--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2016 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 and compute_global_error in parallel
+// see integrate_difference_02.cc for the serial version
+//
+// like the integrate_difference_04_hp test, but this time really do
+// use multiple different finite elements on different
+// cells. comparing the output for these two tests shows that indeed
+// the test with different (and higher order) elements is more
+// accurate, as one might have surmised.
+
+#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/lac/trilinos_vector.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/hp/dof_handler.h>
+#include <deal.II/hp/fe_collection.h>
+#include <deal.II/hp/q_collection.h>
+#include <deal.II/distributed/shared_tria.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>
+
+using namespace dealii;
+
+
+// x+y+z, x^2+y^2, z+xy
+// div = 1+2y+1
+template <int dim>
+class Ref : public Function<dim>
+{
+public:
+ Ref()
+ :Function<dim>(dim)
+ {}
+
+ 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];
+ return 0.0;
+ }
+};
+
+
+
+template <int dim>
+void test(VectorTools::NormType norm, double value, double exp = 2.0)
+{
+ parallel::shared::Triangulation<dim> tria(MPI_COMM_WORLD);
+ GridGenerator::hyper_cube(tria);
+ tria.refine_global(3);
+
+ hp::FECollection<dim> fe;
+ fe.push_back (FESystem<dim> (FE_Q<dim>(4),dim));
+ fe.push_back (FESystem<dim> (FE_Q<dim>(5),dim));
+ fe.push_back (FESystem<dim> (FE_Q<dim>(6),dim));
+ hp::DoFHandler<dim> dofh(tria);
+
+ // assign FEs mostly randomly to each cell
+ for (auto cell : dofh.active_cell_iterators())
+ cell->set_active_fe_index (cell->active_cell_index() %
+ fe.size());
+ dofh.distribute_dofs(fe);
+
+ TrilinosWrappers::MPI::Vector interpolated(dofh.locally_owned_dofs(),
+ MPI_COMM_WORLD);
+
+ VectorTools::interpolate(dofh, Ref<dim>(), interpolated);
+
+ IndexSet relevant_set;
+ DoFTools::extract_locally_relevant_dofs (dofh, relevant_set);
+ TrilinosWrappers::MPI::Vector solution(relevant_set, MPI_COMM_WORLD);
+ solution = interpolated;
+
+ Vector<double> cellwise_errors (tria.n_active_cells());
+ hp::QCollection<dim> quadrature;
+ quadrature.push_back (QIterated<dim> (QTrapez<1>(), 5));
+ quadrature.push_back (QIterated<dim> (QTrapez<1>(), 6));
+ quadrature.push_back (QIterated<dim> (QTrapez<1>(), 7));
+
+ const dealii::Function<dim,double> *w = nullptr;
+ VectorTools::integrate_difference (dofh,
+ solution,
+ ZeroFunction<dim>(dim),
+ cellwise_errors,
+ quadrature,
+ norm,
+ w,
+ exp);
+
+ const double error
+ = VectorTools::compute_global_error(tria, cellwise_errors, norm, exp);
+
+ const double difference = std::abs(error-value);
+ deallog << "computed: " << error
+ << " expected: " << value
+ << " difference: " << difference
+ << std::endl;
+ Assert(difference<2e-3, ExcMessage("Error in integrate_difference"));
+}
+
+template <int dim>
+void test()
+{
+ deallog << "Hdiv_seminorm:" << std::endl;
+ // sqrt(\int (div f)^2 = sqrt(\int (1+2y+1)^2)
+ test<dim>(VectorTools::Hdiv_seminorm, 2.0*std::sqrt(7.0/3.0));
+
+ deallog << "L2_norm:" << std::endl;
+ // sqrt(\int_\Omega f^2) = sqrt(\int (x+y+z)^2+(x^2+y^2)^2+(z+xy)^2)
+ test<dim>(VectorTools::L2_norm, std::sqrt(229.0/60.0));
+
+ deallog << "H1_seminorm:" << std::endl;
+ // sqrt( \int sum_k | d/dxi f_k |_0^2 )
+ // = sqrt( \int 3+ (2x)^2+(2y)^2 + y^2+x^2+1
+ // = sqrt( 22/3 )
+ test<dim>(VectorTools::H1_seminorm, std::sqrt(22.0/3.0));
+
+ deallog << "H1_norm:" << std::endl;
+ test<dim>(VectorTools::H1_norm, std::sqrt(229.0/60.0+22.0/3.0));
+
+ deallog << "L1_norm:" << std::endl;
+ test<dim>(VectorTools::L1_norm, 35.0/12.0);
+
+ deallog << "Linfty_norm:" << std::endl;
+ test<dim>(VectorTools::Linfty_norm, 3.0);
+
+ deallog << "mean:" << std::endl;
+ // int -(x+y+z + x^2+y^2 + z+xy)
+ test<dim>(VectorTools::mean, -35.0/12.0);
+
+ deallog << "Lp_norm:" << std::endl;
+ // (int (x+y+z)^p+(x^2+y^2)^p+(z+xy)^p) ) ^ 1./p
+ // = std::pow(9937.0/1680.0, 1.0/3.0)
+ test<dim>(VectorTools::Lp_norm, std::pow(9937.0/1680.0, 1.0/3.0), 3.0);
+
+ deallog << "W1p_seminorm:" << std::endl;
+ // ( \int_K sum_k | d/dxi f_k |_0^2^(p/2) )^1/p
+ // ( integrate 3^(3/2) + ((2x)^2+(2y)^2)^(3/2) + (y^2+x^2+1)^(3/2) ) ^1/p
+ // = (12.4164) ^1/3 = 2.31560
+ test<dim>(VectorTools::W1p_seminorm, 2.31560, 3.0);
+
+ deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+ Utilities::MPI::MPI_InitFinalize mpi_initialization (argc, argv, 1);
+ MPILogInitAll log;
+ test<3>();
+}
--- /dev/null
+
+DEAL:0::Hdiv_seminorm:
+DEAL:0::computed: 3.05510 expected: 3.05505 difference: 5.01434e-05
+DEAL:0::L2_norm:
+DEAL:0::computed: 1.95383 expected: 1.95363 difference: 0.000196056
+DEAL:0::H1_seminorm:
+DEAL:0::computed: 2.70815 expected: 2.70801 difference: 0.000141421
+DEAL:0::H1_norm:
+DEAL:0::computed: 3.33939 expected: 3.33916 difference: 0.000229397
+DEAL:0::L1_norm:
+DEAL:0::computed: 2.91682 expected: 2.91667 difference: 0.000153192
+DEAL:0::Linfty_norm:
+DEAL:0::computed: 3.00000 expected: 3.00000 difference: 0.00000
+DEAL:0::mean:
+DEAL:0::computed: -2.91682 expected: -2.91667 difference: 0.000153192
+DEAL:0::Lp_norm:
+DEAL:0::computed: 1.80871 expected: 1.80849 difference: 0.000224088
+DEAL:0::W1p_seminorm:
+DEAL:0::computed: 2.31576 expected: 2.31560 difference: 0.000161338
+DEAL:0::OK
+
+DEAL:1::Hdiv_seminorm:
+DEAL:1::computed: 3.05510 expected: 3.05505 difference: 5.01434e-05
+DEAL:1::L2_norm:
+DEAL:1::computed: 1.95383 expected: 1.95363 difference: 0.000196056
+DEAL:1::H1_seminorm:
+DEAL:1::computed: 2.70815 expected: 2.70801 difference: 0.000141421
+DEAL:1::H1_norm:
+DEAL:1::computed: 3.33939 expected: 3.33916 difference: 0.000229397
+DEAL:1::L1_norm:
+DEAL:1::computed: 2.91682 expected: 2.91667 difference: 0.000153192
+DEAL:1::Linfty_norm:
+DEAL:1::computed: 3.00000 expected: 3.00000 difference: 0.00000
+DEAL:1::mean:
+DEAL:1::computed: -2.91682 expected: -2.91667 difference: 0.000153192
+DEAL:1::Lp_norm:
+DEAL:1::computed: 1.80871 expected: 1.80849 difference: 0.000224088
+DEAL:1::W1p_seminorm:
+DEAL:1::computed: 2.31576 expected: 2.31560 difference: 0.000161338
+DEAL:1::OK
+
+
+DEAL:2::Hdiv_seminorm:
+DEAL:2::computed: 3.05510 expected: 3.05505 difference: 5.01434e-05
+DEAL:2::L2_norm:
+DEAL:2::computed: 1.95383 expected: 1.95363 difference: 0.000196056
+DEAL:2::H1_seminorm:
+DEAL:2::computed: 2.70815 expected: 2.70801 difference: 0.000141421
+DEAL:2::H1_norm:
+DEAL:2::computed: 3.33939 expected: 3.33916 difference: 0.000229397
+DEAL:2::L1_norm:
+DEAL:2::computed: 2.91682 expected: 2.91667 difference: 0.000153192
+DEAL:2::Linfty_norm:
+DEAL:2::computed: 3.00000 expected: 3.00000 difference: 0.00000
+DEAL:2::mean:
+DEAL:2::computed: -2.91682 expected: -2.91667 difference: 0.000153192
+DEAL:2::Lp_norm:
+DEAL:2::computed: 1.80871 expected: 1.80849 difference: 0.000224088
+DEAL:2::W1p_seminorm:
+DEAL:2::computed: 2.31576 expected: 2.31560 difference: 0.000161338
+DEAL:2::OK
+
projects / dealii.git / commitdiff