                             const Elem * inf_elem);
 
#ifdef LIBMESH_ENABLE_DEPRECATED
  static unsigned int n_dofs_at_node(const FEType & fet,
                                     const ElemType inf_elem_type,
                                     const unsigned int n);
#endif // LIBMESH_ENABLE_DEPRECATED
 
  static unsigned int n_dofs_at_node(const FEType & fet,
                                     const Elem * inf_elem,
                                     const unsigned int n);
 
#ifdef LIBMESH_ENABLE_DEPRECATED
  static unsigned int n_dofs_per_elem(const FEType & fet,
                                      const ElemType inf_elem_type);
#endif // LIBMESH_ENABLE_DEPRECATED
 
  static unsigned int n_dofs_per_elem(const FEType & fet,
                                      const Elem * inf_elem);
 
  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)
  {
    // libmesh_deprecated(); // soon
    return InfFEMap::map(Dim, inf_elem, reference_point);
  }
 
 
  static Point inverse_map (const Elem * elem,
                            const Point & p,
                            const Real tolerance = TOLERANCE,
                            const bool secure = true)
  {
    // libmesh_deprecated(); // soon
    return InfFEMap::inverse_map(Dim, elem, p, tolerance, secure);
  }
 
 
  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)
  {
    // libmesh_deprecated(); // soon
    return InfFEMap::inverse_map(Dim, elem, physical_points,
                                 reference_points, tolerance, secure);
  }
 
 
  // 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 * inf_elem,
                       const unsigned int s,
                       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 this->_n_total_qp; }
 
  virtual const std::vector<Point> & get_xyz () const override
  { libmesh_assert(!calculations_started || calculate_xyz);
    calculate_xyz = true; return xyz; }
 
  virtual const std::vector<Real> & get_JxW () const override
  {
    libmesh_assert(!calculations_started || calculate_jxw);
    calculate_jxw = true;
    return this->JxW;
  }
 
  virtual const std::vector<Real> & get_JxWxdecay_sq () const override
  { libmesh_assert(!calculations_started || calculate_map_scaled);
    calculate_map_scaled = true; return this->JxWxdecay;}
 
 
  virtual const std::vector<std::vector<OutputShape>> & get_phi_over_decayxR () const override
  { libmesh_assert(!calculations_started || calculate_phi_scaled);
    calculate_phi_scaled = true; return phixr; }
 
 
  virtual const std::vector<std::vector<OutputGradient>> & get_dphi_over_decayxR () const override
  { libmesh_assert(!calculations_started || calculate_dphi_scaled);
    calculate_dphi_scaled = true; return dphixr; }
 
 
  virtual const std::vector<std::vector<OutputGradient>> & get_dphi_over_decay () const override
  { libmesh_assert(!calculations_started || calculate_dphi_scaled);
    calculate_dphi_scaled = true; return dphixr_sq; }
 
 
  virtual const std::vector<RealGradient> & get_dxyzdxi() const override
  { calculate_map = true; libmesh_not_implemented();}
 
 
  virtual const std::vector<RealGradient> & get_dxyzdeta() const override
  { calculate_map = true; libmesh_not_implemented();}
 
 
  virtual const std::vector<RealGradient> & get_dxyzdzeta() const override
  { calculate_map = true; libmesh_not_implemented();}
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  virtual const std::vector<RealGradient> & get_d2xyzdxi2() const override
  { calculate_map = true; libmesh_not_implemented();}
  virtual const std::vector<RealGradient> & get_d2xyzdeta2() const override
  { calculate_map = true; libmesh_not_implemented();}
  virtual const std::vector<RealGradient> & get_d2xyzdzeta2() const override
  { calculate_map = true; libmesh_not_implemented();}
  virtual const std::vector<RealGradient> & get_d2xyzdxideta() const override
  { calculate_map = true; libmesh_not_implemented();}
  virtual const std::vector<RealGradient> & get_d2xyzdxidzeta() const override
  { calculate_map = true; libmesh_not_implemented();}
  virtual const std::vector<RealGradient> & get_d2xyzdetadzeta() const override
  { calculate_map = true; libmesh_not_implemented();}
#endif
 
  virtual const std::vector<Real> & get_dxidx() const override
  {libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dxidx_map;}
 
 
  virtual const std::vector<Real> & get_dxidy() const override
  {libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dxidy_map;}
 
 
  virtual const std::vector<Real> & get_dxidz() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dxidz_map;}
 
 
  virtual const std::vector<Real> & get_detadx() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return detadx_map;}
 
 
  virtual const std::vector<Real> & get_detady() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return detady_map;}
 
 
  virtual const std::vector<Real> & get_detadz() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return detadz_map;}
 
 
  virtual const std::vector<Real> & get_dzetadx() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dzetadx_map;}
 
 
  virtual const std::vector<Real> & get_dzetady() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dzetady_map;}
 
 
  virtual const std::vector<Real> & get_dzetadz() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return dzetadz_map;}
 
 
  virtual const std::vector<Real> & get_Sobolev_weight() const override
  { libmesh_assert(!calculations_started || calculate_phi);
    calculate_phi = true; return weight; }
 
 
  virtual const std::vector<RealGradient> & get_Sobolev_dweight() const override
  {libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = true; return dweight; }
 
 
 
  virtual const std::vector<std::vector<Point>> & get_tangents() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return tangents; }
 
  virtual const std::vector<Point> & get_normals() const override
  { libmesh_assert(!calculations_started || calculate_map);
    calculate_map = true; return normals; }
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  virtual const std::vector<Real> & get_curvatures() const override
  { calculate_map = true; libmesh_not_implemented();}
#endif
 
  virtual const std::vector<Real> & get_Sobolev_weightxR_sq() const override
  { libmesh_assert(!calculations_started || calculate_phi_scaled);
    calculate_phi_scaled = true; return weightxr_sq; }
 
 
  virtual const std::vector<RealGradient> & get_Sobolev_dweightxR_sq() const override
  {libmesh_assert(!calculations_started || calculate_dphi_scaled);
    calculate_dphi_scaled = true; return dweightxr_sq; }
 
 
#ifdef LIBMESH_ENABLE_AMR
 
  static void inf_compute_constraints (DofConstraints & constraints,
                                       DofMap & dof_map,
                                       const unsigned int variable_number,
                                       const Elem * child_elem);
#endif
 
#ifdef LIBMESH_ENABLE_NODE_CONSTRAINTS
  static void inf_compute_node_constraints (NodeConstraints & constraints,
                                            const Elem * elem);
#endif
 
 
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(); }
 
  virtual void determine_calculations() override;
 
  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> &,
                                  const Elem * inf_side);
 
  void compute_shape_functions(const Elem * inf_elem,
                               const std::vector<Point> & base_qp,
                               const std::vector<Point> & radial_qp);
 
  void compute_face_functions();
 
  virtual void compute_shape_functions(const Elem *, const std::vector<Point> & ) override
  {
    //FIXME: it seems this function cannot be left out because
    // it is pure virtual in \p FEBase
    libmesh_not_implemented();
  }
 
  mutable bool calculate_map_scaled;
 
  mutable bool calculate_phi_scaled;
 
  mutable bool calculate_dphi_scaled;
 
 
  mutable bool calculate_xyz;
 
 
  mutable bool calculate_jxw;
 
  // 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);
 
#ifdef LIBMESH_ENABLE_DEPRECATED
  /*
   * \deprecated Call the version of this function that takes an Elem * instead.
   */
  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);
#endif // LIBMESH_ENABLE_DEPRECATED
 
  static void compute_shape_indices (const FEType & fet,
                                     const Elem * inf_elem,
                                     const unsigned int i,
                                     unsigned int & base_shape,
                                     unsigned int & radial_shape);
 
  std::vector<Point> xyz;
 
  std::vector<Real> weightxr_sq;
  std::vector<Real> dweightdv;
 
  std::vector<RealGradient> dweightxr_sq;
 
  std::vector<Real> som;
  std::vector<Real> dsomdv;
 
  std::vector<std::vector<Real>> mode;
 
  std::vector<std::vector<Real>> dmodedv;
 
  // mapping of reference element to physical element
  // These vectors usually belong to \p this->fe_map
  // but for infinite elements, \p FEMap cannot
  // compute them.
  std::vector<Real> dxidx_map;
  std::vector<Real> dxidy_map;
  std::vector<Real> dxidz_map;
  std::vector<Real> detadx_map;
  std::vector<Real> detady_map;
  std::vector<Real> detadz_map;
  std::vector<Real> dzetadx_map;
  std::vector<Real> dzetady_map;
  std::vector<Real> dzetadz_map;
 
  // scaled mapping: Similar to the above
  // vectors, but scaled by radial (infinite) coordinate.
  std::vector<Real> dxidx_map_scaled;
  std::vector<Real> dxidy_map_scaled;
  std::vector<Real> dxidz_map_scaled;
  std::vector<Real> detadx_map_scaled;
  std::vector<Real> detady_map_scaled;
  std::vector<Real> detadz_map_scaled;
  std::vector<Real> dzetadx_map_scaled;
  std::vector<Real> dzetady_map_scaled;
  std::vector<Real> dzetadz_map_scaled;
 
 
  // respectively weighted shape functions.
  //FIXME: these names are correct only in 3D
  //      but avoid long and clumbsy names...
  std::vector<std::vector<Real>> phixr;
  std::vector<std::vector<RealGradient>> dphixr;
  std::vector<std::vector<RealGradient>> dphixr_sq;
 
  std::vector<Real> JxWxdecay;
  std::vector<Real> JxW;
 
  std::vector<Point> normals;
  std::vector<std::vector<Point>> tangents;
 
  // 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;
 
  std::vector<Real> _total_qrule_weights;
 
  std::unique_ptr<QBase> base_qrule;
 
  std::unique_ptr<QBase> radial_qrule;
 
  std::unique_ptr<const 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;
  static bool _warned_for_dshape;
 
#endif
 
  template <unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
  friend class InfFE;
 
  friend class InfFEMap;
};
 
 
 
// InfFERadial class inline members
// FIXME: decay in 3D is a/r
//   thus, this function fixes the mapping v<->r explicitly.
//   This is consistent with the current InfFEMap, which, however, is
//   written such that more general mappings can be implemented.
inline
Real InfFERadial::decay(const unsigned int dim, const Real v)
{
  switch (dim)
    {
    case 3:
      return (1.-v)/2.;
 
    case 2:
      // according to P. Bettess "Infinite Elements",
      // the 2D case is rather tricky:
      //  - the sqrt() requires special integration rules
      //    if not both trial- and test function are involved
      //  - the analytic solutions contain not only the sqrt, but
      //    also a polynomial with rather many terms, so convergence
      //    might be bad.
      return sqrt((1.-v)/2.);
 
    case 1:
      return 1.;
 
    default:
      libmesh_error_msg("Invalid dim = " << dim);
    }
}
 
inline
Real InfFERadial::decay_deriv (const unsigned int dim, const Real v)
{
  switch (dim)
    {
    case 3:
      return -0.5;
 
    case 2:
      // according to P. Bettess "Infinite Elements",
      // the 2D case is rather tricky:
      //  - the sqrt() requires special integration rules
      //    if not both trial- and test function are involved
      //  - the analytic solutions contain not only the sqrt, but
      //    also a polynomial with rather many terms, so convergence
      //    might be bad.
 
      libmesh_assert (-1.-1.e-5 <= v && v < 1.);
      return -0.25/sqrt(1.-v);
 
    case 1:
      return 0.;
 
    default:
      libmesh_error_msg("Invalid dim = " << dim);
    }
}
 
} // namespace libMesh
 
 
#endif // ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
 
 
#endif // LIBMESH_INF_FE_H