mapping_q_eulerian.cc

// ---------------------------------------------------------------------
//
// Copyright (C) 2001 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, 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.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
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#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/std_cxx14/memory.h>
#include <deal.II/base/utilities.h>

#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_handler.h>

#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_tools.h>
#include <deal.II/fe/mapping_q1_eulerian.h>
#include <deal.II/fe/mapping_q_eulerian.h>

#include <deal.II/grid/tria_iterator.h>

#include <deal.II/lac/block_vector.h>
#include <deal.II/lac/la_parallel_block_vector.h>
#include <deal.II/lac/la_parallel_vector.h>
#include <deal.II/lac/la_vector.h>
#include <deal.II/lac/petsc_block_vector.h>
#include <deal.II/lac/petsc_vector.h>
#include <deal.II/lac/trilinos_parallel_block_vector.h>
#include <deal.II/lac/trilinos_vector.h>
#include <deal.II/lac/vector.h>

DEAL_II_NAMESPACE_OPEN



// .... MAPPING Q EULERIAN CONSTRUCTOR

template <int dim, class VectorType, int spacedim>
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerianGeneric::
  MappingQEulerianGeneric(
    const unsigned int                                 degree,
    const MappingQEulerian<dim, VectorType, spacedim> &mapping_q_eulerian)
  : MappingQGeneric<dim, spacedim>(degree)
  , mapping_q_eulerian(mapping_q_eulerian)
  , support_quadrature(degree)
  , fe_values(mapping_q_eulerian.euler_dof_handler->get_fe(),
              support_quadrature,
              update_values | update_quadrature_points)
{}



template <int dim, class VectorType, int spacedim>
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerian(
  const unsigned int               degree,
  const DoFHandler<dim, spacedim> &euler_dof_handler,
  const VectorType &               euler_vector,
  const unsigned int               level)
  : MappingQ<dim, spacedim>(degree, true)
  , euler_vector(&euler_vector)
  , euler_dof_handler(&euler_dof_handler)
  , level(level)
{
  // reset the q1 mapping we use for interior cells (and previously
  // set by the MappingQ constructor) to a MappingQ1Eulerian with the
  // current vector
  this->q1_mapping =
    std::make_shared<MappingQ1Eulerian<dim, VectorType, spacedim>>(
      euler_dof_handler, euler_vector);

  // also reset the qp mapping pointer with our own class
  this->qp_mapping = std::make_shared<MappingQEulerianGeneric>(degree, *this);
}



template <int dim, class VectorType, int spacedim>
std::unique_ptr<Mapping<dim, spacedim>>
MappingQEulerian<dim, VectorType, spacedim>::clone() const
{
  return std_cxx14::make_unique<MappingQEulerian<dim, VectorType, spacedim>>(
    this->get_degree(), *euler_dof_handler, *euler_vector);
}



// .... SUPPORT QUADRATURE CONSTRUCTOR

template <int dim, class VectorType, int spacedim>
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerianGeneric::
  SupportQuadrature::SupportQuadrature(const unsigned int map_degree)
  : Quadrature<dim>(Utilities::fixed_power<dim>(map_degree + 1))
{
  // first we determine the support points on the unit cell in lexicographic
  // order, which are (in accordance with MappingQ) the support points of
  // QGaussLobatto.
  const QGaussLobatto<dim> q_iterated(map_degree + 1);
  const unsigned int       n_q_points = q_iterated.size();

  // we then need to define a renumbering vector that allows us to go from a
  // lexicographic numbering scheme to a hierarchic one.  this fragment is
  // taking almost verbatim from the MappingQ class.
  std::vector<unsigned int> renumber(n_q_points);
  std::vector<unsigned int> dpo(dim + 1, 1U);
  for (unsigned int i = 1; i < dpo.size(); ++i)
    dpo[i] = dpo[i - 1] * (map_degree - 1);

  FETools::lexicographic_to_hierarchic_numbering(
    FiniteElementData<dim>(dpo, 1, map_degree), renumber);

  // finally we assign the quadrature points in the required order.
  for (unsigned int q = 0; q < n_q_points; ++q)
    this->quadrature_points[renumber[q]] = q_iterated.point(q);
}



// .... COMPUTE MAPPING SUPPORT POINTS

template <int dim, class VectorType, int spacedim>
std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell>
MappingQEulerian<dim, VectorType, spacedim>::get_vertices(
  const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
{
  // get the vertices as the first 2^dim mapping support points
  const std::vector<Point<spacedim>> a =
    dynamic_cast<const MappingQEulerianGeneric &>(*this->qp_mapping)
      .compute_mapping_support_points(cell);

  std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell>
    vertex_locations;
  std::copy(a.begin(),
            a.begin() + GeometryInfo<dim>::vertices_per_cell,
            vertex_locations.begin());

  return vertex_locations;
}



template <int dim, class VectorType, int spacedim>
std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell>
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerianGeneric::
  get_vertices(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
{
  return mapping_q_eulerian.get_vertices(cell);
}



template <int dim, class VectorType, int spacedim>
bool
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerianGeneric::
  preserves_vertex_locations() const
{
  return false;
}



template <int dim, class VectorType, int spacedim>
std::vector<Point<spacedim>>
MappingQEulerian<dim, VectorType, spacedim>::MappingQEulerianGeneric::
  compute_mapping_support_points(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
{
  const bool mg_vector =
    mapping_q_eulerian.level != numbers::invalid_unsigned_int;

  const types::global_dof_index n_dofs =
    mg_vector ?
      mapping_q_eulerian.euler_dof_handler->n_dofs(mapping_q_eulerian.level) :
      mapping_q_eulerian.euler_dof_handler->n_dofs();
  const types::global_dof_index vector_size =
    mapping_q_eulerian.euler_vector->size();

  (void)n_dofs;
  (void)vector_size;

  AssertDimension(vector_size, n_dofs);

  // we then transform our tria iterator into a dof iterator so we can access
  // data not associated with triangulations
  typename DoFHandler<dim, spacedim>::cell_iterator dof_cell(
    *cell, mapping_q_eulerian.euler_dof_handler);

  Assert(mg_vector || dof_cell->active() == true, ExcInactiveCell());

  // our quadrature rule is chosen so that each quadrature point corresponds
  // to a support point in the undeformed configuration. We can then query
  // the given displacement field at these points to determine the shift
  // vector that maps the support points to the deformed configuration.

  // We assume that the given field contains dim displacement components, but
  // that there may be other solution components as well (e.g. pressures).
  // this class therefore assumes that the first dim components represent the
  // actual shift vector we need, and simply ignores any components after
  // that. This implies that the user should order components appropriately,
  // or create a separate dof handler for the displacements.
  const unsigned int n_support_pts = support_quadrature.size();
  const unsigned int n_components =
    mapping_q_eulerian.euler_dof_handler->get_fe(0).n_components();

  Assert(n_components >= spacedim,
         ExcDimensionMismatch(n_components, spacedim));

  std::vector<Vector<typename VectorType::value_type>> shift_vector(
    n_support_pts, Vector<typename VectorType::value_type>(n_components));

  std::vector<types::global_dof_index> dof_indices(
    mapping_q_eulerian.euler_dof_handler->get_fe(0).dofs_per_cell);
  // fill shift vector for each support point using an fe_values object. make
  // sure that the fe_values variable isn't used simultaneously from different
  // threads
  Threads::Mutex::ScopedLock lock(fe_values_mutex);
  fe_values.reinit(dof_cell);
  if (mg_vector)
    {
      dof_cell->get_mg_dof_indices(dof_indices);
      fe_values.get_function_values(*mapping_q_eulerian.euler_vector,
                                    dof_indices,
                                    shift_vector);
    }
  else
    fe_values.get_function_values(*mapping_q_eulerian.euler_vector,
                                  shift_vector);

  // and finally compute the positions of the support points in the deformed
  // configuration.
  std::vector<Point<spacedim>> a(n_support_pts);
  for (unsigned int q = 0; q < n_support_pts; ++q)
    {
      a[q] = fe_values.quadrature_point(q);
      for (unsigned int d = 0; d < spacedim; ++d)
        a[q](d) += shift_vector[q](d);
    }

  return a;
}



template <int dim, class VectorType, int spacedim>
CellSimilarity::Similarity
MappingQEulerian<dim, VectorType, spacedim>::fill_fe_values(
  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
  const CellSimilarity::Similarity,
  const Quadrature<dim> &                                  quadrature,
  const typename Mapping<dim, spacedim>::InternalDataBase &internal_data,
  internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
    &output_data) const
{
  // call the function of the base class, but ignoring
  // any potentially detected cell similarity between
  // the current and the previous cell
  MappingQ<dim, spacedim>::fill_fe_values(cell,
                                          CellSimilarity::invalid_next_cell,
                                          quadrature,
                                          internal_data,
                                          output_data);
  // also return the updated flag since any detected
  // similarity wasn't based on the mapped field, but
  // the original vertices which are meaningless
  return CellSimilarity::invalid_next_cell;
}



// explicit instantiations
#include "mapping_q_eulerian.inst"


DEAL_II_NAMESPACE_CLOSE