--- /dev/null
+New: Functions to compute the 2d and 3d rotation matrix have been implemented
+and can be found in the Physics::Transformations::Rotations namespace.
+<br>
+(Jean-Paul Pelteret, 2017/01/09)
// ---------------------------------------------------------------------
//
-// Copyright (C) 2016 by the deal.II authors
+// Copyright (C) 2016 - 2017 by the deal.II authors
//
// This file is part of the deal.II library.
//
#ifndef dealii__transformations_h
#define dealii__transformations_h
+#include <deal.II/base/point.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/symmetric_tensor.h>
namespace Transformations
{
+ /**
+ * Transformation functions and tensors that are defined in terms of
+ * rotation angles and axes of rotation.
+ *
+ * @author Jean-Paul Pelteret, 2017
+ */
+ namespace Rotations
+ {
+ /**
+ * @name Rotation matrices
+ */
+//@{
+
+ /**
+ * Returns the rotation matrix for 2-d Euclidean space, namely
+ * @f[
+ * \mathbf{R} := \left[ \begin{array}{cc}
+ * cos(\theta) & sin(\theta) \\
+ * -sin(\theta) & cos(\theta)
+ * \end{array}\right]
+ * @f]
+ * where $\theta$ is the rotation angle given in radians.
+ * In particular, this describes the counter-clockwise rotation of a vector
+ * relative to a
+ * <a href="http://mathworld.wolfram.com/RotationMatrix.html">fixed set of right-handed axes</a>.
+ *
+ * @param[in] angle The rotation angle (about the z-axis) in radians
+ */
+ template<typename Number>
+ Tensor<2,2,Number>
+ rotation_matrix_2d (const Number &angle);
+
+
+ /**
+ * Returns the rotation matrix for 3-d Euclidean space.
+ * Most concisely stated using the Rodrigues' rotation formula, this
+ * function returns the equivalent of
+ * @f[
+ * \mathbf{R} := cos(\theta)\mathbf{I} + sin(\theta)\mathbf{W}
+ * + (1-cos(\theta))\mathbf{u}\otimes\mathbf{u}
+ * @f]
+ * where $\mathbf{u}$ is the axial vector (an axial vector) and $\theta$
+ * is the rotation angle given in radians, $\mathbf{I}$ is the identity
+ * tensor and $\mathbf{W}$ is the skew symmetric tensor of $\mathbf{u}$.
+ *
+ * @dealiiWriggersA{374,9.194}
+ * This presents Rodrigues' rotation formula, but the implementation used
+ * in this function is described in this
+ * <a href="https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">wikipedia link</a>.
+ * In particular, this describes the counter-clockwise rotation of a vector
+ * <a href="http://mathworld.wolfram.com/RotationMatrix.html">in a plane with its normal</a>.
+ * defined by the @p axis of rotation.
+ * An alternative implementation is discussed at
+ * <a href="https://www.gamedev.net/resources/_/technical/math-and-physics/do-we-really-need-quaternions-r1199">this link</a>,
+ * but is inconsistent (sign-wise) with the Rodrigues' rotation formula as
+ * it describes the rotation of a coordinate system.
+ *
+ * @param[in] axis A unit vector that defines the axis of rotation
+ * @param[in] angle The rotation angle in radians
+ */
+ template<typename Number>
+ Tensor<2,3,Number>
+ rotation_matrix_3d (const Point<3,Number> &axis,
+ const Number &angle);
+
+//@}
+
+ }
+
/**
* Transformation of tensors that are defined in terms of a set of
* contravariant bases. Rank-1 and rank-2 contravariant tensors
+template<typename Number>
+Tensor<2,2,Number>
+Physics::Transformations::Rotations::rotation_matrix_2d (const Number &angle)
+{
+ const double rotation[2][2]
+ = {{
+ std::cos(angle) , -std::sin(angle)
+ },
+ {
+ std::sin(angle) , std::cos(angle)
+ }
+ };
+ return Tensor<2,2> (rotation);
+}
+
+
+
+template<typename Number>
+Tensor<2,3,Number>
+Physics::Transformations::Rotations::rotation_matrix_3d (const Point<3,Number> &axis,
+ const Number &angle)
+{
+ Assert(std::abs(axis.norm() - 1.0) < 1e-9,
+ ExcMessage("The supplied axial vector is not a unit vector."));
+ const Number c = std::cos(angle);
+ const Number s = std::sin(angle);
+ const Number t = 1.-c;
+ const double rotation[3][3]
+ = {{
+ t *axis[0] *axis[0] + c,
+ t *axis[0] *axis[1] - s *axis[2],
+ t *axis[0] *axis[2] + s *axis[1]
+ },
+ {
+ t *axis[0] *axis[1] + s *axis[2],
+ t *axis[1] *axis[1] + c,
+ t *axis[1] *axis[2] - s *axis[0]
+ },
+ {
+ t *axis[0] *axis[2] - s *axis[1],
+ t *axis[1] *axis[2] + s *axis[0],
+ t *axis[2] *axis[2] + c
+ }
+ };
+ return Tensor<2,3,Number>(rotation);
+}
+
+
+
template <int dim, typename Number>
inline
Tensor<1,dim,Number>
--- /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.
+ *
+ * ---------------------------------------------------------------------
+ */
+
+// This is a version of step-18 that employs the rotation matrices defined
+// in the Physics::Transformations::Angular namespace.
+
+#include "../tests.h"
+
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/multithread_info.h>
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/petsc_parallel_vector.h>
+#include <deal.II/lac/petsc_parallel_sparse_matrix.h>
+#include <deal.II/lac/petsc_solver.h>
+#include <deal.II/lac/petsc_precondition.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/sparsity_tools.h>
+#include <deal.II/distributed/shared_tria.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/dofs/dof_renumbering.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/error_estimator.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/grid/filtered_iterator.h>
+#include <deal.II/physics/transformations.h>
+#include <fstream>
+#include <iostream>
+#include <sstream>
+#include <iomanip>
+namespace Step18
+{
+ using namespace dealii;
+ template <int dim>
+ struct PointHistory
+ {
+ SymmetricTensor<2,dim> old_stress;
+ };
+ template <int dim>
+ SymmetricTensor<4,dim>
+ get_stress_strain_tensor (const double lambda, const double mu)
+ {
+ SymmetricTensor<4,dim> tmp;
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=0; j<dim; ++j)
+ for (unsigned int k=0; k<dim; ++k)
+ for (unsigned int l=0; l<dim; ++l)
+ tmp[i][j][k][l] = (((i==k) && (j==l) ? mu : 0.0) +
+ ((i==l) && (j==k) ? mu : 0.0) +
+ ((i==j) && (k==l) ? lambda : 0.0));
+ return tmp;
+ }
+ template <int dim>
+ inline
+ SymmetricTensor<2,dim>
+ get_strain (const FEValues<dim> &fe_values,
+ const unsigned int shape_func,
+ const unsigned int q_point)
+ {
+ SymmetricTensor<2,dim> tmp;
+ for (unsigned int i=0; i<dim; ++i)
+ tmp[i][i] = fe_values.shape_grad_component (shape_func,q_point,i)[i];
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=i+1; j<dim; ++j)
+ tmp[i][j]
+ = (fe_values.shape_grad_component (shape_func,q_point,i)[j] +
+ fe_values.shape_grad_component (shape_func,q_point,j)[i]) / 2;
+ return tmp;
+ }
+ template <int dim>
+ inline
+ SymmetricTensor<2,dim>
+ get_strain (const std::vector<Tensor<1,dim> > &grad)
+ {
+ Assert (grad.size() == dim, ExcInternalError());
+ SymmetricTensor<2,dim> strain;
+ for (unsigned int i=0; i<dim; ++i)
+ strain[i][i] = grad[i][i];
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=i+1; j<dim; ++j)
+ strain[i][j] = (grad[i][j] + grad[j][i]) / 2;
+ return strain;
+ }
+ Tensor<2,2>
+ get_rotation_matrix (const std::vector<Tensor<1,2> > &grad_u)
+ {
+ const double curl = (grad_u[1][0] - grad_u[0][1]);
+ // Note: Here the negative angle suggests that we're computing the rotation
+ // of the coordinate system around a fixed point
+ const double angle = -std::atan (curl);
+ return Physics::Transformations::Rotations::rotation_matrix_2d(angle);
+ }
+ Tensor<2,3>
+ get_rotation_matrix (const std::vector<Tensor<1,3> > &grad_u)
+ {
+ const Point<3> curl (grad_u[2][1] - grad_u[1][2],
+ grad_u[0][2] - grad_u[2][0],
+ grad_u[1][0] - grad_u[0][1]);
+ const double tan_angle = std::sqrt(curl*curl);
+ // Note: Here the negative angle suggests that we're computing the rotation
+ // of the coordinate system around a fixed point
+ const double angle = -std::atan (tan_angle);
+ const Point<3> axis = curl/tan_angle;
+ return Physics::Transformations::Rotations::rotation_matrix_3d(axis,angle);
+ }
+ template <int dim>
+ class TopLevel
+ {
+ public:
+ TopLevel ();
+ ~TopLevel ();
+ void run ();
+ private:
+ void create_coarse_grid ();
+ void setup_system ();
+ void assemble_system ();
+ void solve_timestep ();
+ unsigned int solve_linear_problem ();
+ void output_results () const;
+ void do_initial_timestep ();
+ void do_timestep ();
+ void refine_initial_grid ();
+ void move_mesh ();
+ void setup_quadrature_point_history ();
+ void update_quadrature_point_history ();
+ parallel::shared::Triangulation<dim> triangulation;
+ FESystem<dim> fe;
+ DoFHandler<dim> dof_handler;
+ ConstraintMatrix hanging_node_constraints;
+ const QGauss<dim> quadrature_formula;
+ std::vector<PointHistory<dim> > quadrature_point_history;
+ PETScWrappers::MPI::SparseMatrix system_matrix;
+ PETScWrappers::MPI::Vector system_rhs;
+ Vector<double> incremental_displacement;
+ double present_time;
+ double present_timestep;
+ double end_time;
+ unsigned int timestep_no;
+ MPI_Comm mpi_communicator;
+ const unsigned int n_mpi_processes;
+ const unsigned int this_mpi_process;
+ ConditionalOStream pcout;
+ std::vector<types::global_dof_index> local_dofs_per_process;
+ IndexSet locally_owned_dofs;
+ IndexSet locally_relevant_dofs;
+ unsigned int n_local_cells;
+ static const SymmetricTensor<4,dim> stress_strain_tensor;
+ int monitored_vertex_first_dof;
+ };
+ template <int dim>
+ class BodyForce : public Function<dim>
+ {
+ public:
+ BodyForce ();
+ virtual
+ void
+ vector_value (const Point<dim> &p,
+ Vector<double> &values) const;
+ virtual
+ void
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const;
+ };
+ template <int dim>
+ BodyForce<dim>::BodyForce ()
+ :
+ Function<dim> (dim)
+ {}
+ template <int dim>
+ inline
+ void
+ BodyForce<dim>::vector_value (const Point<dim> &/*p*/,
+ Vector<double> &values) const
+ {
+ Assert (values.size() == dim,
+ ExcDimensionMismatch (values.size(), dim));
+ const double g = 9.81;
+ const double rho = 7700;
+ values = 0;
+ values(dim-1) = -rho * g;
+ }
+ template <int dim>
+ void
+ BodyForce<dim>::vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const
+ {
+ const unsigned int n_points = points.size();
+ Assert (value_list.size() == n_points,
+ ExcDimensionMismatch (value_list.size(), n_points));
+ for (unsigned int p=0; p<n_points; ++p)
+ BodyForce<dim>::vector_value (points[p],
+ value_list[p]);
+ }
+ template <int dim>
+ class IncrementalBoundaryValues : public Function<dim>
+ {
+ public:
+ IncrementalBoundaryValues (const double present_time,
+ const double present_timestep);
+ virtual
+ void
+ vector_value (const Point<dim> &p,
+ Vector<double> &values) const;
+ virtual
+ void
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const;
+ private:
+ const double velocity;
+ const double present_time;
+ const double present_timestep;
+ };
+ template <int dim>
+ IncrementalBoundaryValues<dim>::
+ IncrementalBoundaryValues (const double present_time,
+ const double present_timestep)
+ :
+ Function<dim> (dim),
+ velocity (.1),
+ present_time (present_time),
+ present_timestep (present_timestep)
+ {}
+ template <int dim>
+ void
+ IncrementalBoundaryValues<dim>::
+ vector_value (const Point<dim> &/*p*/,
+ Vector<double> &values) const
+ {
+ Assert (values.size() == dim,
+ ExcDimensionMismatch (values.size(), dim));
+ values = 0;
+ values(2) = -present_timestep * velocity;
+ }
+ template <int dim>
+ void
+ IncrementalBoundaryValues<dim>::
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const
+ {
+ const unsigned int n_points = points.size();
+ Assert (value_list.size() == n_points,
+ ExcDimensionMismatch (value_list.size(), n_points));
+ for (unsigned int p=0; p<n_points; ++p)
+ IncrementalBoundaryValues<dim>::vector_value (points[p],
+ value_list[p]);
+ }
+ template <int dim>
+ const SymmetricTensor<4,dim>
+ TopLevel<dim>::stress_strain_tensor
+ = get_stress_strain_tensor<dim> (/*lambda = */ 9.695e10,
+ /*mu = */ 7.617e10);
+ template <int dim>
+ TopLevel<dim>::TopLevel ()
+ :
+ triangulation(MPI_COMM_WORLD),
+ fe (FE_Q<dim>(1), dim),
+ dof_handler (triangulation),
+ quadrature_formula (2),
+ mpi_communicator (MPI_COMM_WORLD),
+ n_mpi_processes (Utilities::MPI::n_mpi_processes(mpi_communicator)),
+ this_mpi_process (Utilities::MPI::this_mpi_process(mpi_communicator)),
+ pcout (std::cout, this_mpi_process == 0),
+ monitored_vertex_first_dof(0)
+ {}
+ template <int dim>
+ TopLevel<dim>::~TopLevel ()
+ {
+ dof_handler.clear ();
+ }
+ template <int dim>
+ void TopLevel<dim>::run ()
+ {
+ present_time = 0;
+ present_timestep = 1;
+ end_time = 10;
+ timestep_no = 0;
+ do_initial_timestep ();
+ while (present_time < end_time)
+ do_timestep ();
+ }
+ template <int dim>
+ void TopLevel<dim>::create_coarse_grid ()
+ {
+ const double inner_radius = 0.8,
+ outer_radius = 1;
+ GridGenerator::cylinder_shell (triangulation,
+ 3, inner_radius, outer_radius);
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell=triangulation.begin_active();
+ cell!=triangulation.end(); ++cell)
+ for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
+ if (cell->face(f)->at_boundary())
+ {
+ const Point<dim> face_center = cell->face(f)->center();
+ if (face_center[2] == 0)
+ cell->face(f)->set_boundary_id (0);
+ else if (face_center[2] == 3)
+ cell->face(f)->set_boundary_id (1);
+ else if (std::sqrt(face_center[0]*face_center[0] +
+ face_center[1]*face_center[1])
+ <
+ (inner_radius + outer_radius) / 2)
+ cell->face(f)->set_boundary_id (2);
+ else
+ cell->face(f)->set_boundary_id (3);
+ }
+ static const CylindricalManifold<dim> cylindrical_manifold (2);
+ triangulation.set_all_manifold_ids(0);
+ triangulation.set_manifold (0, cylindrical_manifold);
+ // triangulation.refine_global (1);
+ setup_quadrature_point_history ();
+ }
+ template <int dim>
+ void TopLevel<dim>::setup_system ()
+ {
+ dof_handler.distribute_dofs (fe);
+ locally_owned_dofs = dof_handler.locally_owned_dofs();
+ DoFTools::extract_locally_relevant_dofs (dof_handler,locally_relevant_dofs);
+ n_local_cells
+ = GridTools::count_cells_with_subdomain_association (triangulation,
+ triangulation.locally_owned_subdomain ());
+ local_dofs_per_process = dof_handler.n_locally_owned_dofs_per_processor();
+ hanging_node_constraints.clear ();
+ DoFTools::make_hanging_node_constraints (dof_handler,
+ hanging_node_constraints);
+ hanging_node_constraints.close ();
+ DynamicSparsityPattern sparsity_pattern (locally_relevant_dofs);
+ DoFTools::make_sparsity_pattern (dof_handler, sparsity_pattern,
+ hanging_node_constraints, /*keep constrained dofs*/ false);
+ SparsityTools::distribute_sparsity_pattern (sparsity_pattern,
+ local_dofs_per_process,
+ mpi_communicator,
+ locally_relevant_dofs);
+ system_matrix.reinit (locally_owned_dofs,
+ locally_owned_dofs,
+ sparsity_pattern,
+ mpi_communicator);
+ system_rhs.reinit(locally_owned_dofs,mpi_communicator);
+ incremental_displacement.reinit (dof_handler.n_dofs());
+ }
+ template <int dim>
+ void TopLevel<dim>::assemble_system ()
+ {
+ system_rhs = 0;
+ system_matrix = 0;
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values | update_gradients |
+ update_quadrature_points | update_JxW_values);
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+ const unsigned int n_q_points = quadrature_formula.size();
+ FullMatrix<double> cell_matrix (dofs_per_cell, dofs_per_cell);
+ Vector<double> cell_rhs (dofs_per_cell);
+ std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+ BodyForce<dim> body_force;
+ std::vector<Vector<double> > body_force_values (n_q_points,
+ Vector<double>(dim));
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ for (; cell!=endc; ++cell)
+ if (cell->is_locally_owned())
+ {
+ cell_matrix = 0;
+ cell_rhs = 0;
+ fe_values.reinit (cell);
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ for (unsigned int q_point=0; q_point<n_q_points;
+ ++q_point)
+ {
+ const SymmetricTensor<2,dim>
+ eps_phi_i = get_strain (fe_values, i, q_point),
+ eps_phi_j = get_strain (fe_values, j, q_point);
+ cell_matrix(i,j)
+ += (eps_phi_i * stress_strain_tensor * eps_phi_j
+ *
+ fe_values.JxW (q_point));
+ }
+ const PointHistory<dim> *local_quadrature_points_data
+ = reinterpret_cast<PointHistory<dim>*>(cell->user_pointer());
+ body_force.vector_value_list (fe_values.get_quadrature_points(),
+ body_force_values);
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ const unsigned int
+ component_i = fe.system_to_component_index(i).first;
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+ {
+ const SymmetricTensor<2,dim> &old_stress
+ = local_quadrature_points_data[q_point].old_stress;
+ cell_rhs(i) += (body_force_values[q_point](component_i) *
+ fe_values.shape_value (i,q_point)
+ -
+ old_stress *
+ get_strain (fe_values,i,q_point))
+ *
+ fe_values.JxW (q_point);
+ }
+ }
+ cell->get_dof_indices (local_dof_indices);
+ hanging_node_constraints
+ .distribute_local_to_global (cell_matrix, cell_rhs,
+ local_dof_indices,
+ system_matrix, system_rhs);
+ }
+ system_matrix.compress(VectorOperation::add);
+ system_rhs.compress(VectorOperation::add);
+ FEValuesExtractors::Scalar z_component (dim-1);
+ std::map<types::global_dof_index,double> boundary_values;
+ VectorTools::
+ interpolate_boundary_values (dof_handler,
+ 0,
+ ZeroFunction<dim> (dim),
+ boundary_values);
+ VectorTools::
+ interpolate_boundary_values (dof_handler,
+ 1,
+ IncrementalBoundaryValues<dim>(present_time,
+ present_timestep),
+ boundary_values,
+ fe.component_mask(z_component));
+ PETScWrappers::MPI::Vector tmp (locally_owned_dofs,mpi_communicator);
+ MatrixTools::apply_boundary_values (boundary_values,
+ system_matrix, tmp,
+ system_rhs, false);
+ incremental_displacement = tmp;
+ }
+ template <int dim>
+ void TopLevel<dim>::solve_timestep ()
+ {
+ pcout << " Assembling system..." << std::flush;
+ assemble_system ();
+ pcout << " norm of rhs is " << system_rhs.l2_norm()
+ << std::endl;
+ const unsigned int n_iterations = solve_linear_problem ();
+ pcout << " Solver converged in " << n_iterations
+ << " iterations." << std::endl;
+ pcout << " Updating quadrature point data..." << std::flush;
+ update_quadrature_point_history ();
+ pcout << std::endl;
+ }
+ template <int dim>
+ unsigned int TopLevel<dim>::solve_linear_problem ()
+ {
+ PETScWrappers::MPI::Vector
+ distributed_incremental_displacement (locally_owned_dofs,mpi_communicator);
+ distributed_incremental_displacement = incremental_displacement;
+ SolverControl solver_control (dof_handler.n_dofs(),
+ 1e-16*system_rhs.l2_norm(),
+ false,false);
+ PETScWrappers::SolverCG cg (solver_control,
+ mpi_communicator);
+ PETScWrappers::PreconditionBlockJacobi preconditioner(system_matrix);
+ cg.solve (system_matrix, distributed_incremental_displacement, system_rhs,
+ preconditioner);
+ incremental_displacement = distributed_incremental_displacement;
+ hanging_node_constraints.distribute (incremental_displacement);
+ return solver_control.last_step();
+ }
+ template <int dim>
+ void TopLevel<dim>::output_results () const
+ {
+ DataOut<dim> data_out;
+ data_out.attach_dof_handler (dof_handler);
+ std::vector<std::string> solution_names;
+ switch (dim)
+ {
+ case 1:
+ solution_names.push_back ("delta_x");
+ break;
+ case 2:
+ solution_names.push_back ("delta_x");
+ solution_names.push_back ("delta_y");
+ break;
+ case 3:
+ solution_names.push_back ("delta_x");
+ solution_names.push_back ("delta_y");
+ solution_names.push_back ("delta_z");
+ break;
+ default:
+ Assert (false, ExcNotImplemented());
+ }
+ data_out.add_data_vector (incremental_displacement,
+ solution_names);
+ Vector<double> norm_of_stress (triangulation.n_active_cells());
+ {
+ typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active(),
+ endc = triangulation.end();
+ for (; cell!=endc; ++cell)
+ if (cell->is_locally_owned())
+ {
+ SymmetricTensor<2,dim> accumulated_stress;
+ for (unsigned int q=0;
+ q<quadrature_formula.size();
+ ++q)
+ accumulated_stress +=
+ reinterpret_cast<PointHistory<dim>*>(cell->user_pointer())[q]
+ .old_stress;
+ norm_of_stress(cell->active_cell_index())
+ = (accumulated_stress /
+ quadrature_formula.size()).norm();
+ }
+ else
+ norm_of_stress(cell->active_cell_index()) = -1e+20;
+ }
+ data_out.add_data_vector (norm_of_stress, "norm_of_stress");
+ std::vector<types::subdomain_id> partition_int (triangulation.n_active_cells());
+ GridTools::get_subdomain_association (triangulation, partition_int);
+ const Vector<double> partitioning(partition_int.begin(),
+ partition_int.end());
+ data_out.add_data_vector (partitioning, "partitioning");
+ data_out.build_patches ();
+ std::string filename = "solution-" + Utilities::int_to_string(timestep_no,4)
+ + "." + Utilities::int_to_string(this_mpi_process,3)
+ + ".vtu";
+ AssertThrow (n_mpi_processes < 1000, ExcNotImplemented());
+ std::ofstream output (filename.c_str());
+ data_out.write_vtu (output);
+ if (this_mpi_process==0)
+ {
+ std::vector<std::string> filenames;
+ for (unsigned int i=0; i<n_mpi_processes; ++i)
+ filenames.push_back ("solution-" + Utilities::int_to_string(timestep_no,4)
+ + "." + Utilities::int_to_string(i,3)
+ + ".vtu");
+ const std::string
+ visit_master_filename = ("solution-" +
+ Utilities::int_to_string(timestep_no,4) +
+ ".visit");
+ std::ofstream visit_master (visit_master_filename.c_str());
+ DataOutBase::write_visit_record (visit_master, filenames);
+ const std::string
+ pvtu_master_filename = ("solution-" +
+ Utilities::int_to_string(timestep_no,4) +
+ ".pvtu");
+ std::ofstream pvtu_master (pvtu_master_filename.c_str());
+ data_out.write_pvtu_record (pvtu_master, filenames);
+ static std::vector<std::pair<double,std::string> > times_and_names;
+ times_and_names.push_back (std::pair<double,std::string> (present_time, pvtu_master_filename));
+ std::ofstream pvd_output ("solution.pvd");
+ DataOutBase::write_pvd_record (pvd_output, times_and_names);
+ }
+ }
+ template <int dim>
+ void TopLevel<dim>::do_initial_timestep ()
+ {
+ present_time += present_timestep;
+ ++timestep_no;
+ pcout << "Timestep " << timestep_no << " at time " << present_time
+ << std::endl;
+ for (unsigned int cycle=0; cycle<2; ++cycle)
+ {
+ pcout << " Cycle " << cycle << ':' << std::endl;
+ if (cycle == 0)
+ create_coarse_grid ();
+ else
+ refine_initial_grid ();
+ pcout << " Number of active cells: "
+ << triangulation.n_active_cells()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout << (p==0 ? ' ' : '+')
+ << (GridTools::
+ count_cells_with_subdomain_association (triangulation,p));
+ pcout << ")" << std::endl;
+ setup_system ();
+ pcout << " Number of degrees of freedom: "
+ << dof_handler.n_dofs()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout << (p==0 ? ' ' : '+')
+ << (DoFTools::
+ count_dofs_with_subdomain_association (dof_handler,p));
+ pcout << ")" << std::endl;
+ // Get point at which to output displacement
+ // (outer radius of displaced surface)
+ {
+ const Point<dim> soln_pt (1.0, 0.0, 3.0);
+ typename DoFHandler<dim>::active_cell_iterator cell =
+ dof_handler.begin_active(), endc = dof_handler.end();
+ for (; cell != endc; ++cell)
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ if (cell->vertex(v).distance(soln_pt) < 1e-6)
+ {
+ monitored_vertex_first_dof = cell->vertex_dof_index(v,0);
+ }
+ }
+ solve_timestep ();
+ }
+ move_mesh ();
+ // output_results ();
+ pcout << std::endl;
+ }
+ template <int dim>
+ void TopLevel<dim>::do_timestep ()
+ {
+ present_time += present_timestep;
+ ++timestep_no;
+ pcout << "Timestep " << timestep_no << " at time " << present_time
+ << std::endl;
+ if (present_time > end_time)
+ {
+ present_timestep -= (present_time - end_time);
+ present_time = end_time;
+ }
+ solve_timestep ();
+ move_mesh ();
+ // output_results ();
+ // Output displacement at edge of displaced surface
+ {
+ static Tensor<1,dim> soln;
+ for (unsigned int d=0; d<dim; ++d)
+ soln[d] += incremental_displacement(monitored_vertex_first_dof+d);
+ deallog
+ << "Timestep " << timestep_no
+ << ": " << soln << std::endl;
+ }
+ pcout << std::endl;
+ }
+ template <int dim>
+ void TopLevel<dim>::refine_initial_grid ()
+ {
+ Vector<float> error_per_cell (triangulation.n_active_cells());
+ KellyErrorEstimator<dim>::estimate (dof_handler,
+ QGauss<dim-1>(2),
+ typename FunctionMap<dim>::type(),
+ incremental_displacement,
+ error_per_cell,
+ ComponentMask(),
+ 0,
+ MultithreadInfo::n_threads(),
+ this_mpi_process);
+ const unsigned int n_local_cells = triangulation.n_locally_owned_active_cells ();
+ PETScWrappers::MPI::Vector
+ distributed_error_per_cell (mpi_communicator,
+ triangulation.n_active_cells(),
+ n_local_cells);
+ for (unsigned int i=0; i<error_per_cell.size(); ++i)
+ if (error_per_cell(i) != 0)
+ distributed_error_per_cell(i) = error_per_cell(i);
+ distributed_error_per_cell.compress (VectorOperation::insert);
+ error_per_cell = distributed_error_per_cell;
+ GridRefinement::refine_and_coarsen_fixed_number (triangulation,
+ error_per_cell,
+ 0.25, 0.03);
+ triangulation.execute_coarsening_and_refinement ();
+ setup_quadrature_point_history ();
+ }
+ template <int dim>
+ void TopLevel<dim>::move_mesh ()
+ {
+ pcout << " Moving mesh..." << std::endl;
+ std::vector<bool> vertex_touched (triangulation.n_vertices(),
+ false);
+ for (typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active ();
+ cell != dof_handler.end(); ++cell)
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ if (vertex_touched[cell->vertex_index(v)] == false)
+ {
+ vertex_touched[cell->vertex_index(v)] = true;
+ Point<dim> vertex_displacement;
+ for (unsigned int d=0; d<dim; ++d)
+ vertex_displacement[d]
+ = incremental_displacement(cell->vertex_dof_index(v,d));
+ cell->vertex(v) += vertex_displacement;
+ }
+ }
+ template <int dim>
+ void TopLevel<dim>::setup_quadrature_point_history ()
+ {
+ unsigned int our_cells = 0;
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ if (cell->is_locally_owned())
+ ++our_cells;
+ triangulation.clear_user_data();
+ {
+ std::vector<PointHistory<dim> > tmp;
+ tmp.swap (quadrature_point_history);
+ }
+ quadrature_point_history.resize (our_cells *
+ quadrature_formula.size());
+ unsigned int history_index = 0;
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ if (cell->is_locally_owned())
+ {
+ cell->set_user_pointer (&quadrature_point_history[history_index]);
+ history_index += quadrature_formula.size();
+ }
+ Assert (history_index == quadrature_point_history.size(),
+ ExcInternalError());
+ }
+ template <int dim>
+ void TopLevel<dim>::update_quadrature_point_history ()
+ {
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values | update_gradients);
+ std::vector<std::vector<Tensor<1,dim> > >
+ displacement_increment_grads (quadrature_formula.size(),
+ std::vector<Tensor<1,dim> >(dim));
+ for (typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active();
+ cell != dof_handler.end(); ++cell)
+ if (cell->is_locally_owned())
+ {
+ PointHistory<dim> *local_quadrature_points_history
+ = reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
+ Assert (local_quadrature_points_history >=
+ &quadrature_point_history.front(),
+ ExcInternalError());
+ Assert (local_quadrature_points_history <
+ &quadrature_point_history.back(),
+ ExcInternalError());
+ fe_values.reinit (cell);
+ fe_values.get_function_gradients (incremental_displacement,
+ displacement_increment_grads);
+ for (unsigned int q=0; q<quadrature_formula.size(); ++q)
+ {
+ const SymmetricTensor<2,dim> new_stress
+ = (local_quadrature_points_history[q].old_stress
+ +
+ (stress_strain_tensor *
+ get_strain (displacement_increment_grads[q])));
+ const Tensor<2,dim> rotation
+ = get_rotation_matrix (displacement_increment_grads[q]);
+ const SymmetricTensor<2,dim> rotated_new_stress
+ = symmetrize(transpose(rotation) *
+ static_cast<Tensor<2,dim> >(new_stress) *
+ rotation);
+ local_quadrature_points_history[q].old_stress
+ = rotated_new_stress;
+ }
+ }
+ }
+}
+int main (int argc, char **argv)
+{
+ std::ofstream logfile("output");
+ deallog << std::setprecision(3);
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ try
+ {
+ using namespace dealii;
+ using namespace Step18;
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+ TopLevel<3> elastic_problem;
+ elastic_problem.run ();
+ }
+ catch (std::exception &exc)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl
+ << exc.what() << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ catch (...)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ return 0;
+}
--- /dev/null
+
+DEAL::Timestep 2: 0.00982 -1.35e-06 -0.100
+DEAL::Timestep 3: 0.0201 -3.32e-06 -0.200
+DEAL::Timestep 4: 0.0308 -5.19e-06 -0.300
+DEAL::Timestep 5: 0.0424 -5.68e-06 -0.400
+DEAL::Timestep 6: 0.0554 7.87e-07 -0.500
+DEAL::Timestep 7: 0.0720 3.84e-05 -0.600
+DEAL::Timestep 8: 0.0979 0.000188 -0.700
+DEAL::Timestep 9: 0.139 0.000618 -0.800
+DEAL::Timestep 10: 0.178 0.00126 -0.900
--- /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.
+ *
+ * ---------------------------------------------------------------------
+ */
+
+// This is a copy of step-18 (git rev ecafd3f), but with a corrected rotation
+// matrix, to use as a base-line for results produced via different approaches
+// to be compared to.
+
+#include "../tests.h"
+
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/multithread_info.h>
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/petsc_parallel_vector.h>
+#include <deal.II/lac/petsc_parallel_sparse_matrix.h>
+#include <deal.II/lac/petsc_solver.h>
+#include <deal.II/lac/petsc_precondition.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/sparsity_tools.h>
+#include <deal.II/distributed/shared_tria.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/dofs/dof_renumbering.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/error_estimator.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/grid/filtered_iterator.h>
+#include <fstream>
+#include <iostream>
+#include <sstream>
+#include <iomanip>
+namespace Step18
+{
+ using namespace dealii;
+ template <int dim>
+ struct PointHistory
+ {
+ SymmetricTensor<2,dim> old_stress;
+ };
+ template <int dim>
+ SymmetricTensor<4,dim>
+ get_stress_strain_tensor (const double lambda, const double mu)
+ {
+ SymmetricTensor<4,dim> tmp;
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=0; j<dim; ++j)
+ for (unsigned int k=0; k<dim; ++k)
+ for (unsigned int l=0; l<dim; ++l)
+ tmp[i][j][k][l] = (((i==k) && (j==l) ? mu : 0.0) +
+ ((i==l) && (j==k) ? mu : 0.0) +
+ ((i==j) && (k==l) ? lambda : 0.0));
+ return tmp;
+ }
+ template <int dim>
+ inline
+ SymmetricTensor<2,dim>
+ get_strain (const FEValues<dim> &fe_values,
+ const unsigned int shape_func,
+ const unsigned int q_point)
+ {
+ SymmetricTensor<2,dim> tmp;
+ for (unsigned int i=0; i<dim; ++i)
+ tmp[i][i] = fe_values.shape_grad_component (shape_func,q_point,i)[i];
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=i+1; j<dim; ++j)
+ tmp[i][j]
+ = (fe_values.shape_grad_component (shape_func,q_point,i)[j] +
+ fe_values.shape_grad_component (shape_func,q_point,j)[i]) / 2;
+ return tmp;
+ }
+ template <int dim>
+ inline
+ SymmetricTensor<2,dim>
+ get_strain (const std::vector<Tensor<1,dim> > &grad)
+ {
+ Assert (grad.size() == dim, ExcInternalError());
+ SymmetricTensor<2,dim> strain;
+ for (unsigned int i=0; i<dim; ++i)
+ strain[i][i] = grad[i][i];
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=i+1; j<dim; ++j)
+ strain[i][j] = (grad[i][j] + grad[j][i]) / 2;
+ return strain;
+ }
+ Tensor<2,2>
+ get_rotation_matrix (const std::vector<Tensor<1,2> > &grad_u)
+ {
+ const double curl = (grad_u[1][0] - grad_u[0][1]);
+ const double angle = std::atan (curl);
+ const double t[2][2] = {{ cos(angle), sin(angle) },
+ {-sin(angle), cos(angle) }
+ };
+ return Tensor<2,2>(t);
+ }
+ Tensor<2,3>
+ get_rotation_matrix (const std::vector<Tensor<1,3> > &grad_u)
+ {
+ const Point<3> curl (grad_u[2][1] - grad_u[1][2],
+ grad_u[0][2] - grad_u[2][0],
+ grad_u[1][0] - grad_u[0][1]);
+ const double tan_angle = std::sqrt(curl*curl);
+ const double angle = std::atan (tan_angle);
+ if (angle < 1e-9)
+ {
+ static const double rotation[3][3]
+ = {{ 1, 0, 0}, { 0, 1, 0 }, { 0, 0, 1 } };
+ static const Tensor<2,3> rot(rotation);
+ return rot;
+ }
+ const double c = std::cos(angle);
+ const double s = std::sin(angle);
+ const double t = 1-c;
+ const Point<3> axis = curl/tan_angle;
+ // Rotation matrix fixed: See issue #468
+ const double rotation[3][3]
+ = {{
+ t *axis[0] *axis[0]+c,
+ t *axis[0] *axis[1]+s *axis[2],
+ t *axis[0] *axis[2]-s *axis[1]
+ },
+ {
+ t *axis[0] *axis[1]-s *axis[2],
+ t *axis[1] *axis[1]+c,
+ t *axis[1] *axis[2]+s *axis[0]
+ },
+ {
+ t *axis[0] *axis[2]+s *axis[1],
+ t *axis[1] *axis[2]-s *axis[0],
+ t *axis[2] *axis[2]+c
+ }
+ };
+ return Tensor<2,3>(rotation);
+ }
+ template <int dim>
+ class TopLevel
+ {
+ public:
+ TopLevel ();
+ ~TopLevel ();
+ void run ();
+ private:
+ void create_coarse_grid ();
+ void setup_system ();
+ void assemble_system ();
+ void solve_timestep ();
+ unsigned int solve_linear_problem ();
+ void output_results () const;
+ void do_initial_timestep ();
+ void do_timestep ();
+ void refine_initial_grid ();
+ void move_mesh ();
+ void setup_quadrature_point_history ();
+ void update_quadrature_point_history ();
+ parallel::shared::Triangulation<dim> triangulation;
+ FESystem<dim> fe;
+ DoFHandler<dim> dof_handler;
+ ConstraintMatrix hanging_node_constraints;
+ const QGauss<dim> quadrature_formula;
+ std::vector<PointHistory<dim> > quadrature_point_history;
+ PETScWrappers::MPI::SparseMatrix system_matrix;
+ PETScWrappers::MPI::Vector system_rhs;
+ Vector<double> incremental_displacement;
+ double present_time;
+ double present_timestep;
+ double end_time;
+ unsigned int timestep_no;
+ MPI_Comm mpi_communicator;
+ const unsigned int n_mpi_processes;
+ const unsigned int this_mpi_process;
+ ConditionalOStream pcout;
+ std::vector<types::global_dof_index> local_dofs_per_process;
+ IndexSet locally_owned_dofs;
+ IndexSet locally_relevant_dofs;
+ unsigned int n_local_cells;
+ static const SymmetricTensor<4,dim> stress_strain_tensor;
+ int monitored_vertex_first_dof;
+ };
+ template <int dim>
+ class BodyForce : public Function<dim>
+ {
+ public:
+ BodyForce ();
+ virtual
+ void
+ vector_value (const Point<dim> &p,
+ Vector<double> &values) const;
+ virtual
+ void
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const;
+ };
+ template <int dim>
+ BodyForce<dim>::BodyForce ()
+ :
+ Function<dim> (dim)
+ {}
+ template <int dim>
+ inline
+ void
+ BodyForce<dim>::vector_value (const Point<dim> &/*p*/,
+ Vector<double> &values) const
+ {
+ Assert (values.size() == dim,
+ ExcDimensionMismatch (values.size(), dim));
+ const double g = 9.81;
+ const double rho = 7700;
+ values = 0;
+ values(dim-1) = -rho * g;
+ }
+ template <int dim>
+ void
+ BodyForce<dim>::vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const
+ {
+ const unsigned int n_points = points.size();
+ Assert (value_list.size() == n_points,
+ ExcDimensionMismatch (value_list.size(), n_points));
+ for (unsigned int p=0; p<n_points; ++p)
+ BodyForce<dim>::vector_value (points[p],
+ value_list[p]);
+ }
+ template <int dim>
+ class IncrementalBoundaryValues : public Function<dim>
+ {
+ public:
+ IncrementalBoundaryValues (const double present_time,
+ const double present_timestep);
+ virtual
+ void
+ vector_value (const Point<dim> &p,
+ Vector<double> &values) const;
+ virtual
+ void
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const;
+ private:
+ const double velocity;
+ const double present_time;
+ const double present_timestep;
+ };
+ template <int dim>
+ IncrementalBoundaryValues<dim>::
+ IncrementalBoundaryValues (const double present_time,
+ const double present_timestep)
+ :
+ Function<dim> (dim),
+ velocity (.1),
+ present_time (present_time),
+ present_timestep (present_timestep)
+ {}
+ template <int dim>
+ void
+ IncrementalBoundaryValues<dim>::
+ vector_value (const Point<dim> &/*p*/,
+ Vector<double> &values) const
+ {
+ Assert (values.size() == dim,
+ ExcDimensionMismatch (values.size(), dim));
+ values = 0;
+ values(2) = -present_timestep * velocity;
+ }
+ template <int dim>
+ void
+ IncrementalBoundaryValues<dim>::
+ vector_value_list (const std::vector<Point<dim> > &points,
+ std::vector<Vector<double> > &value_list) const
+ {
+ const unsigned int n_points = points.size();
+ Assert (value_list.size() == n_points,
+ ExcDimensionMismatch (value_list.size(), n_points));
+ for (unsigned int p=0; p<n_points; ++p)
+ IncrementalBoundaryValues<dim>::vector_value (points[p],
+ value_list[p]);
+ }
+ template <int dim>
+ const SymmetricTensor<4,dim>
+ TopLevel<dim>::stress_strain_tensor
+ = get_stress_strain_tensor<dim> (/*lambda = */ 9.695e10,
+ /*mu = */ 7.617e10);
+ template <int dim>
+ TopLevel<dim>::TopLevel ()
+ :
+ triangulation(MPI_COMM_WORLD),
+ fe (FE_Q<dim>(1), dim),
+ dof_handler (triangulation),
+ quadrature_formula (2),
+ mpi_communicator (MPI_COMM_WORLD),
+ n_mpi_processes (Utilities::MPI::n_mpi_processes(mpi_communicator)),
+ this_mpi_process (Utilities::MPI::this_mpi_process(mpi_communicator)),
+ pcout (std::cout, this_mpi_process == 0),
+ monitored_vertex_first_dof(0)
+ {}
+ template <int dim>
+ TopLevel<dim>::~TopLevel ()
+ {
+ dof_handler.clear ();
+ }
+ template <int dim>
+ void TopLevel<dim>::run ()
+ {
+ present_time = 0;
+ present_timestep = 1;
+ end_time = 10;
+ timestep_no = 0;
+ do_initial_timestep ();
+ while (present_time < end_time)
+ do_timestep ();
+ }
+ template <int dim>
+ void TopLevel<dim>::create_coarse_grid ()
+ {
+ const double inner_radius = 0.8,
+ outer_radius = 1;
+ GridGenerator::cylinder_shell (triangulation,
+ 3, inner_radius, outer_radius);
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell=triangulation.begin_active();
+ cell!=triangulation.end(); ++cell)
+ for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
+ if (cell->face(f)->at_boundary())
+ {
+ const Point<dim> face_center = cell->face(f)->center();
+ if (face_center[2] == 0)
+ cell->face(f)->set_boundary_id (0);
+ else if (face_center[2] == 3)
+ cell->face(f)->set_boundary_id (1);
+ else if (std::sqrt(face_center[0]*face_center[0] +
+ face_center[1]*face_center[1])
+ <
+ (inner_radius + outer_radius) / 2)
+ cell->face(f)->set_boundary_id (2);
+ else
+ cell->face(f)->set_boundary_id (3);
+ }
+ static const CylindricalManifold<dim> cylindrical_manifold (2);
+ triangulation.set_all_manifold_ids(0);
+ triangulation.set_manifold (0, cylindrical_manifold);
+ // triangulation.refine_global (1);
+ setup_quadrature_point_history ();
+ }
+ template <int dim>
+ void TopLevel<dim>::setup_system ()
+ {
+ dof_handler.distribute_dofs (fe);
+ locally_owned_dofs = dof_handler.locally_owned_dofs();
+ DoFTools::extract_locally_relevant_dofs (dof_handler,locally_relevant_dofs);
+ n_local_cells
+ = GridTools::count_cells_with_subdomain_association (triangulation,
+ triangulation.locally_owned_subdomain ());
+ local_dofs_per_process = dof_handler.n_locally_owned_dofs_per_processor();
+ hanging_node_constraints.clear ();
+ DoFTools::make_hanging_node_constraints (dof_handler,
+ hanging_node_constraints);
+ hanging_node_constraints.close ();
+ DynamicSparsityPattern sparsity_pattern (locally_relevant_dofs);
+ DoFTools::make_sparsity_pattern (dof_handler, sparsity_pattern,
+ hanging_node_constraints, /*keep constrained dofs*/ false);
+ SparsityTools::distribute_sparsity_pattern (sparsity_pattern,
+ local_dofs_per_process,
+ mpi_communicator,
+ locally_relevant_dofs);
+ system_matrix.reinit (locally_owned_dofs,
+ locally_owned_dofs,
+ sparsity_pattern,
+ mpi_communicator);
+ system_rhs.reinit(locally_owned_dofs,mpi_communicator);
+ incremental_displacement.reinit (dof_handler.n_dofs());
+ }
+ template <int dim>
+ void TopLevel<dim>::assemble_system ()
+ {
+ system_rhs = 0;
+ system_matrix = 0;
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values | update_gradients |
+ update_quadrature_points | update_JxW_values);
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+ const unsigned int n_q_points = quadrature_formula.size();
+ FullMatrix<double> cell_matrix (dofs_per_cell, dofs_per_cell);
+ Vector<double> cell_rhs (dofs_per_cell);
+ std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+ BodyForce<dim> body_force;
+ std::vector<Vector<double> > body_force_values (n_q_points,
+ Vector<double>(dim));
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ for (; cell!=endc; ++cell)
+ if (cell->is_locally_owned())
+ {
+ cell_matrix = 0;
+ cell_rhs = 0;
+ fe_values.reinit (cell);
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ for (unsigned int q_point=0; q_point<n_q_points;
+ ++q_point)
+ {
+ const SymmetricTensor<2,dim>
+ eps_phi_i = get_strain (fe_values, i, q_point),
+ eps_phi_j = get_strain (fe_values, j, q_point);
+ cell_matrix(i,j)
+ += (eps_phi_i * stress_strain_tensor * eps_phi_j
+ *
+ fe_values.JxW (q_point));
+ }
+ const PointHistory<dim> *local_quadrature_points_data
+ = reinterpret_cast<PointHistory<dim>*>(cell->user_pointer());
+ body_force.vector_value_list (fe_values.get_quadrature_points(),
+ body_force_values);
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ const unsigned int
+ component_i = fe.system_to_component_index(i).first;
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+ {
+ const SymmetricTensor<2,dim> &old_stress
+ = local_quadrature_points_data[q_point].old_stress;
+ cell_rhs(i) += (body_force_values[q_point](component_i) *
+ fe_values.shape_value (i,q_point)
+ -
+ old_stress *
+ get_strain (fe_values,i,q_point))
+ *
+ fe_values.JxW (q_point);
+ }
+ }
+ cell->get_dof_indices (local_dof_indices);
+ hanging_node_constraints
+ .distribute_local_to_global (cell_matrix, cell_rhs,
+ local_dof_indices,
+ system_matrix, system_rhs);
+ }
+ system_matrix.compress(VectorOperation::add);
+ system_rhs.compress(VectorOperation::add);
+ FEValuesExtractors::Scalar z_component (dim-1);
+ std::map<types::global_dof_index,double> boundary_values;
+ VectorTools::
+ interpolate_boundary_values (dof_handler,
+ 0,
+ ZeroFunction<dim> (dim),
+ boundary_values);
+ VectorTools::
+ interpolate_boundary_values (dof_handler,
+ 1,
+ IncrementalBoundaryValues<dim>(present_time,
+ present_timestep),
+ boundary_values,
+ fe.component_mask(z_component));
+ PETScWrappers::MPI::Vector tmp (locally_owned_dofs,mpi_communicator);
+ MatrixTools::apply_boundary_values (boundary_values,
+ system_matrix, tmp,
+ system_rhs, false);
+ incremental_displacement = tmp;
+ }
+ template <int dim>
+ void TopLevel<dim>::solve_timestep ()
+ {
+ pcout << " Assembling system..." << std::flush;
+ assemble_system ();
+ pcout << " norm of rhs is " << system_rhs.l2_norm()
+ << std::endl;
+ const unsigned int n_iterations = solve_linear_problem ();
+ pcout << " Solver converged in " << n_iterations
+ << " iterations." << std::endl;
+ pcout << " Updating quadrature point data..." << std::flush;
+ update_quadrature_point_history ();
+ pcout << std::endl;
+ }
+ template <int dim>
+ unsigned int TopLevel<dim>::solve_linear_problem ()
+ {
+ PETScWrappers::MPI::Vector
+ distributed_incremental_displacement (locally_owned_dofs,mpi_communicator);
+ distributed_incremental_displacement = incremental_displacement;
+ SolverControl solver_control (dof_handler.n_dofs(),
+ 1e-16*system_rhs.l2_norm(),
+ false,false);
+ PETScWrappers::SolverCG cg (solver_control,
+ mpi_communicator);
+ PETScWrappers::PreconditionBlockJacobi preconditioner(system_matrix);
+ cg.solve (system_matrix, distributed_incremental_displacement, system_rhs,
+ preconditioner);
+ incremental_displacement = distributed_incremental_displacement;
+ hanging_node_constraints.distribute (incremental_displacement);
+ return solver_control.last_step();
+ }
+ template <int dim>
+ void TopLevel<dim>::output_results () const
+ {
+ DataOut<dim> data_out;
+ data_out.attach_dof_handler (dof_handler);
+ std::vector<std::string> solution_names;
+ switch (dim)
+ {
+ case 1:
+ solution_names.push_back ("delta_x");
+ break;
+ case 2:
+ solution_names.push_back ("delta_x");
+ solution_names.push_back ("delta_y");
+ break;
+ case 3:
+ solution_names.push_back ("delta_x");
+ solution_names.push_back ("delta_y");
+ solution_names.push_back ("delta_z");
+ break;
+ default:
+ Assert (false, ExcNotImplemented());
+ }
+ data_out.add_data_vector (incremental_displacement,
+ solution_names);
+ Vector<double> norm_of_stress (triangulation.n_active_cells());
+ {
+ typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active(),
+ endc = triangulation.end();
+ for (; cell!=endc; ++cell)
+ if (cell->is_locally_owned())
+ {
+ SymmetricTensor<2,dim> accumulated_stress;
+ for (unsigned int q=0;
+ q<quadrature_formula.size();
+ ++q)
+ accumulated_stress +=
+ reinterpret_cast<PointHistory<dim>*>(cell->user_pointer())[q]
+ .old_stress;
+ norm_of_stress(cell->active_cell_index())
+ = (accumulated_stress /
+ quadrature_formula.size()).norm();
+ }
+ else
+ norm_of_stress(cell->active_cell_index()) = -1e+20;
+ }
+ data_out.add_data_vector (norm_of_stress, "norm_of_stress");
+ std::vector<types::subdomain_id> partition_int (triangulation.n_active_cells());
+ GridTools::get_subdomain_association (triangulation, partition_int);
+ const Vector<double> partitioning(partition_int.begin(),
+ partition_int.end());
+ data_out.add_data_vector (partitioning, "partitioning");
+ data_out.build_patches ();
+ std::string filename = "solution-" + Utilities::int_to_string(timestep_no,4)
+ + "." + Utilities::int_to_string(this_mpi_process,3)
+ + ".vtu";
+ AssertThrow (n_mpi_processes < 1000, ExcNotImplemented());
+ std::ofstream output (filename.c_str());
+ data_out.write_vtu (output);
+ if (this_mpi_process==0)
+ {
+ std::vector<std::string> filenames;
+ for (unsigned int i=0; i<n_mpi_processes; ++i)
+ filenames.push_back ("solution-" + Utilities::int_to_string(timestep_no,4)
+ + "." + Utilities::int_to_string(i,3)
+ + ".vtu");
+ const std::string
+ visit_master_filename = ("solution-" +
+ Utilities::int_to_string(timestep_no,4) +
+ ".visit");
+ std::ofstream visit_master (visit_master_filename.c_str());
+ DataOutBase::write_visit_record (visit_master, filenames);
+ const std::string
+ pvtu_master_filename = ("solution-" +
+ Utilities::int_to_string(timestep_no,4) +
+ ".pvtu");
+ std::ofstream pvtu_master (pvtu_master_filename.c_str());
+ data_out.write_pvtu_record (pvtu_master, filenames);
+ static std::vector<std::pair<double,std::string> > times_and_names;
+ times_and_names.push_back (std::pair<double,std::string> (present_time, pvtu_master_filename));
+ std::ofstream pvd_output ("solution.pvd");
+ DataOutBase::write_pvd_record (pvd_output, times_and_names);
+ }
+ }
+ template <int dim>
+ void TopLevel<dim>::do_initial_timestep ()
+ {
+ present_time += present_timestep;
+ ++timestep_no;
+ pcout << "Timestep " << timestep_no << " at time " << present_time
+ << std::endl;
+ for (unsigned int cycle=0; cycle<2; ++cycle)
+ {
+ pcout << " Cycle " << cycle << ':' << std::endl;
+ if (cycle == 0)
+ create_coarse_grid ();
+ else
+ refine_initial_grid ();
+ pcout << " Number of active cells: "
+ << triangulation.n_active_cells()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout << (p==0 ? ' ' : '+')
+ << (GridTools::
+ count_cells_with_subdomain_association (triangulation,p));
+ pcout << ")" << std::endl;
+ setup_system ();
+ pcout << " Number of degrees of freedom: "
+ << dof_handler.n_dofs()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout << (p==0 ? ' ' : '+')
+ << (DoFTools::
+ count_dofs_with_subdomain_association (dof_handler,p));
+ pcout << ")" << std::endl;
+ // Get point at which to output displacement
+ // (outer radius of displaced surface)
+ {
+ const Point<dim> soln_pt (1.0, 0.0, 3.0);
+ typename DoFHandler<dim>::active_cell_iterator cell =
+ dof_handler.begin_active(), endc = dof_handler.end();
+ for (; cell != endc; ++cell)
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ if (cell->vertex(v).distance(soln_pt) < 1e-6)
+ {
+ monitored_vertex_first_dof = cell->vertex_dof_index(v,0);
+ }
+ }
+ solve_timestep ();
+ }
+ move_mesh ();
+ // output_results ();
+ pcout << std::endl;
+ }
+ template <int dim>
+ void TopLevel<dim>::do_timestep ()
+ {
+ present_time += present_timestep;
+ ++timestep_no;
+ pcout << "Timestep " << timestep_no << " at time " << present_time
+ << std::endl;
+ if (present_time > end_time)
+ {
+ present_timestep -= (present_time - end_time);
+ present_time = end_time;
+ }
+ solve_timestep ();
+ move_mesh ();
+ // output_results ();
+ // Output displacement at edge of displaced surface
+ {
+ static Tensor<1,dim> soln;
+ for (unsigned int d=0; d<dim; ++d)
+ soln[d] += incremental_displacement(monitored_vertex_first_dof+d);
+ deallog
+ << "Timestep " << timestep_no
+ << ": " << soln << std::endl;
+ }
+ pcout << std::endl;
+ }
+ template <int dim>
+ void TopLevel<dim>::refine_initial_grid ()
+ {
+ Vector<float> error_per_cell (triangulation.n_active_cells());
+ KellyErrorEstimator<dim>::estimate (dof_handler,
+ QGauss<dim-1>(2),
+ typename FunctionMap<dim>::type(),
+ incremental_displacement,
+ error_per_cell,
+ ComponentMask(),
+ 0,
+ MultithreadInfo::n_threads(),
+ this_mpi_process);
+ const unsigned int n_local_cells = triangulation.n_locally_owned_active_cells ();
+ PETScWrappers::MPI::Vector
+ distributed_error_per_cell (mpi_communicator,
+ triangulation.n_active_cells(),
+ n_local_cells);
+ for (unsigned int i=0; i<error_per_cell.size(); ++i)
+ if (error_per_cell(i) != 0)
+ distributed_error_per_cell(i) = error_per_cell(i);
+ distributed_error_per_cell.compress (VectorOperation::insert);
+ error_per_cell = distributed_error_per_cell;
+ GridRefinement::refine_and_coarsen_fixed_number (triangulation,
+ error_per_cell,
+ 0.25, 0.03);
+ triangulation.execute_coarsening_and_refinement ();
+ setup_quadrature_point_history ();
+ }
+ template <int dim>
+ void TopLevel<dim>::move_mesh ()
+ {
+ pcout << " Moving mesh..." << std::endl;
+ std::vector<bool> vertex_touched (triangulation.n_vertices(),
+ false);
+ for (typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active ();
+ cell != dof_handler.end(); ++cell)
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ if (vertex_touched[cell->vertex_index(v)] == false)
+ {
+ vertex_touched[cell->vertex_index(v)] = true;
+ Point<dim> vertex_displacement;
+ for (unsigned int d=0; d<dim; ++d)
+ vertex_displacement[d]
+ = incremental_displacement(cell->vertex_dof_index(v,d));
+ cell->vertex(v) += vertex_displacement;
+ }
+ }
+ template <int dim>
+ void TopLevel<dim>::setup_quadrature_point_history ()
+ {
+ unsigned int our_cells = 0;
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ if (cell->is_locally_owned())
+ ++our_cells;
+ triangulation.clear_user_data();
+ {
+ std::vector<PointHistory<dim> > tmp;
+ tmp.swap (quadrature_point_history);
+ }
+ quadrature_point_history.resize (our_cells *
+ quadrature_formula.size());
+ unsigned int history_index = 0;
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ if (cell->is_locally_owned())
+ {
+ cell->set_user_pointer (&quadrature_point_history[history_index]);
+ history_index += quadrature_formula.size();
+ }
+ Assert (history_index == quadrature_point_history.size(),
+ ExcInternalError());
+ }
+ template <int dim>
+ void TopLevel<dim>::update_quadrature_point_history ()
+ {
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values | update_gradients);
+ std::vector<std::vector<Tensor<1,dim> > >
+ displacement_increment_grads (quadrature_formula.size(),
+ std::vector<Tensor<1,dim> >(dim));
+ for (typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active();
+ cell != dof_handler.end(); ++cell)
+ if (cell->is_locally_owned())
+ {
+ PointHistory<dim> *local_quadrature_points_history
+ = reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
+ Assert (local_quadrature_points_history >=
+ &quadrature_point_history.front(),
+ ExcInternalError());
+ Assert (local_quadrature_points_history <
+ &quadrature_point_history.back(),
+ ExcInternalError());
+ fe_values.reinit (cell);
+ fe_values.get_function_gradients (incremental_displacement,
+ displacement_increment_grads);
+ for (unsigned int q=0; q<quadrature_formula.size(); ++q)
+ {
+ const SymmetricTensor<2,dim> new_stress
+ = (local_quadrature_points_history[q].old_stress
+ +
+ (stress_strain_tensor *
+ get_strain (displacement_increment_grads[q])));
+ const Tensor<2,dim> rotation
+ = get_rotation_matrix (displacement_increment_grads[q]);
+ const SymmetricTensor<2,dim> rotated_new_stress
+ = symmetrize(transpose(rotation) *
+ static_cast<Tensor<2,dim> >(new_stress) *
+ rotation);
+ local_quadrature_points_history[q].old_stress
+ = rotated_new_stress;
+ }
+ }
+ }
+}
+int main (int argc, char **argv)
+{
+ std::ofstream logfile("output");
+ deallog << std::setprecision(3);
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ try
+ {
+ using namespace dealii;
+ using namespace Step18;
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+ TopLevel<3> elastic_problem;
+ elastic_problem.run ();
+ }
+ catch (std::exception &exc)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl
+ << exc.what() << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ catch (...)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ return 0;
+}
--- /dev/null
+
+DEAL::Timestep 2: 0.00982 -1.35e-06 -0.100
+DEAL::Timestep 3: 0.0201 -3.32e-06 -0.200
+DEAL::Timestep 4: 0.0308 -5.19e-06 -0.300
+DEAL::Timestep 5: 0.0424 -5.68e-06 -0.400
+DEAL::Timestep 6: 0.0554 7.87e-07 -0.500
+DEAL::Timestep 7: 0.0720 3.84e-05 -0.600
+DEAL::Timestep 8: 0.0979 0.000188 -0.700
+DEAL::Timestep 9: 0.139 0.000618 -0.800
+DEAL::Timestep 10: 0.178 0.00126 -0.900
--- /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 rotation matrix definitions
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+
+#include <deal.II/base/point.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/base/tensor.h>
+
+#include <deal.II/physics/transformations.h>
+
+#include <fstream>
+#include <iomanip>
+
+using namespace dealii;
+using namespace dealii::Physics;
+
+
+void
+test_rotation_matrix_3d_z_axis (const double angle)
+{
+ Tensor<2,3> R_z = unit_symmetric_tensor<3>();
+ const Tensor<2,2> R_2d = Transformations::Rotations::rotation_matrix_2d(angle);
+ for (unsigned int i=0; i<2; ++i)
+ for (unsigned int j=0; j<2; ++j)
+ R_z[i][j] = R_2d[i][j];
+
+ Assert(std::abs(determinant(R_z) - 1.0) < 1e-9,
+ ExcMessage("Rodrigues rotation matrix determinant is not unity"));
+ const Tensor<2,3> R = Transformations::Rotations::rotation_matrix_3d(Point<3>({0,0,1}),angle);
+ Assert(std::abs(determinant(R) - 1.0) < 1e-9,
+ ExcMessage("Rotation matrix determinant is not unity"));
+
+ Assert((transpose(R)*R - unit_symmetric_tensor<3>()).norm() < 1e-9,
+ ExcMessage("Matrix is not a rotation matrix"));
+ Assert((R - R_z).norm() < 1e-12,
+ ExcMessage("Incorrect computation of R in 3d"));
+}
+
+void
+test_rotation_matrix_3d (const Point<3> &axis,
+ const double angle)
+{
+ // http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
+ // http://en.wikipedia.org/wiki/Rotation_matrix
+ // NOTE: Angle in radians
+ const Tensor<1,3> u = axis / axis.norm(); // Ensure unit vector
+ const Tensor<2,3> u_dyad_u = outer_product (u, u);
+ const double u_skew_array [3][3] =
+ {
+ {0.0, -u[2], u[1]},
+ {u[2], 0.0, -u[0]},
+ {-u[1], u[0], 0.0}
+ };
+
+ const Tensor<2,3> R_rodrigues
+ = u_dyad_u
+ + std::cos(angle)*(static_cast < Tensor<2,3> > (unit_symmetric_tensor<3>()) - u_dyad_u)
+ + std::sin(angle)*Tensor<2,3> (u_skew_array);
+
+
+ Assert(std::abs(determinant(R_rodrigues) - 1.0) < 1e-9,
+ ExcMessage("Rodrigues rotation matrix determinant is not unity"));
+ const Tensor<2,3> R = Transformations::Rotations::rotation_matrix_3d(axis,angle);
+ Assert(std::abs(determinant(R) - 1.0) < 1e-9,
+ ExcMessage("Rotation matrix determinant is not unity"));
+
+ Assert((transpose(R)*R - unit_symmetric_tensor<3>()).norm() < 1e-9,
+ ExcMessage("Matrix is not a rotation matrix"));
+ Assert((R - R_rodrigues).norm() < 1e-12,
+ ExcMessage("Incorrect computation of R in 3d"));
+}
+
+Point<3>
+normalise(const Point<3> &p)
+{
+ Assert(p.norm() > 0.0, ExcMessage("Point vector has zero norm"));
+ return p/p.norm();
+}
+
+int main ()
+{
+ std::ofstream logfile("output");
+ deallog << std::setprecision(3);
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ const double deg_to_rad = M_PI/180.0;
+
+ // 2-d
+ {
+ const double angle = 90.0*deg_to_rad;
+ const Tensor<1,2> in ({1,0});
+ const Tensor<2,2> R = Transformations::Rotations::rotation_matrix_2d(angle);
+ Assert((transpose(R)*R - unit_symmetric_tensor<2>()).norm() < 1e-9, ExcMessage("Matrix is not a rotation matrix"));
+ Assert(std::abs(determinant(R) - 1.0) < 1e-9, ExcMessage("Rotation matrix determinant is not unity"));
+ const Tensor<1,2> out = R*in;
+ Assert((out - Tensor<1,2>({0,1})).norm() < 1e-12,
+ ExcMessage("Incorrect computation of 90 degree R in 2d"));
+ }
+ {
+ const double angle = 135.0*deg_to_rad;
+ const Tensor<1,2> in ({1,0});
+ const Tensor<2,2> R = Transformations::Rotations::rotation_matrix_2d(angle);
+ Assert((transpose(R)*R - unit_symmetric_tensor<2>()).norm() < 1e-9, ExcMessage("Matrix is not a rotation matrix"));
+ Assert(std::abs(determinant(R) - 1.0) < 1e-9, ExcMessage("Rotation matrix determinant is not unity"));
+ const Tensor<1,2> out = R*in;
+ Assert((out - Tensor<1,2>({-1.0/std::sqrt(2.0),1.0/std::sqrt(2.0)})).norm() < 1e-12,
+ ExcMessage("Incorrect computation of 135 degree R in 2d"));
+ }
+ {
+ const double angle = 240.0*deg_to_rad;
+ const Tensor<1,2> in ({1,0});
+ const Tensor<2,2> R = Transformations::Rotations::rotation_matrix_2d(angle);
+ Assert((transpose(R)*R - unit_symmetric_tensor<2>()).norm() < 1e-9, ExcMessage("Matrix is not a rotation matrix"));
+ Assert(std::abs(determinant(R) - 1.0) < 1e-9, ExcMessage("Rotation matrix determinant is not unity"));
+ const Tensor<1,2> out = R*in;
+ Assert((out - Tensor<1,2>({-0.5,-std::sqrt(3.0)/2.0})).norm() < 1e-12,
+ ExcMessage("Incorrect computation of 240 degree R in 2d"));
+ }
+
+ // 3-d
+ test_rotation_matrix_3d_z_axis (90.0*deg_to_rad);
+ test_rotation_matrix_3d_z_axis (45.0*deg_to_rad);
+ test_rotation_matrix_3d_z_axis (60.0*deg_to_rad);
+
+ test_rotation_matrix_3d (normalise(Point<3>({1,1,1})), 90.0*deg_to_rad);
+ test_rotation_matrix_3d (normalise(Point<3>({0,2,1})), 45.0*deg_to_rad);
+ test_rotation_matrix_3d (normalise(Point<3>({-1,3,2})), 60.0*deg_to_rad);
+
+ deallog << "OK" << std::endl;
+}
--- /dev/null
+
+DEAL::OK