--- /dev/null
+//\r
+// This file is part of the deal.II library.\r
+//\r
+// The deal.II library is free software; you can use it, redistribute\r
+// it, and/or modify it under the terms of the GNU Lesser General\r
+// Public License as published by the Free Software Foundation; either\r
+// version 2.1 of the License, or (at your option) any later version.\r
+// The full text of the license can be found in the file LICENSE at\r
+// the top level of the deal.II distribution.\r
+//\r
+// ---------------------------------------------------------------------\r
+#include <deal.II/base/function.h>\r
+#include <deal.II/dofs/dof_handler.h>\r
+#include <deal.II/dofs/dof_accessor.h>\r
+#include <deal.II/dofs/dof_tools.h>\r
+#include <deal.II/grid/grid_generator.h>\r
+#include <deal.II/grid/tria.h>\r
+#include <deal.II/grid/grid_tools.h>\r
+#include <deal.II/grid/grid_refinement.h>\r
+#include <deal.II/fe/fe_nedelec.h>\r
+#include <deal.II/fe/fe_q.h>\r
+#include <deal.II/fe/fe_system.h>\r
+#include <deal.II/fe/fe_raviart_thomas.h>\r
+#include <deal.II/fe/fe_abf.h>\r
+#include <deal.II/fe/fe_values.h>\r
+#include <deal.II/fe/mapping_q.h>\r
+#include <deal.II/lac/constraint_matrix.h>\r
+#include <deal.II/numerics/vector_tools.h>\r
+\r
+#include "../tests.h"\r
+\r
+/*\r
+ * This program projects a function into FE spaces defined on meshes\r
+ * consisting of: rectangular cells, affine cells, non-affine cells\r
+ *\r
+ * The error, curl and divergence are then numerically calculated on a\r
+ * series of globally refined meshes and get output.\r
+ *\r
+ * Among FE spaces tested are: FE_ABF, FE_Nedelec, FE_RaviartThomas,\r
+ * FE_Q^dim (via FESystem)\r
+ *\r
+ * Alexander Grayver\r
+ */\r
+\r
+using namespace dealii;\r
+\r
+static const Point<2> vertices_nonaffine[] =\r
+{\r
+ Point<2> (-1., -1.),\r
+ Point<2> (0., -1.),\r
+ Point<2> (1., -1.),\r
+\r
+ Point<2> (-1., 0.),\r
+ Point<2> (0.3, 0.3),\r
+ Point<2> (1., 0.),\r
+\r
+ Point<2> (-1., 1.),\r
+ Point<2> (0., 1.),\r
+ Point<2> (1., 1.),\r
+};\r
+\r
+static const Point<2> vertices_affine[] =\r
+{\r
+ Point<2> (-1.4, -1.),\r
+ Point<2> (-0.4, -1.),\r
+ Point<2> (0.6, -1.),\r
+\r
+ Point<2> (-1.2, 0.),\r
+ Point<2> (-0.2, 0.),\r
+ Point<2> (0.8, 0.),\r
+\r
+ Point<2> (-1., 1.),\r
+ Point<2> (0., 1.),\r
+ Point<2> (1., 1.),\r
+};\r
+\r
+static const Point<2> vertices_rectangular[] =\r
+{\r
+ Point<2> (-1., -1.),\r
+ Point<2> (0., -1.),\r
+ Point<2> (1., -1.),\r
+\r
+ Point<2> (-1., 0.),\r
+ Point<2> (0., 0.),\r
+ Point<2> (1., 0.),\r
+\r
+ Point<2> (-1., 1.),\r
+ Point<2> (0., 1.),\r
+ Point<2> (1., 1.),\r
+};\r
+\r
+static const unsigned n_vertices = sizeof(vertices_rectangular) / sizeof(vertices_rectangular[0]);\r
+static const unsigned n_cells = 4;\r
+\r
+template<int dim>\r
+class VectorFunction : public Function<dim>\r
+{\r
+public:\r
+ VectorFunction() : Function<dim>(dim) {}\r
+ virtual double value (const Point<dim> &p, const unsigned int component) const;\r
+ virtual void vector_value(const Point<dim> &p, Vector<double> &values) const;\r
+};\r
+\r
+template<>\r
+double VectorFunction<2>::value(const Point<2> &p, const unsigned int component) const\r
+{\r
+ Assert (component < 2, ExcIndexRange (component, 0, 1));\r
+\r
+ const double PI = numbers::PI;\r
+ double val = 0.0;\r
+ switch (component)\r
+ {\r
+ case 0:\r
+ val = cos(PI*p(0))*sin(PI*p(1));\r
+ break;\r
+ case 1:\r
+ val = -sin(PI*p(0))*cos(PI*p(1));\r
+ break;\r
+ }\r
+ return val;\r
+}\r
+\r
+template<int dim>\r
+void VectorFunction<dim>::vector_value(const Point<dim> &p, Vector<double> &values) const\r
+{\r
+ for (int i = 0; i < dim; ++i)\r
+ values(i) = value(p, i);\r
+}\r
+\r
+void create_tria(Triangulation<2> &triangulation, const Point<2> *vertices_parallelograms)\r
+{\r
+ const std::vector<Point<2> > vertices (&vertices_parallelograms[0],\r
+ &vertices_parallelograms[n_vertices]);\r
+\r
+ static const int cell_vertices[][GeometryInfo<2>::vertices_per_cell] =\r
+ {\r
+ {0, 1, 3, 4},\r
+ {1, 2, 4, 5},\r
+ {3, 4, 6, 7},\r
+ {4, 5, 7, 8}\r
+ };\r
+\r
+ std::vector<CellData<2> > cells (n_cells, CellData<2>());\r
+ for (unsigned i = 0; i<cells.size(); ++i)\r
+ {\r
+ for (unsigned int j=0; j<GeometryInfo<2>::vertices_per_cell; ++j)\r
+ cells[i].vertices[j] = cell_vertices[i][j];\r
+ cells[i].material_id = 0;\r
+ }\r
+\r
+ triangulation.create_triangulation (vertices, cells, SubCellData());\r
+ triangulation.refine_global(1);\r
+}\r
+\r
+template <int dim>\r
+void test(const FiniteElement<dim> &fe, unsigned n_cycles, bool global, const Point<dim> *vertices_parallelograms)\r
+{\r
+ deallog << "dim: " << dim << "\t" << fe.get_name() << std::endl;\r
+ deallog << "DoFs\t\t||u-u_h||\tcurl(u_h)\tdiv(u_h)" << std::endl;\r
+\r
+ Triangulation<dim> triangulation;\r
+ create_tria(triangulation, vertices_parallelograms);\r
+\r
+ DoFHandler<dim> dof_handler(triangulation);\r
+\r
+ VectorFunction<dim> fe_function;\r
+ const FEValuesExtractors::Vector vec (0);\r
+ const QGauss<dim> quadrature (fe.degree+1);\r
+ const unsigned int n_q_points = quadrature.size ();\r
+ MappingQ<dim> mapping(1);\r
+ //MappingQ1<dim> mapping;\r
+ std::vector<double> div_v(n_q_points);\r
+ std::vector<typename FEValuesViews::Vector<dim>::curl_type> curl_v(n_q_points);\r
+\r
+ for (unsigned cycle = 0; cycle < n_cycles; ++cycle)\r
+ {\r
+ dof_handler.distribute_dofs(fe);\r
+\r
+ ConstraintMatrix constraints;\r
+ DoFTools::make_hanging_node_constraints(dof_handler, constraints);\r
+ constraints.close();\r
+\r
+ Vector<double> v(dof_handler.n_dofs());\r
+ VectorTools::project(mapping, dof_handler, constraints, quadrature, fe_function, v);\r
+\r
+ Vector<float> diff(triangulation.n_active_cells());\r
+ VectorTools::integrate_difference(mapping, dof_handler, v, fe_function, diff,\r
+ QGauss<dim>(fe.degree + 2), VectorTools::L2_norm);\r
+\r
+ typename FEValuesViews::Vector<dim>::curl_type total_curl;\r
+ double total_div = 0;\r
+ total_curl *= 0.;\r
+\r
+ FEValues<dim> fe_values (mapping, fe, quadrature, update_JxW_values | update_quadrature_points | update_values | update_gradients);\r
+ unsigned int cell_index = 0;\r
+\r
+ for (typename DoFHandler<dim>::active_cell_iterator cell = dof_handler.begin_active ();\r
+ cell != dof_handler.end (); ++cell, ++cell_index)\r
+ {\r
+ fe_values.reinit (cell);\r
+ const std::vector<double> &JxW_values = fe_values.get_JxW_values ();\r
+ fe_values[vec].get_function_divergences (v, div_v);\r
+ fe_values[vec].get_function_curls (v, curl_v);\r
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)\r
+ {\r
+ total_div += JxW_values[q_point] * div_v[q_point];\r
+ total_curl += JxW_values[q_point] * curl_v[q_point];\r
+ }\r
+ }\r
+\r
+ deallog << dof_handler.n_dofs() << "\t\t"\r
+ << diff.l2_norm() << "\t"\r
+ << total_curl << "\t"\r
+ << total_div << std::endl;\r
+\r
+ if (global)\r
+ triangulation.refine_global();\r
+ else\r
+ {\r
+ GridRefinement::refine_and_coarsen_fixed_number(triangulation, diff, 0.3, 0.0);\r
+ triangulation.prepare_coarsening_and_refinement();\r
+ triangulation.execute_coarsening_and_refinement();\r
+ }\r
+ }\r
+}\r
+\r
+int main ()\r
+{\r
+ std::ofstream logfile ("output");\r
+ deallog << std::setprecision(6);\r
+ deallog << std::fixed;\r
+ deallog.attach(logfile);\r
+ deallog.depth_console(0);\r
+ deallog.threshold_double (1e-8);\r
+\r
+ const static unsigned dim = 2;\r
+ unsigned order = 1;\r
+ unsigned n_cycles = 4;\r
+\r
+ deallog << "2d\nRectangular grid:\n";\r
+\r
+ const Point<dim> *vertices = &vertices_rectangular[0];\r
+ test<dim>(FE_Nedelec<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FE_RaviartThomas<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FESystem<dim> (FE_Q<dim>(order), dim), n_cycles, true, vertices);\r
+ test<dim>(FE_ABF<dim> (order), n_cycles, true, vertices);\r
+\r
+ deallog << "\nAffine grid:\n";\r
+\r
+ vertices = &vertices_affine[0];\r
+ test<dim>(FE_Nedelec<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FE_RaviartThomas<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FESystem<dim> (FE_Q<dim>(order), dim), n_cycles, true, vertices);\r
+ test<dim>(FE_ABF<dim> (order), n_cycles, true, vertices);\r
+\r
+ deallog << "\nNon-affine grid:\n";\r
+\r
+ vertices = &vertices_nonaffine[0];\r
+ test<dim>(FE_Nedelec<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FE_RaviartThomas<dim> (order), n_cycles, true, vertices);\r
+ test<dim>(FESystem<dim> (FE_Q<dim>(order), dim), n_cycles, true, vertices);\r
+ test<dim>(FE_ABF<dim> (order), n_cycles, true, vertices);\r
+\r
+ deallog << std::endl;\r
+}\r
--- /dev/null
+DEAL::2d
+Rectangular grid:
+dim: 2 FE_Nedelec<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.127197 0.000000 0
+DEAL::544 0.032385 -0.000000 0
+DEAL::2112 0.008122 0.000000 0
+DEAL::8320 0.002032 -0.000000 0
+DEAL::dim: 2 FE_RaviartThomas<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.127676 0.000000 0
+DEAL::544 0.032425 0.000000 0
+DEAL::2112 0.008124 0.000000 0
+DEAL::8320 0.002032 0.000000 0
+DEAL::dim: 2 FESystem<2>[FE_Q<2>(1)^2]
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::50 0.229086 -0.000000 0
+DEAL::162 0.049159 -0.000000 0
+DEAL::578 0.011701 0.000000 0
+DEAL::2178 0.002887 0.000000 0
+DEAL::dim: 2 FE_ABF<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::208 0.126166 0.000000 0
+DEAL::800 0.032829 -0.000000 0
+DEAL::3136 0.008676 -0.000000 0
+DEAL::12416 0.002544 -0.000000 0
+DEAL::
+Affine grid:
+dim: 2 FE_Nedelec<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.126899 -0.010605 0
+DEAL::544 0.032013 -0.001829 0
+DEAL::2112 0.007983 -0.000255 0
+DEAL::8320 0.001993 -0.000033 0
+DEAL::dim: 2 FE_RaviartThomas<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.142775 -0.000000 0.018305
+DEAL::544 0.036564 0.000000 0.003444
+DEAL::2112 0.009186 0.000000 0.000490
+DEAL::8320 0.002299 0.000000 0.000063
+DEAL::dim: 2 FESystem<2>[FE_Q<2>(1)^2]
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::50 0.250113 -0.021467 -0.051342
+DEAL::162 0.052634 -0.002128 -0.005106
+DEAL::578 0.012425 -0.000250 -0.000600
+DEAL::2178 0.003058 -0.000031 -0.000074
+DEAL::dim: 2 FE_ABF<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::208 0.150632 0.000000 0
+DEAL::800 0.038793 -0.000000 0
+DEAL::3136 0.010523 -0.000000 0
+DEAL::12416 0.003304 0.000000 0
+DEAL::
+Non-affine grid:
+dim: 2 FE_Nedelec<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.153434 0.020872 0
+DEAL::544 0.037846 0.005462 0
+DEAL::2112 0.009393 0.000834 0
+DEAL::8320 0.002340 0.000110 0
+DEAL::dim: 2 FE_RaviartThomas<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::144 0.163372 -0.033531 0
+DEAL::544 0.042792 -0.006665 0
+DEAL::2112 0.010774 -0.001430 0
+DEAL::8320 0.002695 -0.000330 0
+DEAL::dim: 2 FESystem<2>[FE_Q<2>(1)^2]
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::50 0.303441 -0.149674 0
+DEAL::162 0.064869 -0.009370 0
+DEAL::578 0.014893 -0.000911 0
+DEAL::2178 0.003620 -0.000108 0
+DEAL::dim: 2 FE_ABF<2>(1)
+DEAL::DoFs ||u-u_h|| curl(u_h) div(u_h)
+DEAL::208 0.191291 -0.048789 0
+DEAL::800 0.047830 -0.008916 0
+DEAL::3136 0.012716 -0.002205 0
+DEAL::12416 0.003947 -0.000586 0
+DEAL::
projects / dealii.git / commitdiff