virtual std::vector<Point<spacedim>>
compute_mapping_support_points(
const typename Triangulation<dim, spacedim>::cell_iterator &cell) const;
+
+private:
+ Table<2, double> mapping_support_point_weights;
};
class Mapping;
template <int dim>
class Quadrature;
+template <int dim>
+class ScalarPolynomialsBase;
#endif
/**
switch (i)
{
case 0:
- return 1.0 - xi[0] - xi[1];
+ return 1.0 - xi[std::min(0, dim - 1)] - xi[std::min(1, dim - 1)];
+ case 1:
+ return xi[std::min(0, dim - 1)];
+ case 2:
+ return xi[std::min(1, dim - 1)];
+ }
+ }
+
+ if (reference_cell ==
+ Type::Tet) // see also Simplex::ScalarPolynomial::compute_value
+ {
+ switch (i)
+ {
+ case 0:
+ return 1.0 - xi[std::min(0, dim - 1)] - xi[std::min(1, dim - 1)] -
+ xi[std::min(2, dim - 1)];
case 1:
- return xi[0];
+ return xi[std::min(0, dim - 1)];
case 2:
- return xi[1];
+ return xi[std::min(1, dim - 1)];
+ case 3:
+ return xi[std::min(2, dim - 1)];
}
}
+ if (reference_cell ==
+ Type::Wedge) // see also Simplex::ScalarWedgePolynomial::compute_value
+ {
+ return d_linear_shape_function<2>(Type::Tri,
+ Point<2>(xi[std::min(0, dim - 1)],
+ xi[std::min(1, dim - 1)]),
+ i % 3) *
+ d_linear_shape_function<1>(Type::Line,
+ Point<1>(xi[std::min(2, dim - 1)]),
+ i / 3);
+ }
+
+ if (reference_cell ==
+ Type::Pyramid) // see also
+ // Simplex::ScalarPyramidPolynomial::compute_value
+ {
+ const double Q14 = 0.25;
+ double ration;
+
+ const double r = xi[std::min(0, dim - 1)];
+ const double s = xi[std::min(1, dim - 1)];
+ const double t = xi[std::min(2, dim - 1)];
+
+ if (fabs(t - 1.0) > 1.0e-14)
+ {
+ ration = (r * s * t) / (1.0 - t);
+ }
+ else
+ {
+ ration = 0.0;
+ }
+
+ if (i == 0)
+ return Q14 * ((1.0 - r) * (1.0 - s) - t + ration);
+ if (i == 1)
+ return Q14 * ((1.0 + r) * (1.0 - s) - t - ration);
+ if (i == 2)
+ return Q14 * ((1.0 - r) * (1.0 + s) - t - ration);
+ if (i == 3)
+ return Q14 * ((1.0 + r) * (1.0 + s) - t + ration);
+ else
+ return t;
+ }
+
Assert(false, ExcNotImplemented());
return 0.0;
Assert(polynomial_degree >= 1,
ExcMessage("It only makes sense to create polynomial mappings "
"with a polynomial degree greater or equal to one."));
- Assert(fe.tensor_degree() == 1, ExcNotImplemented());
Assert(fe.n_components() == 1, ExcNotImplemented());
+
+ Assert(fe.has_support_points(), ExcNotImplemented());
+
+ const auto &mapping_support_points = fe.get_unit_support_points();
+
+ const auto reference_cell_type = fe.reference_cell_type();
+
+ const unsigned int n_points = mapping_support_points.size();
+ const unsigned int n_shape_functions =
+ ReferenceCell::internal::Info::get_cell(reference_cell_type).n_vertices();
+
+ this->mapping_support_point_weights =
+ Table<2, double>(n_points, n_shape_functions);
+
+ for (unsigned int point = 0; point < n_points; ++point)
+ for (unsigned int i = 0; i < n_shape_functions; ++i)
+ mapping_support_point_weights(point, i) =
+ ReferenceCell::d_linear_shape_function(reference_cell_type,
+ mapping_support_points[point],
+ i);
}
MappingFE<dim, spacedim>::MappingFE(const MappingFE<dim, spacedim> &mapping)
: fe(mapping.fe->clone())
, polynomial_degree(mapping.polynomial_degree)
+ , mapping_support_point_weights(mapping.mapping_support_point_weights)
{}
+namespace
+{
+ template <int spacedim>
+ bool
+ check_all_manifold_ids_identical(
+ const TriaIterator<CellAccessor<1, spacedim>> &)
+ {
+ return true;
+ }
+
+
+
+ template <int spacedim>
+ bool
+ check_all_manifold_ids_identical(
+ const TriaIterator<CellAccessor<2, spacedim>> &cell)
+ {
+ const auto b_id = cell->manifold_id();
+
+ for (const auto f : cell->face_indices())
+ if (b_id != cell->face(f)->manifold_id())
+ return false;
+
+ return true;
+ }
+
+
+
+ template <int spacedim>
+ bool
+ check_all_manifold_ids_identical(
+ const TriaIterator<CellAccessor<3, spacedim>> &cell)
+ {
+ const auto b_id = cell->manifold_id();
+
+ for (const auto f : cell->face_indices())
+ if (b_id != cell->face(f)->manifold_id())
+ return false;
+
+ for (const auto l : cell->line_indices())
+ if (b_id != cell->line(l)->manifold_id())
+ return false;
+
+ return true;
+ }
+} // namespace
+
+
+
template <int dim, int spacedim>
std::vector<Point<spacedim>>
MappingFE<dim, spacedim>::compute_mapping_support_points(
const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
{
- // get the vertices first
- std::vector<Point<spacedim>> a(cell->n_vertices());
+ Assert(
+ check_all_manifold_ids_identical(cell),
+ ExcMessage(
+ "All entities of a cell need to have the same boundary id as the cell has."));
+
+ std::vector<Point<spacedim>> vertices(cell->n_vertices());
for (const unsigned int i : cell->vertex_indices())
- a[i] = cell->vertex(i);
+ vertices[i] = cell->vertex(i);
- if (this->polynomial_degree > 1)
- {
- Assert(false, ExcNotImplemented());
- }
+ std::vector<Point<spacedim>> mapping_support_points(
+ fe->get_unit_support_points().size());
+
+ cell->get_manifold().get_new_points(vertices,
+ mapping_support_point_weights,
+ mapping_support_points);
- return a;
+ return mapping_support_points;
}
//
// ---------------------------------------------------------------------
+#include <deal.II/base/polynomial.h>
#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/fe/mapping_fe.h>
#include <deal.II/fe/mapping_q1.h>
#include <deal.II/grid/tria.h>
#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/polynomials.h>
#include <deal.II/simplex/quadrature_lib.h>
DEAL_II_NAMESPACE_OPEN
}
+
template <int dim, int spacedim>
const Mapping<dim, spacedim> &
get_default_linear_mapping(const Type &reference_cell)
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Distribute Simplex::FE_Wedge on a DoFHandler.
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+
+#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/quadrature_lib.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+void
+test(const unsigned int mapping_degree)
+{
+ const int dim = 2;
+
+ Triangulation<dim> tria, tria_temp;
+ GridGenerator::hyper_shell(tria_temp, Point<dim>(), 1.0, 2.0);
+ GridGenerator::convert_hypercube_to_simplex_mesh(tria_temp, tria);
+ for (const auto i : tria_temp.get_manifold_ids())
+ if (i != numbers::flat_manifold_id)
+ tria.set_manifold(i, tria_temp.get_manifold(i));
+
+ Simplex::FE_P<dim> fe(2);
+
+ DoFHandler<dim> dof_handler(tria);
+ dof_handler.distribute_dofs(fe);
+
+ MappingFE<dim> mapping(Simplex::FE_P<dim>{mapping_degree});
+
+ {
+ DataOut<dim> data_out;
+
+ data_out.attach_dof_handler(dof_handler);
+
+ Vector<double> solution(dof_handler.n_dofs());
+ data_out.add_data_vector(solution, "solution");
+
+ data_out.build_patches(mapping, 2);
+
+#if false
+ std::ofstream output("test." + std::to_string(mapping_degree) + ".vtk");
+ data_out.write_vtk(output);
+#else
+ data_out.write_vtk(deallog.get_file_stream());
+#endif
+ }
+}
+
+int
+main()
+{
+ initlog();
+
+ test(1);
+ test(2);
+}
--- /dev/null
+
+# vtk DataFile Version 3.0
+#This file was generated
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