convergence.cc 8.36 KB
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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:

#ifdef HAVE_CONFIG_H
# include "config.h"
#endif
#include <iostream>
#include <dune/common/parallel/mpihelper.hh> // An initializer of MPI
#include <dune/curvedsurfacegrid/curvedsurfacegrid.hh>
#include <dune/geometry/quadraturerules.hh>
#include <dune/grid/io/file/gmshreader.hh>
#include <dune/localfunctions/lagrange/pk.hh>
//#include <dune/grid/albertagrid.hh>
#include <dune/foamgrid/foamgrid.hh>

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#include <dune/functions/common/differentiablefunctionfromcallables.hh>
#include <dune/functions/gridfunctions/analyticgridviewfunction.hh>

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#define STR(s) STR_HELPER(s)
#define STR_HELPER(s) #s

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const int order = 4;
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const int quad_order = order+5;
const int num_levels = 5;

// Test Hausdorf-distance
template <class Grid, class Projection>
typename Grid::ctype inf_error(Grid const& grid, Projection const& projection)
{
  using QuadProvider = Dune::QuadratureRules<typename Grid::ctype, 2>;
  typename Grid::ctype dist = 0;
  for (auto const& element : elements(grid.leafGridView()))
  {
    auto geometry = element.geometry();

    auto const& quadRule = QuadProvider::rule(element.type(), quad_order);
    for (auto const& qp : quadRule) {
      auto x = geometry.global(qp.position());
      auto y = projection(x);
      dist = std::max(dist, (x - y).two_norm());
    }
  }

  return dist;
}

// Test integrated Hausdorf-distance
template <class Grid, class Projection>
typename Grid::ctype L2_error(Grid const& grid, Projection const& projection)
{
  using QuadProvider = Dune::QuadratureRules<typename Grid::ctype, 2>;
  typename Grid::ctype dist = 0;
  for (auto const& element : elements(grid.leafGridView()))
  {
    auto geometry = element.geometry();

    auto const& quadRule = QuadProvider::rule(element.type(), quad_order);
    for (auto const& qp : quadRule) {
      auto x = geometry.global(qp.position());
      auto y = projection(x);
      dist += (x - y).two_norm2() * qp.weight() * geometry.integrationElement(qp.position());
    }
  }

  return std::sqrt(dist);
}

// Test integrated error in normal vectors
template <class Grid, class Projection>
typename Grid::ctype normal_error(Grid const& grid, Projection const& projection)
{
  using QuadProvider = Dune::QuadratureRules<typename Grid::ctype, 2>;
  typename Grid::ctype dist = 0;
  for (auto const& element : elements(grid.leafGridView()))
  {
    auto geometry = element.geometry();
    auto const& quadRule = QuadProvider::rule(element.type(), quad_order);
    for (auto const& qp : quadRule) {
      auto x = geometry.impl().normal(qp.position());
      auto y = projection(geometry.global(qp.position()));
      if ((y + x).two_norm() < 0.9)
        x *= -1;

      dist += (x - y).two_norm2() * qp.weight() * geometry.integrationElement(qp.position());
    }
  }

  return std::sqrt(dist);
}

// Test integrated error in mean curvature
template <class Grid, class Projection>
typename Grid::ctype curvature_error(Grid const& grid, Projection const& projection)
{
  using GlobalCoordinate = typename Grid::template Codim<0>::Entity::Geometry::GlobalCoordinate;
  using QuadProvider = Dune::QuadratureRules<typename Grid::ctype, 2>;
  using FiniteElementType = Dune::PkLocalFiniteElement<typename Grid::ctype, typename Grid::ctype, 2, order+2>;
  FiniteElementType fe;

  using LBTraits = typename FiniteElementType::Traits::LocalBasisType::Traits;
  std::vector<typename LBTraits::JacobianType> shapeGradients;
  std::vector<GlobalCoordinate> gradients;
  std::vector<GlobalCoordinate> normals;

  typename Grid::ctype dist = 0;
  for (auto const& element : elements(grid.leafGridView()))
  {
    auto geometry = element.geometry();
    auto const& localBasis = fe.localBasis();
    auto const& localInterpolation = fe.localInterpolation();

    auto f = [&](auto const& local) -> GlobalCoordinate
    {
      auto x = geometry.impl().normal(local);
      auto y = projection(geometry.global(local));
      if ((y + x).two_norm() < 0.9)
        x *= -1;
      return x;
    };
    localInterpolation.interpolate(f, normals);

    shapeGradients.resize(localBasis.size());
    gradients.resize(localBasis.size());

    auto const& quadRule = QuadProvider::rule(element.type(), quad_order);
    for (auto const& qp : quadRule) {
      auto jInvT = geometry.jacobianInverseTransposed(qp.position());
      localBasis.evaluateJacobian(qp.position(), shapeGradients);

      for (std::size_t i = 0; i < gradients.size(); ++i)
        jInvT.mv(shapeGradients[i][0], gradients[i]);

      typename Grid::ctype H = 0;
      for (std::size_t i = 0; i < gradients.size(); ++i)
        H += normals[i].dot(gradients[i]);

      dist += std::abs(H - 2) * qp.weight() * geometry.integrationElement(qp.position());
    }
  }

  return dist;
}

// longest edge in the grid
template <class Grid>
typename Grid::ctype edge_length(Grid const& grid)
{
  typename Grid::ctype h = 0;
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  for (auto const& e : edges(grid.hostGrid().leafGridView()))
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    h = std::max(h, e.geometry().volume());

  return h;
}

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// struct Sphere
// {
//   struct DSphere
//   {
//     template <class K, int n>
//     Dune::FieldMatrix<K,n,n> operator() (Dune::FieldVector<K,n> const& x) const
//     {
//       K nrmInv = K(1)/x.two_norm();
//       Dune::FieldMatrix<K,n,n> out;
//       for (int i = 0; i < n; ++i)
//         for (int j = 0; j < n; ++j)
//           out[i][j] = nrmInv * (i == j ? K(1) : K(0)) + x[i] * x[j];
//       return out;
//     }
//   };

//   template <class K, int n>
//   Dune::FieldVector<K,n> operator() (Dune::FieldVector<K,n> const& x) const
//   {
//     return x / x.two_norm();
//   }

//   friend DSphere derivative(Sphere)
//   {
//     return DSphere{};
//   }
// };

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int main(int argc, char** argv)
{
  using namespace Dune;
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  MPIHelper::instance(argc, argv);
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  // using HostGrid = AlbertaGrid<2,3>;
  using HostGrid = FoamGrid<2,3>;
  std::unique_ptr<HostGrid> hostGrid = GmshReader<HostGrid>::read( STR(DUNE_GRID_PATH) "sphere_coarse.msh");

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  using Signature = FieldVector<double,3>(FieldVector<double,3>);
  auto sphere = Functions::makeDifferentiableFunctionFromCallables(
    Functions::SignatureTag<Signature>{},
    [](auto const& x) {
      return x / x.two_norm();
    },
    [](auto const& x) {
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      double nrm = x.two_norm();
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      FieldMatrix<double,3,3> out;
      for (int i = 0; i < 3; ++i)
        for (int j = 0; j < 3; ++j)
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          out[i][j] = ((i == j ? 1 : 0) - (x[i]/nrm) * (x[j]/nrm)) / nrm;
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      return out;
    }
  );
  auto sphereGridFct = Functions::makeAnalyticGridViewFunction(sphere, hostGrid->leafGridView());

  using Grid = CurvedSurfaceGrid<decltype(sphereGridFct)>;
  Grid grid(*hostGrid, sphereGridFct);
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  std::vector<typename Grid::ctype> inf_errors, L2_errors, normal_errors, curvature_errors, edge_lengths;
  for (int i = 0; i < num_levels; ++i) {
    if (i > 0)
      grid.globalRefine(1);

    inf_errors.push_back( inf_error(grid, sphere) );
    L2_errors.push_back( L2_error(grid, sphere) );
    normal_errors.push_back( normal_error(grid, sphere) );
    curvature_errors.push_back( curvature_error(grid, sphere) );
    edge_lengths.push_back( edge_length(grid) );
  }


  std::vector<typename Grid::ctype> eocInf(num_levels, 0), eocL2(num_levels, 0), eocNormal(num_levels, 0), eocCurvature(num_levels, 0);
  for (int i = 1; i < num_levels; ++i) {
    eocInf[i]       = std::log(inf_errors[i]/inf_errors[i-1]) / std::log(edge_lengths[i]/edge_lengths[i-1]);
    eocL2[i]        = std::log(L2_errors[i]/L2_errors[i-1]) / std::log(edge_lengths[i]/edge_lengths[i-1]);
    eocNormal[i]    = std::log(normal_errors[i]/normal_errors[i-1]) / std::log(edge_lengths[i]/edge_lengths[i-1]);
    eocCurvature[i] = std::log(curvature_errors[i]/curvature_errors[i-1]) / std::log(edge_lengths[i]/edge_lengths[i-1]);
  }

  auto print_line = [](auto i, auto const& data) {
    std::cout << i;
    for (auto const& d : data)
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      std::cout << '\t' << "| " << d;
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    std::cout << std::endl;
  };

  auto print_break = [] {
    std::cout.width(8 + 8*16);
    std::cout.fill('-');
    std::cout << '-' << std::endl;
    std::cout.fill(' ');
  };

  std::cout.setf(std::ios::scientific);
  print_line("level", std::vector<std::string>{"err_inf", "eoc_inf", "err_L2", "eoc_L2", "err_norm", "eoc_norm", "err_curv", "eoc_curv"});
  print_break();

  for (int i = 0; i < num_levels; ++i)
    print_line(i, std::vector<double>{inf_errors[i], eocInf[i], L2_errors[i], eocL2[i], normal_errors[i], eocNormal[i], curvature_errors[i], eocCurvature[i]});
}