polynomials_raviart_thomas.cc

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//
// Copyright (C) 2004 - 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/polynomials_raviart_thomas.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/thread_management.h>

#include <iomanip>
#include <iostream>

// TODO[WB]: This class is not thread-safe: it uses mutable member variables
// that contain temporary state. this is not what one would want when one uses a
// finite element object in a number of different contexts on different threads:
// finite element objects should be stateless
// TODO:[GK] This can be achieved by writing a function in Polynomial space
// which does the rotated fill performed below and writes the data into the
// right data structures. The same function would be used by Nedelec
// polynomials.

DEAL_II_NAMESPACE_OPEN


template <int dim>
PolynomialsRaviartThomas<dim>::PolynomialsRaviartThomas(const unsigned int k)
  : my_degree(k)
  , polynomial_space(create_polynomials(k))
  , n_pols(compute_n_pols(k))
{}



template <int dim>
std::vector<std::vector<Polynomials::Polynomial<double>>>
PolynomialsRaviartThomas<dim>::create_polynomials(const unsigned int k)
{
  std::vector<std::vector<Polynomials::Polynomial<double>>> pols(dim);
  pols[0] = Polynomials::LagrangeEquidistant::generate_complete_basis(k + 1);
  if (k == 0)
    for (unsigned int d = 1; d < dim; ++d)
      pols[d] = Polynomials::Legendre::generate_complete_basis(0);
  else
    for (unsigned int d = 1; d < dim; ++d)
      pols[d] = Polynomials::LagrangeEquidistant::generate_complete_basis(k);

  return pols;
}


template <int dim>
void
PolynomialsRaviartThomas<dim>::compute(
  const Point<dim> &           unit_point,
  std::vector<Tensor<1, dim>> &values,
  std::vector<Tensor<2, dim>> &grads,
  std::vector<Tensor<3, dim>> &grad_grads,
  std::vector<Tensor<4, dim>> &third_derivatives,
  std::vector<Tensor<5, dim>> &fourth_derivatives) const
{
  Assert(values.size() == n_pols || values.size() == 0,
         ExcDimensionMismatch(values.size(), n_pols));
  Assert(grads.size() == n_pols || grads.size() == 0,
         ExcDimensionMismatch(grads.size(), n_pols));
  Assert(grad_grads.size() == n_pols || grad_grads.size() == 0,
         ExcDimensionMismatch(grad_grads.size(), n_pols));
  Assert(third_derivatives.size() == n_pols || third_derivatives.size() == 0,
         ExcDimensionMismatch(third_derivatives.size(), n_pols));
  Assert(fourth_derivatives.size() == n_pols || fourth_derivatives.size() == 0,
         ExcDimensionMismatch(fourth_derivatives.size(), n_pols));

  // have a few scratch
  // arrays. because we don't want to
  // re-allocate them every time this
  // function is called, we make them
  // static. however, in return we
  // have to ensure that the calls to
  // the use of these variables is
  // locked with a mutex. if the
  // mutex is removed, several tests
  // (notably
  // deal.II/create_mass_matrix_05)
  // will start to produce random
  // results in multithread mode
  static Threads::Mutex       mutex;
  std::lock_guard<std::mutex> lock(mutex);

  static std::vector<double>         p_values;
  static std::vector<Tensor<1, dim>> p_grads;
  static std::vector<Tensor<2, dim>> p_grad_grads;
  static std::vector<Tensor<3, dim>> p_third_derivatives;
  static std::vector<Tensor<4, dim>> p_fourth_derivatives;

  const unsigned int n_sub = polynomial_space.n();
  p_values.resize((values.size() == 0) ? 0 : n_sub);
  p_grads.resize((grads.size() == 0) ? 0 : n_sub);
  p_grad_grads.resize((grad_grads.size() == 0) ? 0 : n_sub);
  p_third_derivatives.resize((third_derivatives.size() == 0) ? 0 : n_sub);
  p_fourth_derivatives.resize((fourth_derivatives.size() == 0) ? 0 : n_sub);

  for (unsigned int d = 0; d < dim; ++d)
    {
      // First we copy the point. The
      // polynomial space for
      // component d consists of
      // polynomials of degree k+1 in
      // x_d and degree k in the
      // other variables. in order to
      // simplify this, we use the
      // same AnisotropicPolynomial
      // space and simply rotate the
      // coordinates through all
      // directions.
      Point<dim> p;
      for (unsigned int c = 0; c < dim; ++c)
        p(c) = unit_point((c + d) % dim);

      polynomial_space.compute(p,
                               p_values,
                               p_grads,
                               p_grad_grads,
                               p_third_derivatives,
                               p_fourth_derivatives);

      for (unsigned int i = 0; i < p_values.size(); ++i)
        values[i + d * n_sub][d] = p_values[i];

      for (unsigned int i = 0; i < p_grads.size(); ++i)
        for (unsigned int d1 = 0; d1 < dim; ++d1)
          grads[i + d * n_sub][d][(d1 + d) % dim] = p_grads[i][d1];

      for (unsigned int i = 0; i < p_grad_grads.size(); ++i)
        for (unsigned int d1 = 0; d1 < dim; ++d1)
          for (unsigned int d2 = 0; d2 < dim; ++d2)
            grad_grads[i + d * n_sub][d][(d1 + d) % dim][(d2 + d) % dim] =
              p_grad_grads[i][d1][d2];

      for (unsigned int i = 0; i < p_third_derivatives.size(); ++i)
        for (unsigned int d1 = 0; d1 < dim; ++d1)
          for (unsigned int d2 = 0; d2 < dim; ++d2)
            for (unsigned int d3 = 0; d3 < dim; ++d3)
              third_derivatives[i + d * n_sub][d][(d1 + d) % dim]
                               [(d2 + d) % dim][(d3 + d) % dim] =
                                 p_third_derivatives[i][d1][d2][d3];

      for (unsigned int i = 0; i < p_fourth_derivatives.size(); ++i)
        for (unsigned int d1 = 0; d1 < dim; ++d1)
          for (unsigned int d2 = 0; d2 < dim; ++d2)
            for (unsigned int d3 = 0; d3 < dim; ++d3)
              for (unsigned int d4 = 0; d4 < dim; ++d4)
                fourth_derivatives[i + d * n_sub][d][(d1 + d) % dim]
                                  [(d2 + d) % dim][(d3 + d) % dim]
                                  [(d4 + d) % dim] =
                                    p_fourth_derivatives[i][d1][d2][d3][d4];
    }
}


template <int dim>
unsigned int
PolynomialsRaviartThomas<dim>::compute_n_pols(unsigned int k)
{
  if (dim == 1)
    return k + 1;
  if (dim == 2)
    return 2 * (k + 1) * (k + 2);
  if (dim == 3)
    return 3 * (k + 1) * (k + 1) * (k + 2);

  Assert(false, ExcNotImplemented());
  return 0;
}


template class PolynomialsRaviartThomas<1>;
template class PolynomialsRaviartThomas<2>;
template class PolynomialsRaviartThomas<3>;


DEAL_II_NAMESPACE_CLOSE