case Hdiv_seminorm:
for (unsigned int q=0; q<n_q_points; ++q)
{
- Assert (n_components >= dim,
+ unsigned int idx = 0;
+ if (weight!=nullptr)
+ for (; idx<n_components; ++idx)
+ if (data.weight_vectors[0](idx) > 0)
+ break;
+
+ Assert (n_components >= idx+dim,
ExcMessage ("You can only ask for the Hdiv norm for a finite element "
"with at least 'dim' components. In that case, this function "
- "will take the divergence of the first 'dim' components."));
+ "will find the index of the first non-zero weight and take "
+ "the divergence of the 'dim' components that follow it."));
+
Number sum = 0;
// take the trace of the derivatives scaled by the weight and square it
- for (unsigned int k=0; k<dim; ++k)
- sum += data.psi_grads[q][k][k] * std::sqrt(data.weight_vectors[q](k));
+ for (unsigned int k=idx; k<idx+dim; ++k)
+ sum += data.psi_grads[q][k][k-idx] * std::sqrt(data.weight_vectors[q](k));
diff += numbers::NumberTraits<Number>::abs_square(sum) * fe_values.JxW(q);
}
diff = std::sqrt(diff);
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test integrate_difference with Hdiv_seminorm. Specifically this test
+// deals with the case when the ComponentSelectFunction is used and
+// the components selected for the Hdiv seminorm computations are not
+// the first dim components in the Finite Element.
+
+#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_system.h>
+#include <deal.II/base/signaling_nan.h>
+
+
+using namespace dealii;
+
+// First dim components:
+// f_x = x^2+y(+z), f_y = x^2+y^2, f_z = z+xy
+// div(f) = 2x+2y in 2d
+// div(f) = 2x+2y+1 in 3d
+// Second dim components:
+// g(x,y,z) = 2 * f(x,y,z)
+template <int dim>
+class Ref : public Function<dim>
+{
+public:
+ Ref() : Function<dim>(2*dim) {}
+
+ void vector_value (const Point<dim> &p, Vector<double> &values) const
+ {
+ switch (dim)
+ {
+ case 2:
+ values[0] = p[0]*p[0]+p[1];
+ values[1] = p[0]*p[0]+p[1]*p[1];
+ values[2] = 2*(p[0]*p[0]+p[1]);
+ values[3] = 2*(p[0]*p[0]+p[1]*p[1]);
+ break;
+ case 3:
+ values[0] = p[0]*p[0]+p[1]+p[2];
+ values[1] = p[0]*p[0]+p[1]*p[1];
+ values[2] = p[2]+p[0]*p[1];
+ values[3] = 2*(p[0]*p[0]+p[1]+p[2]);
+ values[4] = 2*(p[0]*p[0]+p[1]*p[1]);
+ values[5] = 2*(p[2]+p[0]*p[1]);
+ break;
+ default:
+ Assert(false, ExcNotImplemented());
+ }
+ }
+};
+
+
+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>(3),dim,
+ FE_Q<dim>(3),dim);
+ DoFHandler<dim> dofh(tria);
+ dofh.distribute_dofs(fe);
+
+ Vector<double> solution (dofh.n_dofs ());
+ VectorTools::interpolate(dofh, Ref<dim>(), solution);
+
+ Vector<double> cellwise_errors (tria.n_active_cells());
+
+ const ComponentSelectFunction<dim> mask_2 (std::make_pair(dim,2*dim), 2*dim);
+ VectorTools::integrate_difference (dofh,
+ solution,
+ ZeroFunction<dim>(2*dim),
+ cellwise_errors,
+ QGauss<dim>(5),
+ norm);
+
+ double error = cellwise_errors.l2_norm();
+
+ const double difference_1 = std::abs(error-value);
+ deallog << "computed: " << error
+ << " expected: " << value
+ << " difference: " << difference_1
+ << std::endl;
+ Assert(difference_1<1e-10, ExcMessage("Error in integrate_difference, first components"));
+
+ VectorTools::integrate_difference (dofh,
+ solution,
+ ZeroFunction<dim>(2*dim),
+ cellwise_errors,
+ QGauss<dim>(5),
+ norm,
+ &mask_2);
+
+ error = cellwise_errors.l2_norm();
+ const double difference_2 = std::abs(error-2.0*value);
+ deallog << "computed: " << error
+ << " expected: " << 2.0*value
+ << " difference: " << difference_2
+ << std::endl;
+ Assert(difference_2<1e-10, ExcMessage("Error in integrate_difference, second components"));
+
+}
+
+
+template <int dim>
+void test()
+{
+ deallog << dim << " dimensions, Hdiv_seminorm:" << std::endl;
+ double true_value = 0;
+ switch (dim)
+ {
+ case 2:
+ true_value = std::sqrt(14.0/3.0);
+ break;
+ case 3:
+ true_value = std::sqrt(29.0/3.0);
+ break;
+ default:
+ Assert(false, ExcNotImplemented());
+ }
+
+ test<dim>(VectorTools::Hdiv_seminorm, true_value);
+ deallog << "OK" << std::endl;
+}
+
+
+int main (int argc, char **argv)
+{
+ initlog();
+ test<2>();
+ test<3>();
+}
projects / dealii.git / commitdiff