--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2009 - 2017 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.
+//
+// ---------------------------------------------------------------------
+
+
+
+// Test VectorTools::integrate_difference for parallel computations
+// with the hp::DoFHandler. This includes applying hanging node
+// constraints and consequently verifies that we compute them
+// correctly.
+//
+// The way this test works is this: We create a domain [-1,1]^d
+// and use the following function f(x,y) (or f(x,y,z)):
+// - in the lower left quadrant, f(x,y)=xy
+// - in the lower right quadrant, f(x,y)=xy+(xy)^2
+// - in the upper left quadrant, f(x,y)=xy+(xy)^3
+// - in the upper right quadrant, f(x,y)=xy+(xy)^2+(xy)^3+(xy)*4
+//
+// We interpolate this function onto a finite element space that is
+// chosen as follows:
+// - in the lower left quadrant, Q1
+// - in the lower right quadrant, Q2
+// - in the upper left quadrant, Q3
+// - in the upper right quadrant, Q4
+// In other words, the function f(...) is in the space.
+//
+// We can then run two tests with it:
+// - Interpolate the function onto the finite element space and compute
+// its L2 norm. This can be done analytically. In particular, the
+// area under the square of the functions above is, for the four
+// quadrants:
+// . 1/9
+// . 47/1800
+// . 2332/11025
+// . 1816349/3175200
+// This makes the total sum under the square of the function equal to
+// 2923673/3175200 and the L2 norm under the function equal to
+// sqrt(5847346)/2520, which is about 0.9595748472.
+// (In 3d, we also integrate the same function over z=-1..1, so the
+// volume under f(...)^2 increases by a factor of 2, and the L2 norm
+// by a factor of sqrt(2); the numerical value is then 1.357043763.)
+// - Interpolate the function onto the finite element space and compute
+// the L2 norm of the difference between the interpolated function
+// and the original function. This should be zero.
+// This test does both.
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/tensor.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/hp/dof_handler.h>
+#include <deal.II/hp/q_collection.h>
+
+#include <deal.II/lac/trilinos_vector.h>
+
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+
+
+template <int dim>
+class CheckFunction : public Function<dim>
+{
+public:
+ double
+ value(const Point<dim> &p, const unsigned int) const
+ {
+ const double x = p[0];
+ const double y = p[1];
+
+ // function is bilinear everywhere
+ double f = x * y;
+
+ // on the right half of the domain, add something biquadratic that's
+ // zero at x=0
+ if (x >= 0)
+ f += x * x * y * y;
+
+
+ // in the top half of the domain, add something bicubic that's
+ // zero at y=0
+ if (y >= 0)
+ f += y * y * y * x * x * x;
+
+ // in the top right quadrant, add something biquartic that's
+ // zero at x=0 and y=0
+ if (x >= 0 && y >= 0)
+ f += x * x * x * x * y * y * y * y;
+
+ return f;
+ }
+};
+
+
+template <int dim>
+void
+test()
+{
+ parallel::distributed::Triangulation<dim> tr(MPI_COMM_WORLD);
+
+ GridGenerator::hyper_cube(tr, -1, 1);
+ tr.refine_global(3);
+
+ const hp::FECollection<dim> fe(FE_Q<dim>(1),
+ FE_Q<dim>(2),
+ FE_Q<dim>(3),
+ FE_Q<dim>(4));
+ hp::DoFHandler<dim> dof_handler(tr);
+
+ // set DoF indices as described at the top of the file
+ for (auto &cell : dof_handler.active_cell_iterators())
+ if (cell->is_locally_owned())
+ {
+ const double x = cell->center()[0];
+ const double y = cell->center()[1];
+
+ if (x < 0 && y < 0)
+ cell->set_active_fe_index(0);
+ else if (x > 0 && y < 0)
+ cell->set_active_fe_index(1);
+ else if (x < 0 && y > 0)
+ cell->set_active_fe_index(2);
+ else if (x > 0 && y > 0)
+ cell->set_active_fe_index(3);
+ }
+
+ dof_handler.distribute_dofs(fe);
+
+ // interpolate the function above onto the finite element space
+ TrilinosWrappers::MPI::Vector interpolated(dof_handler.locally_owned_dofs(),
+ MPI_COMM_WORLD);
+ VectorTools::interpolate(dof_handler, CheckFunction<dim>(), interpolated);
+
+ // then also apply constraints
+ AffineConstraints<double> hanging_node_constraints;
+ DoFTools::make_hanging_node_constraints(dof_handler,
+ hanging_node_constraints);
+ hanging_node_constraints.close();
+ hanging_node_constraints.distribute(interpolated);
+
+ // extract a vector that has ghost elements
+ IndexSet relevant_set;
+ DoFTools::extract_locally_relevant_dofs(dof_handler, relevant_set);
+ TrilinosWrappers::MPI::Vector x_rel(relevant_set, MPI_COMM_WORLD);
+ x_rel = interpolated;
+
+ // Create a sufficiently high order quadrature formula
+ hp::QCollection<dim> quadrature(QGauss<dim>(3),
+ QGauss<dim>(4),
+ QGauss<dim>(5),
+ QGauss<dim>(6));
+
+ {
+ // integrate the difference between the function above and
+ // the zero function. for this case, we can compute the exact values
+ // by hand. the ones printed in the output are correct
+ Vector<float> results(tr.n_active_cells());
+ VectorTools::integrate_difference(dof_handler,
+ x_rel,
+ Functions::ZeroFunction<dim>(),
+ results,
+ quadrature,
+ VectorTools::L2_norm);
+ const double global =
+ VectorTools::compute_global_error(tr, results, VectorTools::L2_norm);
+
+ if (Utilities::MPI::this_mpi_process(MPI_COMM_WORLD) == 0)
+ deallog << "L2 norm = " << global << std::endl;
+
+ Assert(std::fabs(global - std::sqrt(5847346.) / 2520. *
+ (dim == 3 ? std::sqrt(2) : 1)) < 1e-7,
+ ExcInternalError());
+ }
+
+
+ {
+ // Now also integrate the difference between the function above and
+ // the its interpolant. This should then of course be zero
+ Vector<float> results(tr.n_active_cells());
+ VectorTools::integrate_difference(dof_handler,
+ x_rel,
+ CheckFunction<dim>(),
+ results,
+ quadrature,
+ VectorTools::L2_norm);
+ const double global =
+ VectorTools::compute_global_error(tr, results, VectorTools::L2_norm);
+
+ if (Utilities::MPI::this_mpi_process(MPI_COMM_WORLD) == 0)
+ deallog << "L2 error = " << global << std::endl;
+
+ Assert(std::fabs(global) < 1e-15, ExcInternalError());
+ }
+}
+
+
+
+int
+main(int argc, char *argv[])
+{
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+
+ unsigned int myid = Utilities::MPI::this_mpi_process(MPI_COMM_WORLD);
+
+
+ deallog.push(Utilities::int_to_string(myid));
+
+ if (myid == 0)
+ {
+ initlog();
+
+ deallog.push("2d");
+ test<2>();
+ deallog.pop();
+
+ deallog.push("3d");
+ test<3>();
+ deallog.pop();
+ }
+ else
+ {
+ deallog.push("2d");
+ test<2>();
+ deallog.pop();
+
+ deallog.push("3d");
+ test<3>();
+ deallog.pop();
+ }
+}
projects / dealii.git / commitdiff