Domaine_PolyMAC_HFV.cpp

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#include <Linear_algebra_tools_impl.h>
#include <Champ_implementation_P1.h>
#include <Connectivite_som_elem.h>
#include <MD_Vector_composite.h>
#include <Domaine_Cl_PolyMAC_family.h>
#include <MD_Vector_tools.h>
#include <Comm_Group_MPI.h>
#include <communications.h>
#include <Poly_geom_base.h>
#include <Matrix_tools.h>
#include <Domaine_PolyMAC_HFV.h>
#include <unordered_map>
#include <Array_tools.h>
#include <TRUSTLists.h>
#include <PE_Groups.h>
#include <Rectangle.h>
#include <Tetraedre.h>
#include <EFichier.h>
#include <SFichier.h>
#include <Hexaedre.h>
#include <Triangle.h>
#include <Segment.h>
#include <Domaine.h>
#include <Scatter.h>
#include <EChaine.h>
#include <Lapack.h>
#include <unistd.h>
#include <numeric>
#include <cfloat>
#include <vector>
#include <tuple>
#include <cmath>
#include <cfenv>
#include <set>
#include <map>
 
Implemente_instanciable(Domaine_PolyMAC_HFV, "Domaine_PolyMAC_HFV", Domaine_PolyMAC_CDO);
 
Sortie& Domaine_PolyMAC_HFV::printOn(Sortie& os) const { return Domaine_Poly_base::printOn(os); }
 
Entree& Domaine_PolyMAC_HFV::readOn(Entree& is) { return Domaine_Poly_base::readOn(is); }
 
void Domaine_PolyMAC_HFV::discretiser()
{
  Domaine_Poly_base::discretiser();
  // orthocentrer();
  discretiser_aretes();
}
 
void Domaine_PolyMAC_HFV::calculer_volumes_entrelaces()
{
  const double tol_r = 1e-12;
  const IntTab& fsom = face_sommets();
  const DoubleTab& xs = domaine().coord_sommets();
 
  //volumes_entrelaces_ and volumes_entrelaces_dir: by projection of the upstream/downstream element onto the face normal
  for (int f = 0, e; f < nb_faces(); f++)
    {
      const bool axis_face = bidim_axi && (face_voisins_(f, 0) < 0 || face_voisins_(f, 1) < 0) && std::fabs(xv_(f, 0)) <= tol_r;
      double axis_length = 0.;
 
      if (axis_face)
        {
          assert(fsom.dimension(1) == 2);
          const int s0 = fsom(f, 0);
          const int s1 = fsom(f, 1);
          const double dr = xs(s1, 0) - xs(s0, 0);
          const double dz = xs(s1, 1) - xs(s0, 1);
          axis_length = std::sqrt(dr * dr + dz * dz);
        }
 
      for (int i = 0; i < 2 && (e = face_voisins_(f, i)) >= 0; i++)
        {
          volumes_entrelaces_dir_(f, i) = axis_face
                                          ? volume_entrelace_axi(std::fabs(xv_(f, 0)), std::fabs(xp_(e, 0)), axis_length)
                                          : std::fabs(dot(&xp_(e, 0), &face_normales_(f, 0), &xv_(f, 0)));
 
          volumes_entrelaces_(f) += volumes_entrelaces_dir_(f, i);
        }
    }
  volumes_entrelaces_.echange_espace_virtuel(), volumes_entrelaces_dir_.echange_espace_virtuel();
}
 
const DoubleTab& Domaine_PolyMAC_HFV::surf_elem_arete() const
{
  if (surf_elem_arete_.nb_dim() == 2) return surf_elem_arete_; //already done
  int e, f, a, s, sb, i, j, k, d, D = dimension, sgn;
  const IntTab& ea_d = elem_arete_d(), e_f = elem_faces(), &f_s = face_sommets(), &e_a = D < 3 ? e_f : domaine().elem_aretes();//in 2D, edges are faces!
  const DoubleTab& xe = xp(), &xf = xv(), &xs = domaine().coord_sommets();
  surf_elem_arete_.resize(ea_d(nb_elem_tot()), D);
  double vecz[3] = { 0, 0, 1 };
  for (e = 0; e < nb_elem_tot(); e++)
    if (D < 3)
      for (i = 0, j = ea_d(e); j < ea_d(e + 1); i++, j++) //2D: edge <-> face, oriented from the first to the second vertex of f_s
        {
          auto vec = cross(D, 3, &xf(f = e_f(e, i), 0), vecz, &xe(e, 0)); //rotation of (xf - xe)
          for (sgn = dot(&xs(f_s(f, 1), 0), &vec[0], &xs(f_s(f, 0), 0)) > 0 ? 1 : -1, d = 0; d < D; d++) surf_elem_arete_(j, d) = sgn * vec[d]; //with correct orientation
        }
    else for (i = 0; i < e_f.dimension(1) && (f = e_f(e, i)) >= 0; i++)
        for (j = 0; j < f_s.dimension(1) && (s = f_s(f, j)) >= 0; j++) //3D: one contribution per (f, a) pair
          {
            sb = f_s(f, j + 1 < f_s.dimension(1) && f_s(f, j + 1) >= 0 ? j + 1 : 0); //other vertex
            a = som_arete[s].at(sb), k = (int)(std::find(&e_a(e, 0), &e_a(e, 0) + ea_d(e + 1) - ea_d(e), a) - &e_a(e, 0) + ea_d(e)); //edge and its index in e_a
            auto vec = cross(D, D, &xf(f, 0), &xa_(a, 0), &xe(e, 0), &xe(e, 0)); //unoriented
            for (sgn = dot(&vec[0], &ta_(a, 0)) >= 0 ? 1 : -1, d = 0; d < D; d++) surf_elem_arete_(k, d) += sgn * vec[d] / 2;
          }
  return surf_elem_arete_;
}
/* "clamping" to 0 of small coefficients in M1/W1/M2/W2 */
inline void clamp(DoubleTab& m)
{
  for (int i = 0; i < m.dimension(0); i++)
    for (int j = 0; j < m.dimension(1); j++)
      for (int n = 0; n < m.dimension(2); n++)
        if (1e6 * std::abs(m(i, j, n)) < std::abs(m(i, i, n)) + std::abs(m(j, j, n))) m(i, j, n) = 0;
}
 
//dual edge normals -> edge tangentials: (nu|a|t_a.v)   = m1 (S_ea.v)
void Domaine_PolyMAC_HFV::M1(const DoubleTab *nu, int e, DoubleTab& m1) const
{
  const IntTab& e_f = elem_faces(), &f_s = face_sommets(), &e_a = dimension < 3 ? e_f : domaine().elem_aretes(), &a_s = dimension < 3 ? f_s : domaine().aretes_som(), &ea_d = elem_arete_d(); //in 2D, edges are faces!
  const DoubleTab& xs = domaine().coord_sommets(), &S_ea = surf_elem_arete();
  const DoubleVect& ve = volumes();
  int i, j, k, a, s, sb, n, N = nu ? nu->dimension(1) : 1, e_nu = nu && nu->dimension_tot(0) == 1 ? 0 : e, n_a = ea_d(e + 1) - ea_d(e), d, D = dimension, idx;
  double prefac, fac, beta = 1 || n_a == 3 * D - 3 ? 1. / D : D == 2 ? 1. / sqrt(2) : 1. / sqrt(3); //stabilization: DGA on simplices, SUSHI otherwise
  m1.resize(n_a, n_a, N), m1 = 0;
  DoubleTrav v_e(n_a, D), v_ea(n_a, n_a, D); //non-stabilized / stabilized interpolations
  //v_e (non-stabilized interpolation)
  for (i = 0; i < n_a; i++)
    for (a = e_a(e, i), s = a_s(a, 0), sb = a_s(a, 1), d = 0; d < D; d++) v_e(i, d) = (xs(sb, d) - xs(s, d)) / ve(e);
  //v_ea (stabilized interpolation)
  for (i = 0, idx = ea_d(e); i < n_a; i++, idx++)
    for (a = e_a(e, i), s = a_s(a, 0), sb = a_s(a, 1), prefac = D * beta / dot(&xs(sb, 0), &S_ea(idx, 0), &xs(s, 0)), j = 0; j < n_a; j++)
      for (fac = prefac * ((j == i) - dot(&S_ea(idx, 0), &v_e(j, 0))), d = 0; d < D; d++)
        v_ea(i, j, d) = v_e(j, d) + fac * (xs(sb, d) - xs(s, d));
  //matrix!
  for (i = 0; i < n_a; i++)
    for (j = 0; j < n_a; j++)
      if (j < i)
        for (n = 0; n < N; n++) m1(i, j, n) = m1(j, i, n); //below diagonal -> copy from the other side
      else for (k = 0, idx = ea_d(e); k < n_a; k++, idx++)
          for (a = e_a(e, k), s = a_s(a, 0), sb = a_s(a, 1), fac = dot(&xs(sb, 0), &S_ea(idx, 0), &xs(s, 0)) / D, n = 0; n < N; n++)
            m1(i, j, n) += fac * nu_dot(nu, e_nu, n, &v_ea(k, i, 0), &v_ea(k, j, 0));
  clamp(m1);
}
 
//edge tangentials -> dual edge normals: (nuS_ea.v) = w1 (|a|t_a.v)
void Domaine_PolyMAC_HFV::W1(const DoubleTab *nu, int e, DoubleTab& w1, DoubleTab& v_e, DoubleTab& v_ea) const
{
  const IntTab& e_f = elem_faces(), &f_s = face_sommets(), &e_a = dimension < 3 ? e_f : domaine().elem_aretes(), &a_s = dimension < 3 ? f_s : domaine().aretes_som(), &ea_d = elem_arete_d(); //in 2D, edges are faces!
  const DoubleTab& xs = domaine().coord_sommets(), &S_ea = surf_elem_arete();
  const DoubleVect& ve = volumes();
  int i, j, k, a, s, sb, n, N = nu ? nu->dimension(1) : 1, e_nu = nu && nu->dimension_tot(0) == 1 ? 0 : e, n_a = ea_d(e + 1) - ea_d(e), d, D = dimension, idx;
  double prefac, fac, beta = n_a == 3 * D - 3 ? 1. / D : D == 2 ? 1. / sqrt(2) : 1. / sqrt(3); //stabilization: DGA on simplices, SUSHI otherwise
  w1.resize(n_a, n_a, N), w1 = 0, v_e.resize(n_a, D), v_ea.resize(n_a, n_a, D); //non-stabilized / stabilized interpolations
  //v_e (non-stabilized interpolation)
  for (i = 0, idx = ea_d(e); i < n_a; i++, idx++)
    for (d = 0; d < D; d++) v_e(i, d) = S_ea(idx, d) / ve(e);
  //v_ea (stabilized interpolation)
  for (i = 0, idx = ea_d(e); i < n_a; i++, idx++)
    for (a = e_a(e, i), s = a_s(a, 0), sb = a_s(a, 1), prefac = D * beta / dot(&xs(sb, 0), &S_ea(idx, 0), &xs(s, 0)), j = 0; j < n_a; j++)
      for (fac = prefac * ((j == i) - dot(&xs(sb, 0), &v_e(j, 0), &xs(s, 0))), d = 0; d < D; d++)
        v_ea(i, j, d) = v_e(j, d) + fac * S_ea(idx, d);
  //matrix!
  for (i = 0; i < n_a; i++)
    for (j = 0; j < n_a; j++)
      if (j < i)
        for (n = 0; n < N; n++) w1(i, j, n) = w1(j, i, n); //below diagonal -> copy from the other side
      else for (k = 0, idx = ea_d(e); k < n_a; k++, idx++)
          for (a = e_a(e, k), s = a_s(a, 0), sb = a_s(a, 1), fac = dot(&xs(sb, 0), &S_ea(idx, 0), &xs(s, 0)) / D, n = 0; n < N; n++)
            w1(i, j, n) += fac * nu_dot(nu, e_nu, n, &v_ea(k, i, 0), &v_ea(k, j, 0));
  clamp(w1);
}