--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 - 2018 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.
+//
+// ---------------------------------------------------------------------
+
+// Header file:
+// This is a modified version of step-44, which tests the implementation of
+// cell-level auto-differentiation (linearisation of a residual vector).
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/parameter_handler.h>
+#include <deal.II/base/point.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/quadrature_point_data.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/base/tensor.h>
+#include <deal.II/base/timer.h>
+#include <deal.II/base/work_stream.h>
+
+#include <deal.II/differentiation/ad.h>
+
+#include <deal.II/dofs/dof_renumbering.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_dgp_monomial.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q_eulerian.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_in.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_vector.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/linear_operator.h>
+#include <deal.II/lac/packaged_operation.h>
+#include <deal.II/lac/precondition_selector.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/solver_selector.h>
+#include <deal.II/lac/sparse_direct.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+#include <functional>
+#include <iostream>
+
+#include "../tests.h"
+namespace Step44
+{
+ using namespace dealii;
+ namespace AD = dealii::Differentiation::AD;
+ namespace Parameters
+ {
+ struct FESystem
+ {
+ unsigned int poly_degree;
+ unsigned int quad_order;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ FESystem::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Finite element system");
+ {
+ prm.declare_entry("Polynomial degree",
+ "2",
+ Patterns::Integer(0),
+ "Displacement system polynomial order");
+ prm.declare_entry("Quadrature order",
+ "3",
+ Patterns::Integer(0),
+ "Gauss quadrature order");
+ }
+ prm.leave_subsection();
+ }
+ void
+ FESystem::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Finite element system");
+ {
+ poly_degree = prm.get_integer("Polynomial degree");
+ quad_order = prm.get_integer("Quadrature order");
+ }
+ prm.leave_subsection();
+ }
+ struct Geometry
+ {
+ unsigned int global_refinement;
+ double scale;
+ double p_p0;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ Geometry::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Geometry");
+ {
+ prm.declare_entry("Global refinement",
+ "2",
+ Patterns::Integer(0),
+ "Global refinement level");
+ prm.declare_entry("Grid scale",
+ "1e-3",
+ Patterns::Double(0.0),
+ "Global grid scaling factor");
+ prm.declare_entry("Pressure ratio p/p0",
+ "100",
+ Patterns::Selection("20|40|60|80|100"),
+ "Ratio of applied pressure to reference pressure");
+ }
+ prm.leave_subsection();
+ }
+ void
+ Geometry::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Geometry");
+ {
+ global_refinement = prm.get_integer("Global refinement");
+ scale = prm.get_double("Grid scale");
+ p_p0 = prm.get_double("Pressure ratio p/p0");
+ }
+ prm.leave_subsection();
+ }
+ struct Materials
+ {
+ double nu;
+ double mu;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ Materials::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Material properties");
+ {
+ prm.declare_entry("Poisson's ratio",
+ "0.4999",
+ Patterns::Double(-1.0, 0.5),
+ "Poisson's ratio");
+ prm.declare_entry("Shear modulus",
+ "80.194e6",
+ Patterns::Double(),
+ "Shear modulus");
+ }
+ prm.leave_subsection();
+ }
+ void
+ Materials::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Material properties");
+ {
+ nu = prm.get_double("Poisson's ratio");
+ mu = prm.get_double("Shear modulus");
+ }
+ prm.leave_subsection();
+ }
+ struct LinearSolver
+ {
+ std::string type_lin;
+ double tol_lin;
+ double max_iterations_lin;
+ bool use_static_condensation;
+ std::string preconditioner_type;
+ double preconditioner_relaxation;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ LinearSolver::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Linear solver");
+ {
+ prm.declare_entry("Solver type",
+ "CG",
+ Patterns::Selection("CG|Direct"),
+ "Type of solver used to solve the linear system");
+ prm.declare_entry("Residual",
+ "1e-6",
+ Patterns::Double(0.0),
+ "Linear solver residual (scaled by residual norm)");
+ prm.declare_entry(
+ "Max iteration multiplier",
+ "1",
+ Patterns::Double(0.0),
+ "Linear solver iterations (multiples of the system matrix size)");
+ prm.declare_entry("Use static condensation",
+ "true",
+ Patterns::Bool(),
+ "Solve the full block system or a reduced problem");
+ prm.declare_entry("Preconditioner type",
+ "ssor",
+ Patterns::Selection("jacobi|ssor"),
+ "Type of preconditioner");
+ prm.declare_entry("Preconditioner relaxation",
+ "0.65",
+ Patterns::Double(0.0),
+ "Preconditioner relaxation value");
+ }
+ prm.leave_subsection();
+ }
+ void
+ LinearSolver::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Linear solver");
+ {
+ type_lin = prm.get("Solver type");
+ tol_lin = prm.get_double("Residual");
+ max_iterations_lin = prm.get_double("Max iteration multiplier");
+ use_static_condensation = prm.get_bool("Use static condensation");
+ preconditioner_type = prm.get("Preconditioner type");
+ preconditioner_relaxation = prm.get_double("Preconditioner relaxation");
+ }
+ prm.leave_subsection();
+ }
+ struct NonlinearSolver
+ {
+ unsigned int max_iterations_NR;
+ double tol_f;
+ double tol_u;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ NonlinearSolver::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Nonlinear solver");
+ {
+ prm.declare_entry("Max iterations Newton-Raphson",
+ "10",
+ Patterns::Integer(0),
+ "Number of Newton-Raphson iterations allowed");
+ prm.declare_entry("Tolerance force",
+ "1.0e-9",
+ Patterns::Double(0.0),
+ "Force residual tolerance");
+ prm.declare_entry("Tolerance displacement",
+ "1.0e-6",
+ Patterns::Double(0.0),
+ "Displacement error tolerance");
+ }
+ prm.leave_subsection();
+ }
+ void
+ NonlinearSolver::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Nonlinear solver");
+ {
+ max_iterations_NR = prm.get_integer("Max iterations Newton-Raphson");
+ tol_f = prm.get_double("Tolerance force");
+ tol_u = prm.get_double("Tolerance displacement");
+ }
+ prm.leave_subsection();
+ }
+ struct Time
+ {
+ double delta_t;
+ double end_time;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void
+ Time::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Time");
+ {
+ prm.declare_entry("End time", "1", Patterns::Double(), "End time");
+ prm.declare_entry("Time step size",
+ "0.1",
+ Patterns::Double(),
+ "Time step size");
+ }
+ prm.leave_subsection();
+ }
+ void
+ Time::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Time");
+ {
+ end_time = prm.get_double("End time");
+ delta_t = prm.get_double("Time step size");
+ }
+ prm.leave_subsection();
+ }
+ struct AllParameters : public FESystem,
+ public Geometry,
+ public Materials,
+ public LinearSolver,
+ public NonlinearSolver,
+ public Time
+ {
+ AllParameters(const std::string &input_file);
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ AllParameters::AllParameters(const std::string &input_file)
+ {
+ ParameterHandler prm;
+ declare_parameters(prm);
+ prm.parse_input(input_file);
+ parse_parameters(prm);
+ }
+ void
+ AllParameters::declare_parameters(ParameterHandler &prm)
+ {
+ FESystem::declare_parameters(prm);
+ Geometry::declare_parameters(prm);
+ Materials::declare_parameters(prm);
+ LinearSolver::declare_parameters(prm);
+ NonlinearSolver::declare_parameters(prm);
+ Time::declare_parameters(prm);
+ }
+ void
+ AllParameters::parse_parameters(ParameterHandler &prm)
+ {
+ FESystem::parse_parameters(prm);
+ Geometry::parse_parameters(prm);
+ Materials::parse_parameters(prm);
+ LinearSolver::parse_parameters(prm);
+ NonlinearSolver::parse_parameters(prm);
+ Time::parse_parameters(prm);
+ }
+ } // namespace Parameters
+ template <int dim>
+ class StandardTensors
+ {
+ public:
+ static const SymmetricTensor<2, dim> I;
+ static const SymmetricTensor<4, dim> IxI;
+ static const SymmetricTensor<4, dim> II;
+ static const SymmetricTensor<4, dim> dev_P;
+ };
+ template <int dim>
+ const SymmetricTensor<2, dim>
+ StandardTensors<dim>::I = unit_symmetric_tensor<dim>();
+ template <int dim>
+ const SymmetricTensor<4, dim> StandardTensors<dim>::IxI = outer_product(I, I);
+ template <int dim>
+ const SymmetricTensor<4, dim>
+ StandardTensors<dim>::II = identity_tensor<dim>();
+ template <int dim>
+ const SymmetricTensor<4, dim>
+ StandardTensors<dim>::dev_P = deviator_tensor<dim>();
+ class Time
+ {
+ public:
+ Time(const double time_end, const double delta_t)
+ : timestep(0)
+ , time_current(0.0)
+ , time_end(time_end)
+ , delta_t(delta_t)
+ {}
+ virtual ~Time()
+ {}
+ double
+ current() const
+ {
+ return time_current;
+ }
+ double
+ end() const
+ {
+ return time_end;
+ }
+ double
+ get_delta_t() const
+ {
+ return delta_t;
+ }
+ unsigned int
+ get_timestep() const
+ {
+ return timestep;
+ }
+ void
+ increment()
+ {
+ time_current += delta_t;
+ ++timestep;
+ }
+
+ private:
+ unsigned int timestep;
+ double time_current;
+ const double time_end;
+ const double delta_t;
+ };
+ template <int dim>
+ class Material_Compressible_Neo_Hook_Three_Field
+ {
+ public:
+ Material_Compressible_Neo_Hook_Three_Field(const double mu, const double nu)
+ : kappa((2.0 * mu * (1.0 + nu)) / (3.0 * (1.0 - 2.0 * nu)))
+ , c_1(mu / 2.0)
+ {
+ Assert(kappa > 0, ExcInternalError());
+ }
+ ~Material_Compressible_Neo_Hook_Three_Field()
+ {}
+
+ template <typename NumberType>
+ SymmetricTensor<2, dim, NumberType>
+ get_tau(const Tensor<2, dim, NumberType> &F,
+ const NumberType & p_tilde) const
+ {
+ return get_tau_iso(F) + get_tau_vol(F, p_tilde);
+ }
+ template <typename NumberType>
+ NumberType
+ get_dPsi_vol_dJ(const NumberType &J_tilde) const
+ {
+ return (kappa / 2.0) * (J_tilde - 1.0 / J_tilde);
+ }
+
+ protected:
+ const double kappa;
+ const double c_1;
+
+ template <typename NumberType>
+ SymmetricTensor<2, dim, NumberType>
+ get_tau_vol(const Tensor<2, dim, NumberType> &F,
+ const NumberType & p_tilde) const
+ {
+ const NumberType det_F = determinant(F);
+ // return p_tilde * det_F * StandardTensors<dim>::I;
+ SymmetricTensor<2, dim, NumberType> tau_vol(StandardTensors<dim>::I);
+ tau_vol *= p_tilde * det_F;
+ return tau_vol;
+ }
+ template <typename NumberType>
+ SymmetricTensor<2, dim, NumberType>
+ get_tau_iso(const Tensor<2, dim, NumberType> &F) const
+ {
+ // return StandardTensors<dim>::dev_P * get_tau_bar(F);
+
+ const SymmetricTensor<2, dim, NumberType> tau_bar = get_tau_bar(F);
+ SymmetricTensor<2, dim, NumberType> tau_iso;
+ for (unsigned int i = 0; i < dim; ++i)
+ for (unsigned int j = i; j < dim; ++j)
+ for (unsigned int k = 0; k < dim; ++k)
+ for (unsigned int l = 0; l < dim; ++l)
+ tau_iso[i][j] +=
+ StandardTensors<dim>::dev_P[i][j][k][l] * tau_bar[k][l];
+
+ return tau_iso;
+ }
+ template <typename NumberType>
+ SymmetricTensor<2, dim, NumberType>
+ get_tau_bar(const Tensor<2, dim, NumberType> &F) const
+ {
+ using adtl::pow;
+ using std::pow;
+
+ const NumberType det_F = determinant(F);
+ SymmetricTensor<2, dim, NumberType> b_bar = symmetrize(F * transpose(F));
+ b_bar *= std::pow(det_F, -2.0 / dim);
+ return 2.0 * c_1 * b_bar;
+ }
+ };
+ template <int dim>
+ class PointHistory
+ {
+ public:
+ PointHistory()
+ {}
+ virtual ~PointHistory()
+ {}
+ void
+ setup_lqp(const Parameters::AllParameters ¶meters)
+ {
+ material.reset(
+ new Material_Compressible_Neo_Hook_Three_Field<dim>(parameters.mu,
+ parameters.nu));
+ }
+
+ template <typename NumberType>
+ SymmetricTensor<2, dim, NumberType>
+ get_tau(const Tensor<2, dim, NumberType> &F,
+ const NumberType & p_tilde) const
+ {
+ return material->get_tau(F, p_tilde);
+ }
+ template <typename NumberType>
+ NumberType
+ get_dPsi_vol_dJ(const NumberType &J_tilde) const
+ {
+ return material->get_dPsi_vol_dJ(J_tilde);
+ }
+
+ private:
+ std::shared_ptr<Material_Compressible_Neo_Hook_Three_Field<dim>> material;
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ class Solid
+ {
+ public:
+ Solid(const std::string &input_file);
+ virtual ~Solid();
+ void
+ run();
+
+ private:
+ struct PerTaskData_ASM;
+ struct ScratchData_ASM;
+ struct PerTaskData_SC;
+ struct ScratchData_SC;
+ void
+ make_grid();
+ void
+ system_setup();
+ void
+ determine_component_extractors();
+ void
+ assemble_system(const BlockVector<double> &solution_delta);
+ void
+ assemble_system_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_ASM & scratch,
+ PerTaskData_ASM & data) const;
+ void
+ copy_local_to_global_system(const PerTaskData_ASM &data);
+ void
+ assemble_sc();
+ void
+ assemble_sc_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_SC & scratch,
+ PerTaskData_SC & data);
+ void
+ copy_local_to_global_sc(const PerTaskData_SC &data);
+ void
+ make_constraints(const int &it_nr);
+ void
+ setup_qph();
+ void
+ solve_nonlinear_timestep(BlockVector<double> &solution_delta);
+ std::pair<unsigned int, double>
+ solve_linear_system(BlockVector<double> &newton_update);
+ BlockVector<double>
+ get_total_solution(const BlockVector<double> &solution_delta) const;
+ void
+ output_results() const;
+ Parameters::AllParameters parameters;
+ double vol_reference;
+ Triangulation<dim> triangulation;
+ Time time;
+ mutable TimerOutput timer;
+ CellDataStorage<typename Triangulation<dim>::cell_iterator,
+ PointHistory<dim>>
+ quadrature_point_history;
+ const unsigned int degree;
+ const FESystem<dim> fe;
+ DoFHandler<dim> dof_handler_ref;
+ const unsigned int dofs_per_cell;
+ const FEValuesExtractors::Vector u_fe;
+ const FEValuesExtractors::Scalar p_fe;
+ const FEValuesExtractors::Scalar J_fe;
+ static const unsigned int n_blocks = 3;
+ static const unsigned int n_components = dim + 2;
+ static const unsigned int first_u_component = 0;
+ static const unsigned int p_component = dim;
+ static const unsigned int J_component = dim + 1;
+ enum
+ {
+ u_dof = 0,
+ p_dof = 1,
+ J_dof = 2
+ };
+ std::vector<types::global_dof_index> dofs_per_block;
+ std::vector<types::global_dof_index> element_indices_u;
+ std::vector<types::global_dof_index> element_indices_p;
+ std::vector<types::global_dof_index> element_indices_J;
+ const QGauss<dim> qf_cell;
+ const QGauss<dim - 1> qf_face;
+ const unsigned int n_q_points;
+ const unsigned int n_q_points_f;
+ ConstraintMatrix constraints;
+ BlockSparsityPattern sparsity_pattern;
+ BlockSparseMatrix<double> tangent_matrix;
+ BlockVector<double> system_rhs;
+ BlockVector<double> solution_n;
+ struct Errors
+ {
+ Errors()
+ : norm(1.0)
+ , u(1.0)
+ , p(1.0)
+ , J(1.0)
+ {}
+ void
+ reset()
+ {
+ norm = 1.0;
+ u = 1.0;
+ p = 1.0;
+ J = 1.0;
+ }
+ void
+ normalise(const Errors &rhs)
+ {
+ if (rhs.norm != 0.0)
+ norm /= rhs.norm;
+ if (rhs.u != 0.0)
+ u /= rhs.u;
+ if (rhs.p != 0.0)
+ p /= rhs.p;
+ if (rhs.J != 0.0)
+ J /= rhs.J;
+ }
+ double norm, u, p, J;
+ };
+ Errors error_residual, error_residual_0, error_residual_norm, error_update,
+ error_update_0, error_update_norm;
+ void
+ get_error_residual(Errors &error_residual);
+ void
+ get_error_update(const BlockVector<double> &newton_update,
+ Errors & error_update);
+ std::pair<double, double>
+ get_error_dilation(const BlockVector<double> &solution_total) const;
+ void
+ print_conv_header();
+ void
+ print_conv_footer(const BlockVector<double> &solution_delta);
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ Solid<dim, number_t, ad_type_code>::Solid(const std::string &input_file)
+ : parameters(input_file)
+ , triangulation(Triangulation<dim>::maximum_smoothing)
+ , time(parameters.end_time, parameters.delta_t)
+ , timer(std::cout, TimerOutput::never, TimerOutput::wall_times)
+ , degree(parameters.poly_degree)
+ , fe(FE_Q<dim>(parameters.poly_degree),
+ dim, // displacement
+ FE_DGPMonomial<dim>(parameters.poly_degree - 1),
+ 1, // pressure
+ FE_DGPMonomial<dim>(parameters.poly_degree - 1),
+ 1)
+ , // dilatation
+ dof_handler_ref(triangulation)
+ , dofs_per_cell(fe.dofs_per_cell)
+ , u_fe(first_u_component)
+ , p_fe(p_component)
+ , J_fe(J_component)
+ , dofs_per_block(n_blocks)
+ , qf_cell(parameters.quad_order)
+ , qf_face(parameters.quad_order)
+ , n_q_points(qf_cell.size())
+ , n_q_points_f(qf_face.size())
+ {
+ Assert(dim == 2 || dim == 3,
+ ExcMessage("This problem only works in 2 or 3 space dimensions."));
+ determine_component_extractors();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ Solid<dim, number_t, ad_type_code>::~Solid()
+ {
+ dof_handler_ref.clear();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::run()
+ {
+ make_grid();
+ system_setup();
+ {
+ ConstraintMatrix constraints;
+ constraints.close();
+ const ComponentSelectFunction<dim> J_mask(J_component, n_components);
+ VectorTools::project(dof_handler_ref,
+ constraints,
+ QGauss<dim>(degree + 2),
+ J_mask,
+ solution_n);
+ }
+ output_results();
+ time.increment();
+ BlockVector<double> solution_delta(dofs_per_block);
+ while (time.current() < time.end())
+ {
+ solution_delta = 0.0;
+ solve_nonlinear_timestep(solution_delta);
+ solution_n += solution_delta;
+ output_results();
+ // Output displacement at centre of traction surface
+ {
+ const Point<dim> soln_pt(
+ dim == 3 ? Point<dim>(0.0, 1.0, 0.0) * parameters.scale :
+ Point<dim>(0.0, 1.0) * parameters.scale);
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler_ref.begin_active(),
+ endc = dof_handler_ref.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 * parameters.scale)
+ {
+ Tensor<1, dim> soln;
+ for (unsigned int d = 0; d < dim; ++d)
+ soln[d] = solution_n(cell->vertex_dof_index(v, u_dof + d));
+ deallog << "Timestep " << time.get_timestep() << ": " << soln
+ << std::endl;
+ }
+ }
+ time.increment();
+ }
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ struct Solid<dim, number_t, ad_type_code>::PerTaskData_ASM
+ {
+ FullMatrix<double> cell_matrix;
+ Vector<double> cell_rhs;
+ std::vector<types::global_dof_index> local_dof_indices;
+ PerTaskData_ASM(const unsigned int dofs_per_cell)
+ : cell_matrix(dofs_per_cell, dofs_per_cell)
+ , cell_rhs(dofs_per_cell)
+ , local_dof_indices(dofs_per_cell)
+ {}
+ void
+ reset()
+ {
+ cell_matrix = 0.0;
+ cell_rhs = 0.0;
+ }
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ struct Solid<dim, number_t, ad_type_code>::ScratchData_ASM
+ {
+ const BlockVector<double> &solution_total;
+ FEValues<dim> fe_values_ref;
+ FEFaceValues<dim> fe_face_values_ref;
+ ScratchData_ASM(const FiniteElement<dim> & fe_cell,
+ const QGauss<dim> & qf_cell,
+ const UpdateFlags uf_cell,
+ const QGauss<dim - 1> & qf_face,
+ const UpdateFlags uf_face,
+ const BlockVector<double> &solution_total)
+ : solution_total(solution_total)
+ , fe_values_ref(fe_cell, qf_cell, uf_cell)
+ , fe_face_values_ref(fe_cell, qf_face, uf_face)
+ {}
+ ScratchData_ASM(const ScratchData_ASM &rhs)
+ : solution_total(rhs.solution_total)
+ , fe_values_ref(rhs.fe_values_ref.get_fe(),
+ rhs.fe_values_ref.get_quadrature(),
+ rhs.fe_values_ref.get_update_flags())
+ , fe_face_values_ref(rhs.fe_face_values_ref.get_fe(),
+ rhs.fe_face_values_ref.get_quadrature(),
+ rhs.fe_face_values_ref.get_update_flags())
+ {}
+ void
+ reset()
+ {}
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ struct Solid<dim, number_t, ad_type_code>::PerTaskData_SC
+ {
+ FullMatrix<double> cell_matrix;
+ std::vector<types::global_dof_index> local_dof_indices;
+ FullMatrix<double> k_orig;
+ FullMatrix<double> k_pu;
+ FullMatrix<double> k_pJ;
+ FullMatrix<double> k_JJ;
+ FullMatrix<double> k_pJ_inv;
+ FullMatrix<double> k_bbar;
+ FullMatrix<double> A;
+ FullMatrix<double> B;
+ FullMatrix<double> C;
+ PerTaskData_SC(const unsigned int dofs_per_cell,
+ const unsigned int n_u,
+ const unsigned int n_p,
+ const unsigned int n_J)
+ : cell_matrix(dofs_per_cell, dofs_per_cell)
+ , local_dof_indices(dofs_per_cell)
+ , k_orig(dofs_per_cell, dofs_per_cell)
+ , k_pu(n_p, n_u)
+ , k_pJ(n_p, n_J)
+ , k_JJ(n_J, n_J)
+ , k_pJ_inv(n_p, n_J)
+ , k_bbar(n_u, n_u)
+ , A(n_J, n_u)
+ , B(n_J, n_u)
+ , C(n_p, n_u)
+ {}
+ void
+ reset()
+ {}
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ struct Solid<dim, number_t, ad_type_code>::ScratchData_SC
+ {
+ void
+ reset()
+ {}
+ };
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::make_grid()
+ {
+ GridGenerator::hyper_rectangle(
+ triangulation,
+ (dim == 3 ? Point<dim>(0.0, 0.0, 0.0) : Point<dim>(0.0, 0.0)),
+ (dim == 3 ? Point<dim>(1.0, 1.0, 1.0) : Point<dim>(1.0, 1.0)),
+ true);
+ GridTools::scale(parameters.scale, triangulation);
+ triangulation.refine_global(std::max(1U, parameters.global_refinement));
+ vol_reference = GridTools::volume(triangulation);
+ std::cout << "Grid:\n\t Reference volume: " << vol_reference << std::endl;
+ typename Triangulation<dim>::active_cell_iterator cell = triangulation
+ .begin_active(),
+ endc =
+ triangulation.end();
+ for (; cell != endc; ++cell)
+ for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell;
+ ++face)
+ {
+ if (cell->face(face)->at_boundary() == true &&
+ cell->face(face)->center()[1] == 1.0 * parameters.scale)
+ {
+ if (dim == 3)
+ {
+ if (cell->face(face)->center()[0] < 0.5 * parameters.scale &&
+ cell->face(face)->center()[2] < 0.5 * parameters.scale)
+ cell->face(face)->set_boundary_id(6);
+ }
+ else
+ {
+ if (cell->face(face)->center()[0] < 0.5 * parameters.scale)
+ cell->face(face)->set_boundary_id(6);
+ }
+ }
+ }
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::system_setup()
+ {
+ timer.enter_subsection("Setup system");
+ std::vector<unsigned int> block_component(n_components,
+ u_dof); // Displacement
+ block_component[p_component] = p_dof; // Pressure
+ block_component[J_component] = J_dof; // Dilatation
+ dof_handler_ref.distribute_dofs(fe);
+ DoFRenumbering::Cuthill_McKee(dof_handler_ref);
+ DoFRenumbering::component_wise(dof_handler_ref, block_component);
+ DoFTools::count_dofs_per_block(dof_handler_ref,
+ dofs_per_block,
+ block_component);
+ std::cout << "Triangulation:"
+ << "\n\t Number of active cells: "
+ << triangulation.n_active_cells()
+ << "\n\t Number of degrees of freedom: "
+ << dof_handler_ref.n_dofs() << std::endl;
+ tangent_matrix.clear();
+ {
+ const types::global_dof_index n_dofs_u = dofs_per_block[u_dof];
+ const types::global_dof_index n_dofs_p = dofs_per_block[p_dof];
+ const types::global_dof_index n_dofs_J = dofs_per_block[J_dof];
+ BlockDynamicSparsityPattern dsp(n_blocks, n_blocks);
+ dsp.block(u_dof, u_dof).reinit(n_dofs_u, n_dofs_u);
+ dsp.block(u_dof, p_dof).reinit(n_dofs_u, n_dofs_p);
+ dsp.block(u_dof, J_dof).reinit(n_dofs_u, n_dofs_J);
+ dsp.block(p_dof, u_dof).reinit(n_dofs_p, n_dofs_u);
+ dsp.block(p_dof, p_dof).reinit(n_dofs_p, n_dofs_p);
+ dsp.block(p_dof, J_dof).reinit(n_dofs_p, n_dofs_J);
+ dsp.block(J_dof, u_dof).reinit(n_dofs_J, n_dofs_u);
+ dsp.block(J_dof, p_dof).reinit(n_dofs_J, n_dofs_p);
+ dsp.block(J_dof, J_dof).reinit(n_dofs_J, n_dofs_J);
+ dsp.collect_sizes();
+ Table<2, DoFTools::Coupling> coupling(n_components, n_components);
+ for (unsigned int ii = 0; ii < n_components; ++ii)
+ for (unsigned int jj = 0; jj < n_components; ++jj)
+ if (((ii < p_component) && (jj == J_component)) ||
+ ((ii == J_component) && (jj < p_component)) ||
+ ((ii == p_component) && (jj == p_component)))
+ coupling[ii][jj] = DoFTools::none;
+ else
+ coupling[ii][jj] = DoFTools::always;
+ DoFTools::make_sparsity_pattern(
+ dof_handler_ref, coupling, dsp, constraints, false);
+ sparsity_pattern.copy_from(dsp);
+ }
+ tangent_matrix.reinit(sparsity_pattern);
+ system_rhs.reinit(dofs_per_block);
+ system_rhs.collect_sizes();
+ solution_n.reinit(dofs_per_block);
+ solution_n.collect_sizes();
+ setup_qph();
+ timer.leave_subsection();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::determine_component_extractors()
+ {
+ element_indices_u.clear();
+ element_indices_p.clear();
+ element_indices_J.clear();
+ for (unsigned int k = 0; k < fe.dofs_per_cell; ++k)
+ {
+ const unsigned int k_group = fe.system_to_base_index(k).first.first;
+ if (k_group == u_dof)
+ element_indices_u.push_back(k);
+ else if (k_group == p_dof)
+ element_indices_p.push_back(k);
+ else if (k_group == J_dof)
+ element_indices_J.push_back(k);
+ else
+ {
+ Assert(k_group <= J_dof, ExcInternalError());
+ }
+ }
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::setup_qph()
+ {
+ std::cout << " Setting up quadrature point data..." << std::endl;
+ quadrature_point_history.initialize(triangulation.begin_active(),
+ triangulation.end(),
+ n_q_points);
+ for (typename Triangulation<dim>::active_cell_iterator cell =
+ triangulation.begin_active();
+ cell != triangulation.end();
+ ++cell)
+ {
+ const std::vector<std::shared_ptr<PointHistory<dim>>> lqph =
+ quadrature_point_history.get_data(cell);
+ Assert(lqph.size() == n_q_points, ExcInternalError());
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ lqph[q_point]->setup_lqp(parameters);
+ }
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::solve_nonlinear_timestep(
+ BlockVector<double> &solution_delta)
+ {
+ std::cout << std::endl
+ << "Timestep " << time.get_timestep() << " @ " << time.current()
+ << "s" << std::endl;
+ BlockVector<double> newton_update(dofs_per_block);
+ error_residual.reset();
+ error_residual_0.reset();
+ error_residual_norm.reset();
+ error_update.reset();
+ error_update_0.reset();
+ error_update_norm.reset();
+ print_conv_header();
+ unsigned int newton_iteration = 0;
+ for (; newton_iteration < parameters.max_iterations_NR; ++newton_iteration)
+ {
+ std::cout << " " << std::setw(2) << newton_iteration << " "
+ << std::flush;
+ make_constraints(newton_iteration);
+ assemble_system(solution_delta);
+ get_error_residual(error_residual);
+ if (newton_iteration == 0)
+ error_residual_0 = error_residual;
+ error_residual_norm = error_residual;
+ error_residual_norm.normalise(error_residual_0);
+ if (newton_iteration > 0 && error_update_norm.u <= parameters.tol_u &&
+ error_residual_norm.u <= parameters.tol_f)
+ {
+ std::cout << " CONVERGED! " << std::endl;
+ print_conv_footer(solution_delta);
+ break;
+ }
+ const std::pair<unsigned int, double> lin_solver_output =
+ solve_linear_system(newton_update);
+ get_error_update(newton_update, error_update);
+ if (newton_iteration == 0)
+ error_update_0 = error_update;
+ error_update_norm = error_update;
+ error_update_norm.normalise(error_update_0);
+ solution_delta += newton_update;
+ std::cout << " | " << std::fixed << std::setprecision(3) << std::setw(7)
+ << std::scientific << lin_solver_output.first << " "
+ << lin_solver_output.second << " "
+ << error_residual_norm.norm << " " << error_residual_norm.u
+ << " " << error_residual_norm.p << " "
+ << error_residual_norm.J << " " << error_update_norm.norm
+ << " " << error_update_norm.u << " " << error_update_norm.p
+ << " " << error_update_norm.J << " " << std::endl;
+ }
+ AssertThrow(newton_iteration <= parameters.max_iterations_NR,
+ ExcMessage("No convergence in nonlinear solver!"));
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::print_conv_header()
+ {
+ static const unsigned int l_width = 144;
+ for (unsigned int i = 0; i < l_width; ++i)
+ std::cout << "_";
+ std::cout << std::endl;
+ std::cout << " SOLVER STEP "
+ << " | LIN_IT LIN_RES RES_NORM "
+ << " RES_U RES_P RES_J NU_NORM "
+ << " NU_U NU_P NU_J " << std::endl;
+ for (unsigned int i = 0; i < l_width; ++i)
+ std::cout << "_";
+ std::cout << std::endl;
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::print_conv_footer(
+ const BlockVector<double> &solution_delta)
+ {
+ static const unsigned int l_width = 144;
+ for (unsigned int i = 0; i < l_width; ++i)
+ std::cout << "_";
+ std::cout << std::endl;
+ const std::pair<double, double> error_dil =
+ get_error_dilation(get_total_solution(solution_delta));
+ std::cout << "Relative errors:" << std::endl
+ << "Displacement:\t" << error_update.u / error_update_0.u
+ << std::endl
+ << "Force: \t\t" << error_residual.u / error_residual_0.u
+ << std::endl
+ << "Dilatation:\t" << error_dil.first << std::endl
+ << "v / V_0:\t" << error_dil.second * vol_reference << " / "
+ << vol_reference << " = " << error_dil.second << std::endl;
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ std::pair<double, double>
+ Solid<dim, number_t, ad_type_code>::get_error_dilation(
+ const BlockVector<double> &solution_total) const
+ {
+ double vol_current = 0.0;
+ double dil_L2_error = 0.0;
+ FEValues<dim> fe_values_ref(
+ fe, qf_cell, update_values | update_gradients | update_JxW_values);
+ std::vector<Tensor<2, dim>> solution_grads_u_total(qf_cell.size());
+ std::vector<double> solution_values_J_total(qf_cell.size());
+ for (typename DoFHandler<dim>::active_cell_iterator cell =
+ dof_handler_ref.begin_active();
+ cell != dof_handler_ref.end();
+ ++cell)
+ {
+ fe_values_ref.reinit(cell);
+ fe_values_ref[u_fe].get_function_gradients(solution_total,
+ solution_grads_u_total);
+ fe_values_ref[J_fe].get_function_values(solution_total,
+ solution_values_J_total);
+ const std::vector<std::shared_ptr<const PointHistory<dim>>> lqph =
+ quadrature_point_history.get_data(cell);
+ Assert(lqph.size() == n_q_points, ExcInternalError());
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const double det_F_qp = determinant(
+ StandardTensors<dim>::I + solution_grads_u_total[q_point]);
+ const double J_tilde_qp = solution_values_J_total[q_point];
+ const double the_error_qp_squared =
+ std::pow((det_F_qp - J_tilde_qp), 2);
+ const double JxW = fe_values_ref.JxW(q_point);
+ dil_L2_error += the_error_qp_squared * JxW;
+ vol_current += det_F_qp * JxW;
+ }
+ }
+ Assert(vol_current > 0.0, ExcInternalError());
+
+ return std::make_pair(std::sqrt(dil_L2_error), vol_current / vol_reference);
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::get_error_residual(Errors &error_residual)
+ {
+ BlockVector<double> error_res(dofs_per_block);
+ for (unsigned int i = 0; i < dof_handler_ref.n_dofs(); ++i)
+ if (!constraints.is_constrained(i))
+ error_res(i) = system_rhs(i);
+ error_residual.norm = error_res.l2_norm();
+ error_residual.u = error_res.block(u_dof).l2_norm();
+ error_residual.p = error_res.block(p_dof).l2_norm();
+ error_residual.J = error_res.block(J_dof).l2_norm();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::get_error_update(
+ const BlockVector<double> &newton_update,
+ Errors & error_update)
+ {
+ BlockVector<double> error_ud(dofs_per_block);
+ for (unsigned int i = 0; i < dof_handler_ref.n_dofs(); ++i)
+ if (!constraints.is_constrained(i))
+ error_ud(i) = newton_update(i);
+ error_update.norm = error_ud.l2_norm();
+ error_update.u = error_ud.block(u_dof).l2_norm();
+ error_update.p = error_ud.block(p_dof).l2_norm();
+ error_update.J = error_ud.block(J_dof).l2_norm();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ BlockVector<double>
+ Solid<dim, number_t, ad_type_code>::get_total_solution(
+ const BlockVector<double> &solution_delta) const
+ {
+ BlockVector<double> solution_total(solution_n);
+ solution_total += solution_delta;
+ return solution_total;
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::assemble_system(
+ const BlockVector<double> &solution_delta)
+ {
+ timer.enter_subsection("Assemble system");
+ std::cout << " ASM_SYS " << std::flush;
+ tangent_matrix = 0.0;
+ system_rhs = 0.0;
+ const BlockVector<double> solution_total(
+ get_total_solution(solution_delta));
+ const UpdateFlags uf_cell(update_values | update_gradients |
+ update_JxW_values);
+ const UpdateFlags uf_face(update_values | update_normal_vectors |
+ update_JxW_values);
+ PerTaskData_ASM per_task_data(dofs_per_cell);
+ ScratchData_ASM scratch_data(
+ fe, qf_cell, uf_cell, qf_face, uf_face, solution_total);
+ // ADOL-C is incompatible with TBB
+ // WorkStream::run(dof_handler_ref.begin_active(),
+ // dof_handler_ref.end(),
+ // std::bind(&Solid<dim,number_t,ad_type_code>::assemble_system_one_cell,
+ // this,
+ // std::placeholders::_1,
+ // std::placeholders::_2,
+ // std::placeholders::_3),
+ // std::bind(&Solid<dim,number_t,ad_type_code>::copy_local_to_global_system,
+ // this,
+ // std::placeholders::_1),
+ // scratch_data,
+ // per_task_data);
+ for (typename DoFHandler<dim>::active_cell_iterator cell =
+ dof_handler_ref.begin_active();
+ cell != dof_handler_ref.end();
+ ++cell)
+ {
+ assemble_system_one_cell(cell, scratch_data, per_task_data);
+ copy_local_to_global_system(per_task_data);
+ }
+ timer.leave_subsection();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::copy_local_to_global_system(
+ const PerTaskData_ASM &data)
+ {
+ if (data.cell_matrix.frobenius_norm() > 1e-12)
+ constraints.distribute_local_to_global(data.cell_matrix,
+ data.cell_rhs,
+ data.local_dof_indices,
+ tangent_matrix,
+ system_rhs);
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::assemble_system_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_ASM & scratch,
+ PerTaskData_ASM & data) const
+ {
+ data.reset();
+ scratch.reset();
+ scratch.fe_values_ref.reinit(cell);
+ cell->get_dof_indices(data.local_dof_indices);
+
+ const std::vector<std::shared_ptr<const PointHistory<dim>>> lqph =
+ quadrature_point_history.get_data(cell);
+ Assert(lqph.size() == n_q_points, ExcInternalError());
+
+ const unsigned int n_independent_variables = data.local_dof_indices.size();
+ const unsigned int n_dependent_variables = dofs_per_cell;
+ Assert(n_dependent_variables == n_independent_variables,
+ ExcMessage("Expect square system."));
+
+ typedef AD::ADHelperResidualLinearization<ad_type_code, number_t> ADHelper;
+ typedef typename ADHelper::ad_type ADNumberType;
+ ADHelper ad_helper(n_independent_variables, n_dependent_variables);
+ ad_helper.set_tape_buffer_sizes(); // Increase the buffer size from the
+ // default values
+
+ const int tape_no = 1;
+ const bool is_recording =
+ ad_helper.start_recording_operations(tape_no, // material_id
+ true, // overwrite_tape
+ true); // keep
+
+ if (is_recording == true)
+ {
+ // Set the values for all DoFs
+ ad_helper.register_dof_values(scratch.solution_total,
+ data.local_dof_indices);
+ const std::vector<ADNumberType> dof_values_ad =
+ ad_helper.get_sensitive_dof_values();
+
+ // Compute all values, gradients etc. based on sensitive AD DoF values
+ std::vector<Tensor<2, dim, ADNumberType>> Grad_u(
+ n_q_points, Tensor<2, dim, ADNumberType>());
+ std::vector<ADNumberType> p_tilde(n_q_points, ADNumberType(0.0));
+ std::vector<ADNumberType> J_tilde(n_q_points, ADNumberType(0.0));
+ scratch.fe_values_ref[u_fe]
+ .get_function_gradients_from_local_dof_values(dof_values_ad, Grad_u);
+ scratch.fe_values_ref[p_fe].get_function_values_from_local_dof_values(
+ dof_values_ad, p_tilde);
+ scratch.fe_values_ref[J_fe].get_function_values_from_local_dof_values(
+ dof_values_ad, J_tilde);
+
+ // Compute the residual
+ // Note: It is critical that this vector be initialised with zero'd
+ // values otherwise the results may be garbage!
+ std::vector<ADNumberType> residual_ad(n_dependent_variables,
+ ADNumberType(0.0));
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const Tensor<2, dim, ADNumberType> F =
+ unit_symmetric_tensor<dim>() + Grad_u[q_point];
+ const Tensor<2, dim, ADNumberType> F_inv = invert(F);
+ const ADNumberType det_F = determinant(F);
+ Assert(numbers::value_is_greater_than(det_F, 0.0),
+ ExcMessage("Negative jacobian detected!"));
+
+ const SymmetricTensor<2, dim, ADNumberType> tau =
+ lqph[q_point]->get_tau(F, p_tilde[q_point]);
+ const ADNumberType dPsi_vol_dJ =
+ lqph[q_point]->get_dPsi_vol_dJ(J_tilde[q_point]);
+
+ const double JxW = scratch.fe_values_ref.JxW(q_point);
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ {
+ const unsigned int i_group =
+ fe.system_to_base_index(i).first.first;
+ if (i_group == u_dof)
+ {
+ const SymmetricTensor<2, dim, ADNumberType> symm_grad_Nx_i =
+ symmetrize(
+ scratch.fe_values_ref[u_fe].gradient(i, q_point) *
+ F_inv);
+ residual_ad[i] += (symm_grad_Nx_i * tau) * JxW;
+ }
+ else if (i_group == p_dof)
+ {
+ const double N_i =
+ scratch.fe_values_ref[p_fe].value(i, q_point);
+ residual_ad[i] += N_i * (det_F - J_tilde[q_point]) * JxW;
+ }
+ else if (i_group == J_dof)
+ {
+ const double N_i =
+ scratch.fe_values_ref[J_fe].value(i, q_point);
+ residual_ad[i] +=
+ N_i * (dPsi_vol_dJ - p_tilde[q_point]) * JxW;
+ }
+ else
+ Assert(i_group <= J_dof, ExcInternalError());
+ }
+ }
+ for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell;
+ ++face)
+ if (cell->face(face)->at_boundary() == true &&
+ cell->face(face)->boundary_id() == 6)
+ {
+ scratch.fe_face_values_ref.reinit(cell, face);
+ for (unsigned int f_q_point = 0; f_q_point < n_q_points_f;
+ ++f_q_point)
+ {
+ const Tensor<1, dim> &N =
+ scratch.fe_face_values_ref.normal_vector(f_q_point);
+ static const double p0 =
+ -4.0 / (parameters.scale * parameters.scale);
+ const double time_ramp = (time.current() / time.end());
+ const double pressure = p0 * parameters.p_p0 * time_ramp;
+ const Tensor<1, dim> traction = pressure * N;
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ {
+ const unsigned int i_group =
+ fe.system_to_base_index(i).first.first;
+ if (i_group == u_dof)
+ {
+ const unsigned int component_i =
+ fe.system_to_component_index(i).first;
+ const double Ni =
+ scratch.fe_face_values_ref.shape_value(i,
+ f_q_point);
+ const double JxW =
+ scratch.fe_face_values_ref.JxW(f_q_point);
+ residual_ad[i] -= (Ni * traction[component_i]) * JxW;
+ }
+ }
+ }
+ }
+
+ ad_helper.register_residual_vector(residual_ad);
+ ad_helper.stop_recording_operations(false /*write_tapes_to_file*/);
+ }
+ else
+ {
+ Assert(is_recording == true, ExcInternalError());
+ }
+
+ // Unnecessary when keep == true
+ // ad_helper.activate_recorded_tape(tape_no);
+ // ad_helper.set_dof_values(scratch.solution_total,
+ // data.local_dof_indices);
+
+ // Compute the residual values and their jacobian for the new evaluation
+ // point
+ ad_helper.compute_residual(data.cell_rhs);
+ data.cell_rhs *= -1.0; // RHS = - residual
+ ad_helper.compute_linearization(data.cell_matrix);
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::make_constraints(const int &it_nr)
+ {
+ std::cout << " CST " << std::flush;
+ if (it_nr > 1)
+ return;
+ constraints.clear();
+ const bool apply_dirichlet_bc = (it_nr == 0);
+ const FEValuesExtractors::Scalar x_displacement(0);
+ const FEValuesExtractors::Scalar y_displacement(1);
+ {
+ const int boundary_id = 0;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(x_displacement));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(x_displacement));
+ }
+ {
+ const int boundary_id = 2;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ }
+ if (dim == 3)
+ {
+ const FEValuesExtractors::Scalar z_displacement(2);
+ {
+ const int boundary_id = 3;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement) |
+ fe.component_mask(z_displacement)));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement) |
+ fe.component_mask(z_displacement)));
+ }
+ {
+ const int boundary_id = 4;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ }
+ {
+ const int boundary_id = 6;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement) |
+ fe.component_mask(z_displacement)));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement) |
+ fe.component_mask(z_displacement)));
+ }
+ }
+ else
+ {
+ {
+ const int boundary_id = 3;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement)));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement)));
+ }
+ {
+ const int boundary_id = 6;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement)));
+ else
+ VectorTools::interpolate_boundary_values(
+ dof_handler_ref,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ (fe.component_mask(x_displacement)));
+ }
+ }
+ constraints.close();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::assemble_sc()
+ {
+ timer.enter_subsection("Perform static condensation");
+ std::cout << " ASM_SC " << std::flush;
+ PerTaskData_SC per_task_data(dofs_per_cell,
+ element_indices_u.size(),
+ element_indices_p.size(),
+ element_indices_J.size());
+ ScratchData_SC scratch_data;
+ WorkStream::run(dof_handler_ref.begin_active(),
+ dof_handler_ref.end(),
+ *this,
+ &Solid::assemble_sc_one_cell,
+ &Solid::copy_local_to_global_sc,
+ scratch_data,
+ per_task_data);
+ timer.leave_subsection();
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::copy_local_to_global_sc(
+ const PerTaskData_SC &data)
+ {
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ for (unsigned int j = 0; j < dofs_per_cell; ++j)
+ tangent_matrix.add(data.local_dof_indices[i],
+ data.local_dof_indices[j],
+ data.cell_matrix(i, j));
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::assemble_sc_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_SC & scratch,
+ PerTaskData_SC & data)
+ {
+ data.reset();
+ scratch.reset();
+ cell->get_dof_indices(data.local_dof_indices);
+ data.k_orig.extract_submatrix_from(tangent_matrix,
+ data.local_dof_indices,
+ data.local_dof_indices);
+ data.k_pu.extract_submatrix_from(data.k_orig,
+ element_indices_p,
+ element_indices_u);
+ data.k_pJ.extract_submatrix_from(data.k_orig,
+ element_indices_p,
+ element_indices_J);
+ data.k_JJ.extract_submatrix_from(data.k_orig,
+ element_indices_J,
+ element_indices_J);
+ data.k_pJ_inv.invert(data.k_pJ);
+ data.k_pJ_inv.mmult(data.A, data.k_pu);
+ data.k_JJ.mmult(data.B, data.A);
+ data.k_pJ_inv.Tmmult(data.C, data.B);
+ data.k_pu.Tmmult(data.k_bbar, data.C);
+ data.k_bbar.scatter_matrix_to(element_indices_u,
+ element_indices_u,
+ data.cell_matrix);
+ data.k_pJ_inv.add(-1.0, data.k_pJ);
+ data.k_pJ_inv.scatter_matrix_to(element_indices_p,
+ element_indices_J,
+ data.cell_matrix);
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ std::pair<unsigned int, double>
+ Solid<dim, number_t, ad_type_code>::solve_linear_system(
+ BlockVector<double> &newton_update)
+ {
+ unsigned int lin_it = 0;
+ double lin_res = 0.0;
+ if (parameters.use_static_condensation == true)
+ {
+ BlockVector<double> A(dofs_per_block);
+ BlockVector<double> B(dofs_per_block);
+ {
+ assemble_sc();
+ tangent_matrix.block(p_dof, J_dof)
+ .vmult(A.block(J_dof), system_rhs.block(p_dof));
+ tangent_matrix.block(J_dof, J_dof)
+ .vmult(B.block(J_dof), A.block(J_dof));
+ A.block(J_dof) = system_rhs.block(J_dof);
+ A.block(J_dof) -= B.block(J_dof);
+ tangent_matrix.block(p_dof, J_dof)
+ .Tvmult(A.block(p_dof), A.block(J_dof));
+ tangent_matrix.block(u_dof, p_dof)
+ .vmult(A.block(u_dof), A.block(p_dof));
+ system_rhs.block(u_dof) -= A.block(u_dof);
+ timer.enter_subsection("Linear solver");
+ std::cout << " SLV " << std::flush;
+ if (parameters.type_lin == "CG")
+ {
+ const int solver_its = tangent_matrix.block(u_dof, u_dof).m() *
+ parameters.max_iterations_lin;
+ const double tol_sol =
+ parameters.tol_lin * system_rhs.block(u_dof).l2_norm();
+ SolverControl solver_control(solver_its, tol_sol, false, false);
+ GrowingVectorMemory<Vector<double>> GVM;
+ SolverCG<Vector<double>> solver_CG(solver_control, GVM);
+ PreconditionSelector<SparseMatrix<double>, Vector<double>>
+ preconditioner(parameters.preconditioner_type,
+ parameters.preconditioner_relaxation);
+ preconditioner.use_matrix(tangent_matrix.block(u_dof, u_dof));
+ solver_CG.solve(tangent_matrix.block(u_dof, u_dof),
+ newton_update.block(u_dof),
+ system_rhs.block(u_dof),
+ preconditioner);
+ lin_it = solver_control.last_step();
+ lin_res = solver_control.last_value();
+ }
+ else if (parameters.type_lin == "Direct")
+ {
+ SparseDirectUMFPACK A_direct;
+ A_direct.initialize(tangent_matrix.block(u_dof, u_dof));
+ A_direct.vmult(newton_update.block(u_dof),
+ system_rhs.block(u_dof));
+ lin_it = 1;
+ lin_res = 0.0;
+ }
+ else
+ Assert(false, ExcMessage("Linear solver type not implemented"));
+ timer.leave_subsection();
+ }
+ constraints.distribute(newton_update);
+ timer.enter_subsection("Linear solver postprocessing");
+ std::cout << " PP " << std::flush;
+ {
+ tangent_matrix.block(p_dof, u_dof)
+ .vmult(A.block(p_dof), newton_update.block(u_dof));
+ A.block(p_dof) *= -1.0;
+ A.block(p_dof) += system_rhs.block(p_dof);
+ tangent_matrix.block(p_dof, J_dof)
+ .vmult(newton_update.block(J_dof), A.block(p_dof));
+ }
+ constraints.distribute(newton_update);
+ {
+ tangent_matrix.block(J_dof, J_dof)
+ .vmult(A.block(J_dof), newton_update.block(J_dof));
+ A.block(J_dof) *= -1.0;
+ A.block(J_dof) += system_rhs.block(J_dof);
+ tangent_matrix.block(p_dof, J_dof)
+ .Tvmult(newton_update.block(p_dof), A.block(J_dof));
+ }
+ constraints.distribute(newton_update);
+ timer.leave_subsection();
+ }
+ else
+ {
+ std::cout << " ------ " << std::flush;
+ timer.enter_subsection("Linear solver");
+ std::cout << " SLV " << std::flush;
+ if (parameters.type_lin == "CG")
+ {
+ const Vector<double> &f_u = system_rhs.block(u_dof);
+ const Vector<double> &f_p = system_rhs.block(p_dof);
+ const Vector<double> &f_J = system_rhs.block(J_dof);
+ Vector<double> & d_u = newton_update.block(u_dof);
+ Vector<double> & d_p = newton_update.block(p_dof);
+ Vector<double> & d_J = newton_update.block(J_dof);
+ const auto K_uu =
+ linear_operator(tangent_matrix.block(u_dof, u_dof));
+ const auto K_up =
+ linear_operator(tangent_matrix.block(u_dof, p_dof));
+ const auto K_pu =
+ linear_operator(tangent_matrix.block(p_dof, u_dof));
+ const auto K_Jp =
+ linear_operator(tangent_matrix.block(J_dof, p_dof));
+ const auto K_JJ =
+ linear_operator(tangent_matrix.block(J_dof, J_dof));
+ PreconditionSelector<SparseMatrix<double>, Vector<double>>
+ preconditioner_K_Jp_inv("jacobi");
+ preconditioner_K_Jp_inv.use_matrix(
+ tangent_matrix.block(J_dof, p_dof));
+ ReductionControl solver_control_K_Jp_inv(
+ tangent_matrix.block(J_dof, p_dof).m() *
+ parameters.max_iterations_lin,
+ 1.0e-30,
+ parameters.tol_lin);
+ SolverSelector<Vector<double>> solver_K_Jp_inv;
+ solver_K_Jp_inv.select("cg");
+ solver_K_Jp_inv.set_control(solver_control_K_Jp_inv);
+ const auto K_Jp_inv =
+ inverse_operator(K_Jp, solver_K_Jp_inv, preconditioner_K_Jp_inv);
+ const auto K_pJ_inv = transpose_operator(K_Jp_inv);
+ const auto K_pp_bar = K_Jp_inv * K_JJ * K_pJ_inv;
+ const auto K_uu_bar_bar = K_up * K_pp_bar * K_pu;
+ const auto K_uu_con = K_uu + K_uu_bar_bar;
+ PreconditionSelector<SparseMatrix<double>, Vector<double>>
+ preconditioner_K_con_inv(parameters.preconditioner_type,
+ parameters.preconditioner_relaxation);
+ preconditioner_K_con_inv.use_matrix(
+ tangent_matrix.block(u_dof, u_dof));
+ ReductionControl solver_control_K_con_inv(
+ tangent_matrix.block(u_dof, u_dof).m() *
+ parameters.max_iterations_lin,
+ 1.0e-30,
+ parameters.tol_lin);
+ SolverSelector<Vector<double>> solver_K_con_inv;
+ solver_K_con_inv.select("cg");
+ solver_K_con_inv.set_control(solver_control_K_con_inv);
+ const auto K_uu_con_inv =
+ inverse_operator(K_uu_con,
+ solver_K_con_inv,
+ preconditioner_K_con_inv);
+ d_u =
+ K_uu_con_inv * (f_u - K_up * (K_Jp_inv * f_J - K_pp_bar * f_p));
+ timer.leave_subsection();
+ timer.enter_subsection("Linear solver postprocessing");
+ std::cout << " PP " << std::flush;
+ d_J = K_pJ_inv * (f_p - K_pu * d_u);
+ d_p = K_Jp_inv * (f_J - K_JJ * d_J);
+ lin_it = solver_control_K_con_inv.last_step();
+ lin_res = solver_control_K_con_inv.last_value();
+ }
+ else if (parameters.type_lin == "Direct")
+ {
+ SparseDirectUMFPACK A_direct;
+ A_direct.initialize(tangent_matrix);
+ A_direct.vmult(newton_update, system_rhs);
+ lin_it = 1;
+ lin_res = 0.0;
+ std::cout << " -- " << std::flush;
+ }
+ else
+ Assert(false, ExcMessage("Linear solver type not implemented"));
+ timer.leave_subsection();
+ constraints.distribute(newton_update);
+ }
+ return std::make_pair(lin_it, lin_res);
+ }
+ template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+ void
+ Solid<dim, number_t, ad_type_code>::output_results() const
+ {
+ DataOut<dim> data_out;
+ std::vector<DataComponentInterpretation::DataComponentInterpretation>
+ data_component_interpretation(
+ dim, DataComponentInterpretation::component_is_part_of_vector);
+ data_component_interpretation.push_back(
+ DataComponentInterpretation::component_is_scalar);
+ data_component_interpretation.push_back(
+ DataComponentInterpretation::component_is_scalar);
+ std::vector<std::string> solution_name(dim, "displacement");
+ solution_name.push_back("pressure");
+ solution_name.push_back("dilatation");
+ data_out.attach_dof_handler(dof_handler_ref);
+ data_out.add_data_vector(solution_n,
+ solution_name,
+ DataOut<dim>::type_dof_data,
+ data_component_interpretation);
+ Vector<double> soln(solution_n.size());
+ for (unsigned int i = 0; i < soln.size(); ++i)
+ soln(i) = solution_n(i);
+ MappingQEulerian<dim> q_mapping(degree, dof_handler_ref, soln);
+ data_out.build_patches(q_mapping, degree);
+ std::ostringstream filename;
+ filename << "solution-" << dim << "d-" << time.get_timestep() << ".vtk";
+ std::ofstream output(filename.str().c_str());
+ data_out.write_vtk(output);
+ }
+} // namespace Step44
projects / dealii.git / commitdiff