getfem_convect.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
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/**@file getfem_convect.h
   @author Yves Renard <[email protected]>,
   @date October 27, 2009.
   @brief Compute the convection of a quantity with respect to a vector field.
*/
#ifndef GETFEM_CONVECT_H__
#define GETFEM_CONVECT_H__
 
#include "getfem_mesh_fem.h"
#include "getfem_interpolation.h"
#include "gmm/gmm_dense_qr.h"
 
namespace getfem {
 
  enum convect_boundary_option { CONVECT_EXTRAPOLATION, CONVECT_UNCHANGED, CONVECT_PERIODICITY };
 
  /** Compute the convection of a quantity on a getfem::mesh_fem with respect
      to a velocity field
      @param mf the source mesh_fem. Should be of Lagrange type.
      @param U the source field.
      @param mf_v the mesh_fem on which the vector field is described
      @param V contains the vector field described on mf_v.
      @param nt number of time integration step.
      @param option concerns the entrant boundary.
      @param per_min, per_max : the periodicity box for the PERIODICITY option
  */
  template<class VECT1, class VECT2>
  void convect(const mesh_fem &mf, VECT1 &U, const mesh_fem &mf_v,
               const VECT2 &V, scalar_type dt, size_type nt,
               convect_boundary_option option = CONVECT_EXTRAPOLATION,
               const base_node &per_min = base_node(),
               const base_node &per_max = base_node()) {
    // Should be robustified on the boundaries -> control of the nodes going
    //   out the mesh.
    // Should control that the point do not move to fast ( < h/2 for instance).
    // Could be extended to non-lagragian fem with a projection (moving the 
    //   gauss points).
    // Can take into account a source term by integration on the
    //   characteristics.
 
    typedef typename gmm::linalg_traits<VECT1>::value_type T;
    int extra = (option == CONVECT_EXTRAPOLATION) ? 2 : 0;
 
    if (nt == 0) return;
 
    GMM_ASSERT1(!(mf.is_reduced()),
                "This convection algorithm work only on pure Lagrange fems");
    /* test if mf is really of Lagrange type.         */
    for (dal::bv_visitor cv(mf.convex_index()); !cv.finished();++cv) {
      pfem pf_t = mf.fem_of_element(cv);
      GMM_ASSERT1(pf_t->target_dim() == 1 && pf_t->is_lagrange(),
                  "This convection algorithm work only on pure Lagrange fems");
    }
 
    // Get the nodes of mf
    const mesh &msh(mf.linked_mesh());
    size_type N = msh.dim();
    if (option == CONVECT_PERIODICITY)
      GMM_ASSERT1(per_min.size() == N && per_max.size() == N,
                  "Wrong size of box extremity for PERIODICITY option");
 
    getfem::mesh_trans_inv mti(msh, 1E-10);
    size_type qdim = mf.get_qdim();
    size_type nbpts = mf.nb_basic_dof() / qdim;
    std::vector<base_node> nodes(nbpts);
    for (size_type i = 0; i < nbpts; ++i)
      nodes[i] = mf.point_of_basic_dof(i * qdim);
 
    // Obtain the first interpolation of v (same mesh)
    size_type qqdimt = (gmm::vect_size(V) / mf_v.nb_dof()) * mf_v.get_qdim();
    GMM_ASSERT1(qqdimt == N, "The velocity field should be a vector field "
               "of the same dimension as the mesh");
    std::vector<T> VI(nbpts*N);
    getfem::interpolation(mf_v, mf, V, VI);
 
    // Convect the nodes with respect to v
    scalar_type ddt = dt / scalar_type(nt);
    for (size_type i = 0; i < nt; ++i) {
      if (i > 0) {
        mti.clear();
        mti.add_points(nodes);
        gmm::clear(VI);
        dal::bit_vector dof_untouched; 
        interpolation(mf_v, mti, V, VI, extra, &dof_untouched);
        for (dal::bv_visitor j(dof_untouched); !j.finished();++j)
          VI[j] = V[j]; 
      }
 
      for (size_type j = 0; j < nbpts; ++j) {
        gmm::add(gmm::scaled(gmm::sub_vector(VI, gmm::sub_interval(N*j, N)),
                             -ddt), nodes[j]);
        if (option == CONVECT_PERIODICITY) {
          for (size_type k = 0; k < N; ++k) 
            if (per_max[k] > per_min[k]) {
              while (nodes[j][k] > per_max[k]) nodes[j][k] -= per_max[k];
              while (nodes[j][k] < per_min[k]) nodes[j][k] += per_max[k];
            }
        }
      }
    }
 
    // 3 final interpolation
    std::vector<T> UI(nbpts*qdim);
    mti.clear();
    mti.add_points(nodes);
    dal::bit_vector dof_untouched; 
    interpolation(mf, mti, U, UI, extra, &dof_untouched);
    for (dal::bv_visitor i(dof_untouched); !i.finished();++i)
      UI[i] = U[i];    
    gmm::copy(UI, U);
  }
 
 
}
 
 
#endif