const unsigned int q_point,
const unsigned int component = 0) const;
+ /**
+ * Return the jump in the Hessian $[\nabla^2 u] = \nabla^2 u_{\text{cell0}} -
+ * \nabla^2 u_{\text{cell1}}$ on the interface for the shape function
+ * @p interface_dof_index at the quadrature point @p q_point of component
+ * @p component.
+ *
+ * If this is a boundary face (at_boundary() returns true), then
+ * $[\nabla^2 u] = \nabla^2 u_{\text{cell0}}$.
+ */
+ Tensor<2, dim>
+ jump_hessian(const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component = 0) const;
+
+ /**
+ * Return the jump in the third derivative $[\nabla^3 u] = \nabla^3
+ * u_{\text{cell0}} - \nabla^3 u_{\text{cell1}}$ on the interface for the
+ * shape function @p interface_dof_index at the quadrature point @p q_point of
+ * component @p component.
+ *
+ * If this is a boundary face (at_boundary() returns true), then
+ * $[\nabla^3 u] = \nabla^3 u_{\text{cell0}}$.
+ */
+ Tensor<3, dim>
+ jump_3rd_derivative(const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component = 0) const;
+
/**
* @}
*/
}
+
+template <int dim, int spacedim>
+Tensor<2, dim>
+FEInterfaceValues<dim, spacedim>::jump_hessian(
+ const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component) const
+{
+ const auto dof_pair = dofmap[interface_dof_index];
+
+ if (at_boundary())
+ return get_fe_face_values(0).shape_hessian_component(dof_pair[0],
+ q_point,
+ component);
+
+ Tensor<2, dim> value;
+
+ if (dof_pair[0] != numbers::invalid_unsigned_int)
+ value += 1.0 * get_fe_face_values(0).shape_hessian_component(dof_pair[0],
+ q_point,
+ component);
+ if (dof_pair[1] != numbers::invalid_unsigned_int)
+ value += -1.0 * get_fe_face_values(1).shape_hessian_component(dof_pair[1],
+ q_point,
+ component);
+
+ return value;
+}
+
+
+template <int dim, int spacedim>
+Tensor<3, dim>
+FEInterfaceValues<dim, spacedim>::jump_3rd_derivative(
+ const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component) const
+{
+ const auto dof_pair = dofmap[interface_dof_index];
+
+ if (at_boundary())
+ return get_fe_face_values(0).shape_3rd_derivative_component(dof_pair[0],
+ q_point,
+ component);
+
+ Tensor<3, dim> value;
+
+ if (dof_pair[0] != numbers::invalid_unsigned_int)
+ value +=
+ 1.0 * get_fe_face_values(0).shape_3rd_derivative_component(dof_pair[0],
+ q_point,
+ component);
+ if (dof_pair[1] != numbers::invalid_unsigned_int)
+ value +=
+ -1.0 * get_fe_face_values(1).shape_3rd_derivative_component(dof_pair[1],
+ q_point,
+ component);
+
+ return value;
+}
+
+
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2018 - 2019 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.
+//
+// ---------------------------------------------------------------------
+
+
+// evaluate jump_hessian and jump_third_derivative of FEInterfaceValues
+
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_interface_values.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria.h>
+
+#include <fstream>
+#include <iostream>
+
+#include "../tests.h"
+
+template <int dim>
+void
+make_2_cells(Triangulation<dim> &tria);
+
+
+
+template <>
+void make_2_cells<2>(Triangulation<2> &tria)
+{
+ const unsigned int dim = 2;
+ std::vector<unsigned int> repetitions = {2, 1};
+ Point<dim> p1;
+ Point<dim> p2(2.0, 1.0);
+
+ GridGenerator::subdivided_hyper_rectangle(tria, repetitions, p1, p2);
+}
+
+
+
+template <>
+void make_2_cells<3>(Triangulation<3> &tria)
+{
+ const unsigned int dim = 3;
+ std::vector<unsigned int> repetitions = {2, 1, 1};
+ Point<dim> p1;
+ Point<dim> p2(2.0, 1.0, 1.0);
+
+ GridGenerator::subdivided_hyper_rectangle(tria, repetitions, p1, p2);
+}
+
+
+
+template <int dim>
+void
+print_norm_of_average_over_quadrature_points(const FEInterfaceValues<dim> &fiv)
+{
+ const unsigned int n_dofs = fiv.n_current_interface_dofs();
+ Vector<double> cell_vector(n_dofs);
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < fiv.n_quadrature_points; ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) +=
+ fiv.jump_hessian(i, qpoint).norm() * fiv.get_JxW_values()[qpoint];
+ deallog << "jump_hessian.norm(): " << cell_vector;
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < fiv.n_quadrature_points; ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) += fiv.jump_3rd_derivative(i, qpoint).norm() *
+ fiv.get_JxW_values()[qpoint];
+ deallog << "jump_3rd_derivative.norm(): " << cell_vector;
+}
+
+
+
+template <int dim>
+void
+test(const FiniteElement<dim> &fe)
+{
+ Triangulation<dim> tria;
+ make_2_cells(tria);
+
+ DoFHandler<dim> dofh(tria);
+ deallog << fe.get_name() << std::endl;
+ dofh.distribute_dofs(fe);
+
+ MappingQ<dim> mapping(1);
+ const UpdateFlags update_flags =
+ update_hessians | update_3rd_derivatives | update_JxW_values;
+
+ FEInterfaceValues<dim> fiv(mapping,
+ fe,
+ QGauss<dim - 1>(fe.degree + 1),
+ update_flags);
+
+ auto cell = dofh.begin();
+
+ // Print jump in Hessian and third derivative for a face at the boundary.
+ {
+ unsigned int face = 0;
+ Assert(cell->at_boundary(face), ExcInternalError());
+
+ fiv.reinit(cell, face);
+
+ print_norm_of_average_over_quadrature_points(fiv);
+ }
+
+ // Print jump in Hessian and third derivative for a face between two cells.
+ {
+ const unsigned int face = 1;
+ Assert(!cell->at_boundary(face), ExcInternalError());
+
+ fiv.reinit(cell,
+ face,
+ numbers::invalid_unsigned_int,
+ cell->neighbor(face),
+ cell->neighbor_of_neighbor(face),
+ numbers::invalid_unsigned_int);
+
+ print_norm_of_average_over_quadrature_points(fiv);
+ }
+}
+
+
+
+int
+main()
+{
+ initlog();
+ // Test the lowest order cg and dg elements which have a non-zero third
+ // derivative.
+ test<2>(FE_Q<2>(2));
+ test<2>(FE_DGQ<2>(2));
+ test<3>(FE_Q<3>(1));
+ test<3>(FE_DGQ<3>(1));
+}
--- /dev/null
+
+DEAL::FE_Q<2>(2)
+DEAL::jump_hessian.norm(): 7.17398 2.12446 7.17398 2.12446 12.5704 4.36931 7.68564 7.68564 13.4538
+DEAL::jump_3rd_derivative.norm(): 23.1831 11.8202 23.1831 11.8202 44.4667 20.3528 34.2248 34.2248 63.5828
+DEAL::jump_hessian.norm(): 2.12446 11.0742 2.12446 11.0742 4.36931 14.6059 7.68564 7.68564 13.4538 2.12446 2.12446 4.36931 7.68564 7.68564 13.4538
+DEAL::jump_3rd_derivative.norm(): 11.8202 41.5692 11.8202 41.5692 20.3528 83.1384 34.2248 34.2248 63.5828 11.8202 11.8202 20.3528 34.2248 34.2248 63.5828
+DEAL::FE_DGQ<2>(2)
+DEAL::jump_hessian.norm(): 7.17398 7.68564 2.12446 12.5704 13.4538 4.36931 7.17398 7.68564 2.12446
+DEAL::jump_3rd_derivative.norm(): 23.1831 34.2248 11.8202 44.4667 63.5828 20.3528 23.1831 34.2248 11.8202
+DEAL::jump_hessian.norm(): 2.12446 7.68564 7.17398 4.36931 13.4538 12.5704 2.12446 7.68564 7.17398 7.17398 7.68564 2.12446 12.5704 13.4538 4.36931 7.17398 7.68564 2.12446
+DEAL::jump_3rd_derivative.norm(): 11.8202 34.2248 23.1831 20.3528 63.5828 44.4667 11.8202 34.2248 23.1831 23.1831 34.2248 11.8202 44.4667 63.5828 20.3528 23.1831 34.2248 11.8202
+DEAL::FE_Q<3>(1)
+DEAL::jump_hessian.norm(): 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735
+DEAL::jump_3rd_derivative.norm(): 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949
+DEAL::jump_hessian.norm(): 1.07735 2.15470 1.07735 2.15470 1.07735 2.15470 1.07735 2.15470 1.07735 1.07735 1.07735 1.07735
+DEAL::jump_3rd_derivative.norm(): 2.44949 4.89898 2.44949 4.89898 2.44949 4.89898 2.44949 4.89898 2.44949 2.44949 2.44949 2.44949
+DEAL::FE_DGQ<3>(1)
+DEAL::jump_hessian.norm(): 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735
+DEAL::jump_3rd_derivative.norm(): 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949
+DEAL::jump_hessian.norm(): 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735
+DEAL::jump_3rd_derivative.norm(): 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949 2.44949
projects / dealii.git / commitdiff