const unsigned int q_point,
const unsigned int component = 0) const;
+ /**
+ * Return the average of the gradient $\{\nabla u \} = \frac{1}{2}\nabla
+ * u_{\text{cell0}} + \frac{1}{2} \nabla u_{\text{cell1}}$ 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
+ * $\{\nabla u\}=\nabla u_{\text{cell0}}$.
+ */
+ Tensor<1, dim>
+ average_gradient(const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component = 0) const;
+
+ /**
+ * Return the average of the hessian $\{\nabla^2 u \} = \frac{1}{2}\nabla^2
+ * u_{\text{cell0}} + \frac{1}{2} \nabla^2 u_{\text{cell1}}$ 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>
+ average_hessian(const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component = 0) const;
+
+ /**
+ * Return the jump if the gradient $[\nabla u]=\nabla u_{\text{cell0}} -
+ * \nabla u_{\text{cell1}}$ 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
+ * $[\nabla u]=\nabla u_{\text{cell0}}$.
+ */
+ Tensor<1, dim>
+ jump_gradient(const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component = 0) const;
/**
* @}
return value;
}
+
+
+template <int dim, int spacedim>
+Tensor<1, dim>
+FEInterfaceValues<dim, spacedim>::average_gradient(
+ const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component) const
+{
+ const auto dofpair = dofmap[interface_dof_index];
+
+ if (at_boundary())
+ return get_fe_face_values(0).shape_grad_component(dofpair[0],
+ q_point,
+ component);
+
+ Tensor<1, dim> value;
+
+ if (dofpair[0] != numbers::invalid_unsigned_int)
+ value += 0.5 * get_fe_face_values(0).shape_grad_component(dofpair[0],
+ q_point,
+ component);
+ if (dofpair[1] != numbers::invalid_unsigned_int)
+ value += 0.5 * get_fe_face_values(1).shape_grad_component(dofpair[1],
+ q_point,
+ component);
+
+ return value;
+}
+
+
+
+template <int dim, int spacedim>
+Tensor<2, dim>
+FEInterfaceValues<dim, spacedim>::average_hessian(
+ const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component) const
+{
+ const auto dofpair = dofmap[interface_dof_index];
+
+ if (at_boundary())
+ return get_fe_face_values(0).shape_hessian_component(dofpair[0],
+ q_point,
+ component);
+
+ Tensor<2, dim> value;
+
+ if (dofpair[0] != numbers::invalid_unsigned_int)
+ value += 0.5 * get_fe_face_values(0).shape_hessian_component(dofpair[0],
+ q_point,
+ component);
+ if (dofpair[1] != numbers::invalid_unsigned_int)
+ value += 0.5 * get_fe_face_values(1).shape_hessian_component(dofpair[1],
+ q_point,
+ component);
+
+ return value;
+}
+
+template <int dim, int spacedim>
+Tensor<1, dim>
+FEInterfaceValues<dim, spacedim>::jump_gradient(
+ const unsigned int interface_dof_index,
+ const unsigned int q_point,
+ const unsigned int component) const
+{
+ const auto dofpair = dofmap[interface_dof_index];
+
+ if (at_boundary())
+ return get_fe_face_values(0).shape_grad_component(dofpair[0],
+ q_point,
+ component);
+
+ Tensor<1, dim> value;
+
+ if (dofpair[0] != numbers::invalid_unsigned_int)
+ value += 1.0 * get_fe_face_values(0).shape_grad_component(dofpair[0],
+ q_point,
+ component);
+ if (dofpair[1] != numbers::invalid_unsigned_int)
+ value += -1.0 * get_fe_face_values(1).shape_grad_component(dofpair[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 average_gradient average_hessian jump_gradient 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
+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);
+ UpdateFlags update_flags = update_values | update_gradients |
+ update_hessians | update_quadrature_points |
+ update_JxW_values;
+
+ FEInterfaceValues<dim> fiv(mapping,
+ fe,
+ QGauss<dim - 1>(fe.degree + 1),
+ update_flags);
+
+
+ auto cell = dofh.begin();
+
+ {
+ unsigned int f = 0;
+ Assert(cell->at_boundary(f), ExcInternalError());
+
+ fiv.reinit(cell, f);
+
+ const unsigned int n_dofs = fiv.n_current_interface_dofs();
+ Vector<double> cell_vector(n_dofs);
+
+ const auto &q_points = fiv.get_quadrature_points();
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) +=
+ fiv.average_gradient(i, qpoint).norm() * fiv.get_JxW_values()[qpoint];
+ deallog << "average_gradient.norm(): " << cell_vector;
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) +=
+ fiv.average_hessian(i, qpoint).norm() * fiv.get_JxW_values()[qpoint];
+ deallog << "average_hessian.norm(): " << cell_vector;
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) +=
+ fiv.jump_gradient(i, qpoint).norm() * fiv.get_JxW_values()[qpoint];
+ deallog << "jump_gradient.norm(): " << cell_vector;
+ }
+
+
+ for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
+ if (!cell->at_boundary(f))
+ {
+ fiv.reinit(cell,
+ f,
+ numbers::invalid_unsigned_int,
+ cell->neighbor(f),
+ cell->neighbor_of_neighbor(f),
+ numbers::invalid_unsigned_int);
+
+ const unsigned int n_dofs = fiv.n_current_interface_dofs();
+ Vector<double> cell_vector(n_dofs);
+
+ const auto &q_points = fiv.get_quadrature_points();
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) += fiv.average_gradient(i, qpoint).norm() *
+ fiv.get_JxW_values()[qpoint];
+ deallog << "average_gradient.norm(): " << cell_vector;
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) += fiv.average_hessian(i, qpoint).norm() *
+ fiv.get_JxW_values()[qpoint];
+ deallog << "average_hessian.norm(): " << cell_vector;
+
+ cell_vector = 0.0;
+ for (unsigned int qpoint = 0; qpoint < q_points.size(); ++qpoint)
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ cell_vector(i) += fiv.jump_gradient(i, qpoint).norm() *
+ fiv.get_JxW_values()[qpoint];
+ deallog << "jump_gradient.norm(): " << cell_vector;
+ }
+}
+
+
+
+int
+main()
+{
+ initlog();
+ test<2>(FE_Q<2>(1));
+ test<2>(FE_DGQ<2>(0));
+ test<2>(FE_DGQ<2>(1));
+ test<2>(FE_DGQ<2>(2));
+ test<3>(FE_Q<3>(1));
+ test<3>(FE_DGQ<3>(0));
+ test<3>(FE_DGQ<3>(1));
+}
--- /dev/null
+
+DEAL::FE_Q<2>(1)
+DEAL::average_gradient.norm(): 1.14783 0.500000 1.14783 0.500000
+DEAL::average_hessian.norm(): 1.41421 1.41421 1.41421 1.41421
+DEAL::jump_gradient.norm(): 1.14783 0.500000 1.14783 0.500000
+DEAL::average_gradient.norm(): 0.250000 1.00000 0.250000 1.00000 0.250000 0.250000
+DEAL::average_hessian.norm(): 0.707107 0.00000 0.707107 0.00000 0.707107 0.707107
+DEAL::jump_gradient.norm(): 0.500000 1.00000 0.500000 1.00000 0.500000 0.500000
+DEAL::FE_DGQ<2>(0)
+DEAL::average_gradient.norm(): 0.00000
+DEAL::average_hessian.norm(): 0.00000
+DEAL::jump_gradient.norm(): 0.00000
+DEAL::average_gradient.norm(): 0.00000 0.00000
+DEAL::average_hessian.norm(): 0.00000 0.00000
+DEAL::jump_gradient.norm(): 0.00000 0.00000
+DEAL::FE_DGQ<2>(1)
+DEAL::average_gradient.norm(): 1.14783 0.500000 1.14783 0.500000
+DEAL::average_hessian.norm(): 1.41421 1.41421 1.41421 1.41421
+DEAL::jump_gradient.norm(): 1.14783 0.500000 1.14783 0.500000
+DEAL::average_gradient.norm(): 0.250000 0.573917 0.250000 0.573917 0.573917 0.250000 0.573917 0.250000
+DEAL::average_hessian.norm(): 0.707107 0.707107 0.707107 0.707107 0.707107 0.707107 0.707107 0.707107
+DEAL::jump_gradient.norm(): 0.500000 1.14783 0.500000 1.14783 1.14783 0.500000 1.14783 0.500000
+DEAL::FE_DGQ<2>(2)
+DEAL::average_gradient.norm(): 1.52420 0.860663 0.215166 3.17925 2.66667 0.666667 1.52420 0.860663 0.215166
+DEAL::average_hessian.norm(): 7.17398 7.68564 2.12446 12.5704 13.4538 4.36931 7.17398 7.68564 2.12446
+DEAL::jump_gradient.norm(): 1.52420 0.860663 0.215166 3.17925 2.66667 0.666667 1.52420 0.860663 0.215166
+DEAL::average_gradient.norm(): 0.107583 0.430331 0.762102 0.333333 1.33333 1.58962 0.107583 0.430331 0.762102 0.762102 0.430331 0.107583 1.58962 1.33333 0.333333 0.762102 0.430331 0.107583
+DEAL::average_hessian.norm(): 1.06223 3.84282 3.58699 2.18466 6.72690 6.28519 1.06223 3.84282 3.58699 3.58699 3.84282 1.06223 6.28519 6.72690 2.18466 3.58699 3.84282 1.06223
+DEAL::jump_gradient.norm(): 0.215166 0.860663 1.52420 0.666667 2.66667 3.17925 0.215166 0.860663 1.52420 1.52420 0.860663 0.215166 3.17925 2.66667 0.666667 1.52420 0.860663 0.215166
+DEAL::FE_Q<3>(1)
+DEAL::average_gradient.norm(): 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000
+DEAL::average_hessian.norm(): 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735
+DEAL::jump_gradient.norm(): 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000
+DEAL::average_gradient.norm(): 0.125000 0.761802 0.125000 0.761802 0.125000 0.761802 0.125000 0.761802 0.125000 0.125000 0.125000 0.125000
+DEAL::average_hessian.norm(): 0.538675 1.41421 0.538675 1.41421 0.538675 1.41421 0.538675 1.41421 0.538675 0.538675 0.538675 0.538675
+DEAL::jump_gradient.norm(): 0.250000 0.500000 0.250000 0.500000 0.250000 0.500000 0.250000 0.500000 0.250000 0.250000 0.250000 0.250000
+DEAL::FE_DGQ<3>(0)
+DEAL::average_gradient.norm(): 0.00000
+DEAL::average_hessian.norm(): 0.00000
+DEAL::jump_gradient.norm(): 0.00000
+DEAL::average_gradient.norm(): 0.00000 0.00000
+DEAL::average_hessian.norm(): 0.00000 0.00000
+DEAL::jump_gradient.norm(): 0.00000 0.00000
+DEAL::FE_DGQ<3>(1)
+DEAL::average_gradient.norm(): 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000
+DEAL::average_hessian.norm(): 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735 1.81150 1.07735
+DEAL::jump_gradient.norm(): 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000
+DEAL::average_gradient.norm(): 0.125000 0.405739 0.125000 0.405739 0.125000 0.405739 0.125000 0.405739 0.405739 0.125000 0.405739 0.125000 0.405739 0.125000 0.405739 0.125000
+DEAL::average_hessian.norm(): 0.538675 0.905750 0.538675 0.905750 0.538675 0.905750 0.538675 0.905750 0.905750 0.538675 0.905750 0.538675 0.905750 0.538675 0.905750 0.538675
+DEAL::jump_gradient.norm(): 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000 0.811479 0.250000
projects / dealii.git / commitdiff