From: Luca Heltai <luca.heltai@sissa.it>
Date: Tue, 1 Mar 2016 10:48:50 +0000 (+0100)
Subject: Test for bug #1646
X-Git-Tag: v8.5.0-rc1~1131^2~35
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=08d2d30fd40c32740eab02e749a38da501a5ee45;p=dealii.git

Test for bug #1646
---

diff --git a/tests/fe/mapping_q_manifold_01.cc b/tests/fe/mapping_q_manifold_01.cc
new file mode 100644
index 0000000000..898de99926
--- /dev/null
+++ b/tests/fe/mapping_q_manifold_01.cc
@@ -0,0 +1,193 @@
+#include <fstream>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/manifold.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_q.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/numerics/data_out.h>
+
+using namespace dealii;
+
+double zvalue (const double x, const double y)
+{
+  double xh = x * 5., yh = y * 5.;
+  return (xh * exp(-xh*xh - yh*yh)) / 10.;
+}
+
+template<int dim>
+class Geometry: public ChartManifold<dim>
+{
+public:
+  virtual Point<dim> pull_back(const Point<dim> &space_point) const;
+  virtual Point<dim> push_forward(const Point<dim> &chart_point) const;
+};
+
+template<int dim>
+Point<dim> Geometry<dim>::pull_back(const Point<dim> &space_point) const
+{
+  const double d = space_point[dim - 1];
+  const double z = zvalue(space_point[0], dim == 3 ? space_point[1] : 0);
+
+  double d_hat = 0.;
+  if ((d - z) <= 0)
+    d_hat = (d - z) / (1. + z);
+  else
+    d_hat = (d - z) / (1. - z);
+
+  Point<dim> p;
+  for (unsigned i = 0; i < dim - 1; ++i)
+    p[i] = space_point[i];
+  p[dim - 1] = d_hat;
+
+  return p;
+}
+
+template<int dim>
+Point<dim> Geometry<dim>::push_forward(const Point<dim> &chart_point) const
+{
+  const double d_hat = chart_point[dim - 1];
+  const double z = zvalue(chart_point[0], dim == 3 ? chart_point[1] : 0);
+
+  double d = 0.;
+  if (d_hat <= 0)
+    d = d_hat + (d_hat + 1.) * z;
+  else
+    d = d_hat - (d_hat - 1.) * z;
+
+  Point<dim> p;
+  for (unsigned i = 0; i < dim - 1; ++i)
+    p[i] = chart_point[i];
+  p[dim - 1] = d;
+
+  return p;
+}
+
+template<int dim>
+class VectorFunction : public Function<dim>
+{
+public:
+  VectorFunction(unsigned n_components):
+    Function<dim>(n_components)
+  {}
+  virtual double value (const Point<dim> &p, const unsigned int component) const;
+  virtual void value (const Point<dim> &p, Vector<double> &values) const;
+  virtual void vector_value(const Point<dim> &p, Vector<double> &values) const;
+};
+
+template<>
+double VectorFunction<3>::value(const Point<3> &p, const unsigned int component) const
+{
+  return (1 - p(0)*p(0)) * (1 - p(1)*p(1)) * (1 - p(2)*p(2));
+}
+
+template<>
+double VectorFunction<2>::value(const Point<2> &p, const unsigned int component) const
+{
+  return (1 - p(0)*p(0)) * (1 - p(1)*p(1));
+}
+
+template<int dim>
+void VectorFunction<dim>::value(const Point<dim> &p, Vector<double> &values) const
+{
+  for (unsigned i = 0; i < values.size(); ++i)
+    values[i] = value(p, i);
+}
+
+template<int dim>
+void VectorFunction<dim>::vector_value(const Point<dim> &p, Vector<double> &values) const
+{
+  for (int i = 0; i < dim; ++i)
+    values(i) = value(p, i);
+}
+
+template <int dim>
+void create_tria(Triangulation<dim> &triangulation, const Geometry<dim> &geometry)
+{
+  GridGenerator::hyper_cube (triangulation, -1., 1.);
+  triangulation.refine_global(3);
+
+  GridTools::transform (std_cxx11::bind(&Geometry<dim>::push_forward,
+                                        std_cxx11::cref(geometry),
+                                        std_cxx11::_1),
+                        triangulation);
+
+  triangulation.set_manifold(0, geometry);
+  for (Triangulation<3>::active_cell_iterator cell=triangulation.begin_active();
+       cell!=triangulation.end(); ++cell)
+    cell->set_all_manifold_ids(0);
+}
+
+template <int dim>
+void test(const FiniteElement<dim> &fe)
+{
+  deallog << "dim: " << dim << "\t" << fe.get_name() << std::endl;
+  deallog << "Mapping degree\t||u-u_h||" << std::endl;
+
+  Geometry<dim> geometry;
+  Triangulation<dim> triangulation;
+  create_tria(triangulation, geometry);
+
+  DoFHandler<dim> dof_handler(triangulation);
+  dof_handler.distribute_dofs(fe);
+
+  VectorFunction<dim> fe_function(fe.n_components());
+
+  for (unsigned mapping_p = 1; mapping_p <= 5; ++mapping_p)
+    {
+      MappingQ<dim> mapping(mapping_p, true);
+
+      ConstraintMatrix constraints;
+      DoFTools::make_hanging_node_constraints(dof_handler, constraints);
+      constraints.close();
+
+      Vector<double> v(dof_handler.n_dofs());
+      VectorTools::project(mapping, dof_handler, constraints,
+                           QGauss<dim>(fe.degree + 1), fe_function, v);
+
+      Vector<float> diff(triangulation.n_active_cells());
+      VectorTools::integrate_difference(mapping, dof_handler, v, fe_function, diff,
+                                        QGauss<dim>(fe.degree + 2), VectorTools::L2_norm);
+
+      deallog << mapping.get_degree() << "\t"
+              << diff.l2_norm() << std::endl;
+
+      DataOut<dim> data_out;
+      std::ofstream output("output_" + Utilities::int_to_string(mapping_p) + ".vtk");
+      data_out.attach_dof_handler (dof_handler);
+      data_out.add_data_vector(v, "v");
+      data_out.add_data_vector(diff, "e");
+      data_out.build_patches(mapping, fe.degree);
+      data_out.write_vtk(output);
+      output.close();
+    }
+}
+
+int main ()
+{
+  deallog << std::setprecision (5);
+  deallog.attach (std::cout);
+  deallog.depth_console (0);
+  deallog.threshold_double (1e-12);
+
+  const static unsigned dim = 3;
+
+  for (unsigned p = 1; p < 5; ++p)
+    {
+      test<dim>(FE_Q<dim>(QGaussLobatto<1>(p+1)));
+
+      //test<dim>(FE_RaviartThomas<dim> (p));
+      //test<dim>(FE_Nedelec<dim> (p));
+      //test<dim>(FESystem<dim> (FE_Q<dim>(p), dim));
+    }
+}
diff --git a/tests/fe/mapping_q_manifold_01.output b/tests/fe/mapping_q_manifold_01.output
new file mode 100644
index 0000000000..b39f7eeef1
--- /dev/null
+++ b/tests/fe/mapping_q_manifold_01.output
@@ -0,0 +1,8 @@
+
+DEAL::dim: 3 FE_Q<3>(QGaussLobatto(5))
+DEAL::Mapping degree ||u-u_h||
+DEAL::1 6.8494e-13
+DEAL::2 6.8495e-13
+DEAL::3 6.8497e-13
+DEAL::4 6.8491e-13
+DEAL::5 6.8492e-13