Add tests for VectorTools::integrate_difference() using complex data types.

diff --git a/tests/vector_tools/integrate_difference_01_complex_01.cc b/tests/vector_tools/integrate_difference_01_complex_01.cc
new file mode 100644 (file)
index 0000000..ecaf6fe
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_01.cc
@@ -0,0 +1,116 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test integrate_difference for complex-valued vectors. This test is
+// like integrate_difference_01, using a real-valued function but
+// using complex data types
+
+#include "../tests.h"
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/base/signaling_nan.h>
+
+using namespace dealii;
+
+
+// x+y(+z), x^2+y^2 (, z+xy)
+// div = 1+2y (+1)
+template <int dim>
+class Ref : public Function<dim, std::complex<double> >
+{
+public:
+  Ref()
+    :Function<dim,std::complex<double> >(dim)
+  {}
+
+  std::complex<double> value (const Point<dim> &p, const unsigned int c) const
+  {
+    if (c==0)
+      return p[0]+p[1]+((dim==3)?p[2]:0.0);
+    if (c==1)
+      return p[0]*p[0]+p[1]*p[1];
+    if (c==2)
+      return p[2]+p[0]*p[1];
+    else
+      return numbers::signaling_nan<double>();
+  }
+};
+
+
+
+template <int dim>
+void test(VectorTools::NormType norm, double value)
+{
+  Triangulation<dim> tria;
+  GridGenerator::hyper_cube(tria);
+  tria.refine_global(1);
+
+  FESystem<dim> fe(FE_Q<dim>(4),dim);
+  DoFHandler<dim> dofh(tria);
+  dofh.distribute_dofs(fe);
+
+  Vector<std::complex<double> > solution (dofh.n_dofs ());
+  VectorTools::interpolate(dofh, Ref<dim>(), solution);
+
+  Vector<double> cellwise_errors (tria.n_active_cells());
+  VectorTools::integrate_difference (dofh,
+                                     solution,
+                                     Functions::ZeroFunction<dim>(dim),
+                                     cellwise_errors,
+                                     QGauss<dim>(5),
+                                     norm);
+
+  const double error = cellwise_errors.l2_norm();
+
+  const double difference = std::abs(error-value);
+  deallog << "computed: " << error
+          << " expected: " << value
+          << " difference: " << difference
+          << std::endl;
+  Assert(difference<1e-10, ExcMessage("Error in integrate_difference"));
+}
+
+template <int dim>
+void test()
+{
+  deallog << "Hdiv_seminorm:" << std::endl;
+  // sqrt(\int (div f)^2 = sqrt(\int (1+2y)^2)
+  test<dim>(VectorTools::Hdiv_seminorm, std::sqrt(13.0/3.0));
+  deallog << "L2_norm:" << std::endl;
+  // sqrt(\int_\Omega f^2) = sqrt(\int (x+y)^2+(x^2+y^2)^2)
+  test<dim>(VectorTools::L2_norm, std::sqrt(161.0/90.0));
+  deallog << "H1_seminorm:" << std::endl;
+  // sqrt( sum | d/dxi f |_0^2 ) = sqrt( sum \int   )
+  test<dim>(VectorTools::H1_seminorm, std::sqrt(14.0/3.0));
+
+  deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+  initlog();
+  test<2>();
+}

diff --git a/tests/vector_tools/integrate_difference_01_complex_01.output b/tests/vector_tools/integrate_difference_01_complex_01.output
new file mode 100644 (file)
index 0000000..9706d0f
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_01.output
@@ -0,0 +1,8 @@
+
+DEAL::Hdiv_seminorm:
+DEAL::computed: 2.08167 expected: 2.08167 difference: 4.44089e-16
+DEAL::L2_norm:
+DEAL::computed: 1.33749 expected: 1.33749 difference: 2.22045e-16
+DEAL::H1_seminorm:
+DEAL::computed: 2.16025 expected: 2.16025 difference: 4.44089e-16
+DEAL::OK

diff --git a/tests/vector_tools/integrate_difference_01_complex_02.cc b/tests/vector_tools/integrate_difference_01_complex_02.cc
new file mode 100644 (file)
index 0000000..7b20a50
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_02.cc
@@ -0,0 +1,116 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test integrate_difference for complex-valued vectors. This test is
+// like integrate_difference_01, but multiplies the real-valued
+// function by sqrt(-1) and stores everything using complex data types
+
+#include "../tests.h"
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/base/signaling_nan.h>
+
+using namespace dealii;
+
+
+// x+y(+z), x^2+y^2 (, z+xy) times i
+// div = (1+2y (+1))i
+template <int dim>
+class Ref : public Function<dim, std::complex<double> >
+{
+public:
+  Ref()
+    :Function<dim,std::complex<double> >(dim)
+  {}
+
+  std::complex<double> value (const Point<dim> &p, const unsigned int c) const
+  {
+    if (c==0)
+      return std::complex<double>(0, p[0]+p[1]+((dim==3)?p[2]:0.0));
+    if (c==1)
+      return std::complex<double>(0, p[0]*p[0]+p[1]*p[1]);
+    if (c==2)
+      return std::complex<double>(0, p[2]+p[0]*p[1]);
+    else
+      return numbers::signaling_nan<double>();
+  }
+};
+
+
+
+template <int dim>
+void test(VectorTools::NormType norm, double value)
+{
+  Triangulation<dim> tria;
+  GridGenerator::hyper_cube(tria);
+  tria.refine_global(1);
+
+  FESystem<dim> fe(FE_Q<dim>(4),dim);
+  DoFHandler<dim> dofh(tria);
+  dofh.distribute_dofs(fe);
+
+  Vector<std::complex<double> > solution (dofh.n_dofs ());
+  VectorTools::interpolate(dofh, Ref<dim>(), solution);
+
+  Vector<double> cellwise_errors (tria.n_active_cells());
+  VectorTools::integrate_difference (dofh,
+                                     solution,
+                                     Functions::ZeroFunction<dim>(dim),
+                                     cellwise_errors,
+                                     QGauss<dim>(5),
+                                     norm);
+
+  const double error = cellwise_errors.l2_norm();
+
+  const double difference = std::abs(error-value);
+  deallog << "computed: " << error
+          << " expected: " << value
+          << " difference: " << difference
+          << std::endl;
+  Assert(difference<1e-10, ExcMessage("Error in integrate_difference"));
+}
+
+template <int dim>
+void test()
+{
+  deallog << "Hdiv_seminorm:" << std::endl;
+  // sqrt(\int (div f)^2 = sqrt(\int (1+2y)^2)
+  test<dim>(VectorTools::Hdiv_seminorm, std::sqrt(13.0/3.0));
+  deallog << "L2_norm:" << std::endl;
+  // sqrt(\int_\Omega f^2) = sqrt(\int (x+y)^2+(x^2+y^2)^2)
+  test<dim>(VectorTools::L2_norm, std::sqrt(161.0/90.0));
+  deallog << "H1_seminorm:" << std::endl;
+  // sqrt( sum | d/dxi f |_0^2 ) = sqrt( sum \int   )
+  test<dim>(VectorTools::H1_seminorm, std::sqrt(14.0/3.0));
+
+  deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+  initlog();
+  test<2>();
+}

diff --git a/tests/vector_tools/integrate_difference_01_complex_02.output b/tests/vector_tools/integrate_difference_01_complex_02.output
new file mode 100644 (file)
index 0000000..9706d0f
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_02.output
@@ -0,0 +1,8 @@
+
+DEAL::Hdiv_seminorm:
+DEAL::computed: 2.08167 expected: 2.08167 difference: 4.44089e-16
+DEAL::L2_norm:
+DEAL::computed: 1.33749 expected: 1.33749 difference: 2.22045e-16
+DEAL::H1_seminorm:
+DEAL::computed: 2.16025 expected: 2.16025 difference: 4.44089e-16
+DEAL::OK

diff --git a/tests/vector_tools/integrate_difference_01_complex_03.cc b/tests/vector_tools/integrate_difference_01_complex_03.cc
new file mode 100644 (file)
index 0000000..7662c67
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_03.cc
@@ -0,0 +1,116 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test integrate_difference for complex-valued vectors. This test is
+// like integrate_difference_01, but multiplies the real-valued
+// function by (1/sqrt(2)+1/sqrt(2)i) and stores everything using complex data types
+
+#include "../tests.h"
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/base/signaling_nan.h>
+
+using namespace dealii;
+
+
+// x+y(+z), x^2+y^2 (, z+xy) times (1+i)/sqrt(2)
+// div = (1+2y (+1)) times (1+i)/sqrt(2)
+template <int dim>
+class Ref : public Function<dim, std::complex<double> >
+{
+public:
+  Ref()
+    :Function<dim,std::complex<double> >(dim)
+  {}
+
+  std::complex<double> value (const Point<dim> &p, const unsigned int c) const
+  {
+    if (c==0)
+      return (p[0]+p[1]+((dim==3)?p[2]:0.0)) * std::complex<double>(1./std::sqrt(2.), 1./std::sqrt(2.));
+    if (c==1)
+      return (p[0]*p[0]+p[1]*p[1]) * std::complex<double>(1./std::sqrt(2.), 1./std::sqrt(2.));
+    if (c==2)
+      return (p[2]+p[0]*p[1]) * std::complex<double>(1./std::sqrt(2.), 1./std::sqrt(2.));
+    else
+      return numbers::signaling_nan<double>();
+  }
+};
+
+
+
+template <int dim>
+void test(VectorTools::NormType norm, double value)
+{
+  Triangulation<dim> tria;
+  GridGenerator::hyper_cube(tria);
+  tria.refine_global(1);
+
+  FESystem<dim> fe(FE_Q<dim>(4),dim);
+  DoFHandler<dim> dofh(tria);
+  dofh.distribute_dofs(fe);
+
+  Vector<std::complex<double> > solution (dofh.n_dofs ());
+  VectorTools::interpolate(dofh, Ref<dim>(), solution);
+
+  Vector<double> cellwise_errors (tria.n_active_cells());
+  VectorTools::integrate_difference (dofh,
+                                     solution,
+                                     Functions::ZeroFunction<dim>(dim),
+                                     cellwise_errors,
+                                     QGauss<dim>(5),
+                                     norm);
+
+  const double error = cellwise_errors.l2_norm();
+
+  const double difference = std::abs(error-value);
+  deallog << "computed: " << error
+          << " expected: " << value
+          << " difference: " << difference
+          << std::endl;
+  Assert(difference<1e-10, ExcMessage("Error in integrate_difference"));
+}
+
+template <int dim>
+void test()
+{
+  deallog << "Hdiv_seminorm:" << std::endl;
+  // sqrt(\int (div f)^2 = sqrt(\int (1+2y)^2)
+  test<dim>(VectorTools::Hdiv_seminorm, std::sqrt(13.0/3.0));
+  deallog << "L2_norm:" << std::endl;
+  // sqrt(\int_\Omega f^2) = sqrt(\int (x+y)^2+(x^2+y^2)^2)
+  test<dim>(VectorTools::L2_norm, std::sqrt(161.0/90.0));
+  deallog << "H1_seminorm:" << std::endl;
+  // sqrt( sum | d/dxi f |_0^2 ) = sqrt( sum \int   )
+  test<dim>(VectorTools::H1_seminorm, std::sqrt(14.0/3.0));
+
+  deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+  initlog();
+  test<2>();
+}

diff --git a/tests/vector_tools/integrate_difference_01_complex_03.output b/tests/vector_tools/integrate_difference_01_complex_03.output
new file mode 100644 (file)
index 0000000..9706d0f
--- /dev/null
+++ b/tests/vector_tools/integrate_difference_01_complex_03.output
@@ -0,0 +1,8 @@
+
+DEAL::Hdiv_seminorm:
+DEAL::computed: 2.08167 expected: 2.08167 difference: 4.44089e-16
+DEAL::L2_norm:
+DEAL::computed: 1.33749 expected: 1.33749 difference: 2.22045e-16
+DEAL::H1_seminorm:
+DEAL::computed: 2.16025 expected: 2.16025 difference: 4.44089e-16
+DEAL::OK