--- /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.
+//
+// ---------------------------------------------------------------------
+
+// This is a copy of step-44 (git rev 3f7e617), with modifications made
+// to test the implementation of the line-search algorithm.
+
+#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/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/affine_constraints.h>
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_vector.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 <deal.II/optimization/line_minimization.h>
+
+#include <fstream>
+#include <functional>
+#include <iostream>
+
+namespace Step44
+{
+ using namespace dealii;
+ 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;
+ bool use_line_search;
+ bool use_line_search_ptrb;
+ 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.declare_entry("Use line search",
+ "false",
+ Patterns::Bool(),
+ "Use line-search minimization algorithm");
+ prm.declare_entry(
+ "Use line search approximate gradient",
+ "false",
+ Patterns::Bool(),
+ "Use an approximation for the gradient during line search");
+ }
+ 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");
+ use_line_search = prm.get_bool("Use line search");
+ use_line_search_ptrb =
+ prm.get_bool("Use line search approximate gradient");
+ }
+ 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)
+ , det_F(1.0)
+ , p_tilde(0.0)
+ , J_tilde(1.0)
+ , b_bar(StandardTensors<dim>::I)
+ {
+ Assert(kappa > 0, ExcInternalError());
+ }
+ ~Material_Compressible_Neo_Hook_Three_Field()
+ {}
+ void
+ update_material_data(const Tensor<2, dim> &F,
+ const double p_tilde_in,
+ const double J_tilde_in)
+ {
+ det_F = determinant(F);
+ b_bar = std::pow(det_F, -2.0 / dim) * symmetrize(F * transpose(F));
+ p_tilde = p_tilde_in;
+ J_tilde = J_tilde_in;
+ Assert(det_F > 0, ExcInternalError());
+ }
+ SymmetricTensor<2, dim>
+ get_tau()
+ {
+ return get_tau_iso() + get_tau_vol();
+ }
+ SymmetricTensor<4, dim>
+ get_Jc() const
+ {
+ return get_Jc_vol() + get_Jc_iso();
+ }
+ double
+ get_dPsi_vol_dJ() const
+ {
+ return (kappa / 2.0) * (J_tilde - 1.0 / J_tilde);
+ }
+ double
+ get_d2Psi_vol_dJ2() const
+ {
+ return ((kappa / 2.0) * (1.0 + 1.0 / (J_tilde * J_tilde)));
+ }
+ double
+ get_det_F() const
+ {
+ return det_F;
+ }
+ double
+ get_p_tilde() const
+ {
+ return p_tilde;
+ }
+ double
+ get_J_tilde() const
+ {
+ return J_tilde;
+ }
+
+ protected:
+ const double kappa;
+ const double c_1;
+ double det_F;
+ double p_tilde;
+ double J_tilde;
+ SymmetricTensor<2, dim> b_bar;
+ SymmetricTensor<2, dim>
+ get_tau_vol() const
+ {
+ return p_tilde * det_F * StandardTensors<dim>::I;
+ }
+ SymmetricTensor<2, dim>
+ get_tau_iso() const
+ {
+ return StandardTensors<dim>::dev_P * get_tau_bar();
+ }
+ SymmetricTensor<2, dim>
+ get_tau_bar() const
+ {
+ return 2.0 * c_1 * b_bar;
+ }
+ SymmetricTensor<4, dim>
+ get_Jc_vol() const
+ {
+ return p_tilde * det_F *
+ (StandardTensors<dim>::IxI - (2.0 * StandardTensors<dim>::II));
+ }
+ SymmetricTensor<4, dim>
+ get_Jc_iso() const
+ {
+ const SymmetricTensor<2, dim> tau_bar = get_tau_bar();
+ const SymmetricTensor<2, dim> tau_iso = get_tau_iso();
+ const SymmetricTensor<4, dim> tau_iso_x_I =
+ outer_product(tau_iso, StandardTensors<dim>::I);
+ const SymmetricTensor<4, dim> I_x_tau_iso =
+ outer_product(StandardTensors<dim>::I, tau_iso);
+ const SymmetricTensor<4, dim> c_bar = get_c_bar();
+ return (2.0 / dim) * trace(tau_bar) * StandardTensors<dim>::dev_P -
+ (2.0 / dim) * (tau_iso_x_I + I_x_tau_iso) +
+ StandardTensors<dim>::dev_P * c_bar * StandardTensors<dim>::dev_P;
+ }
+ SymmetricTensor<4, dim>
+ get_c_bar() const
+ {
+ return SymmetricTensor<4, dim>();
+ }
+ };
+ template <int dim>
+ class PointHistory
+ {
+ public:
+ PointHistory()
+ : F_inv(StandardTensors<dim>::I)
+ , tau(SymmetricTensor<2, dim>())
+ , d2Psi_vol_dJ2(0.0)
+ , dPsi_vol_dJ(0.0)
+ , Jc(SymmetricTensor<4, dim>())
+ {}
+ virtual ~PointHistory()
+ {}
+ void
+ setup_lqp(const Parameters::AllParameters ¶meters)
+ {
+ material.reset(
+ new Material_Compressible_Neo_Hook_Three_Field<dim>(parameters.mu,
+ parameters.nu));
+ update_values(Tensor<2, dim>(), 0.0, 1.0);
+ }
+ void
+ update_values(const Tensor<2, dim> &Grad_u_n,
+ const double p_tilde,
+ const double J_tilde)
+ {
+ const Tensor<2, dim> F =
+ (Tensor<2, dim>(StandardTensors<dim>::I) + Grad_u_n);
+ material->update_material_data(F, p_tilde, J_tilde);
+ F_inv = invert(F);
+ tau = material->get_tau();
+ Jc = material->get_Jc();
+ dPsi_vol_dJ = material->get_dPsi_vol_dJ();
+ d2Psi_vol_dJ2 = material->get_d2Psi_vol_dJ2();
+ }
+ double
+ get_J_tilde() const
+ {
+ return material->get_J_tilde();
+ }
+ double
+ get_det_F() const
+ {
+ return material->get_det_F();
+ }
+ const Tensor<2, dim> &
+ get_F_inv() const
+ {
+ return F_inv;
+ }
+ double
+ get_p_tilde() const
+ {
+ return material->get_p_tilde();
+ }
+ const SymmetricTensor<2, dim> &
+ get_tau() const
+ {
+ return tau;
+ }
+ double
+ get_dPsi_vol_dJ() const
+ {
+ return dPsi_vol_dJ;
+ }
+ double
+ get_d2Psi_vol_dJ2() const
+ {
+ return d2Psi_vol_dJ2;
+ }
+ const SymmetricTensor<4, dim> &
+ get_Jc() const
+ {
+ return Jc;
+ }
+
+ private:
+ std::shared_ptr<Material_Compressible_Neo_Hook_Three_Field<dim>> material;
+ Tensor<2, dim> F_inv;
+ SymmetricTensor<2, dim> tau;
+ double d2Psi_vol_dJ2;
+ double dPsi_vol_dJ;
+ SymmetricTensor<4, dim> Jc;
+ };
+ template <int dim>
+ class Solid
+ {
+ public:
+ Solid(const std::string &input_file);
+ virtual ~Solid();
+ void
+ run();
+
+ private:
+ struct PerTaskData_K;
+ struct ScratchData_K;
+ struct PerTaskData_RHS;
+ struct ScratchData_RHS;
+ struct PerTaskData_SC;
+ struct ScratchData_SC;
+ struct PerTaskData_UQPH;
+ struct ScratchData_UQPH;
+ void
+ make_grid();
+ void
+ system_setup();
+ void
+ determine_component_extractors();
+ void
+ assemble_system_tangent(BlockSparseMatrix<double> &tangent_matrix,
+ const bool print = true);
+ void
+ assemble_system_tangent_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_K & scratch,
+ PerTaskData_K & data) const;
+ void
+ copy_local_to_global_K(const PerTaskData_K &data);
+ void
+ assemble_system_rhs(BlockVector<double> &system_rhs,
+ const bool print = true);
+ void
+ assemble_system_rhs_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_RHS & scratch,
+ PerTaskData_RHS & data) const;
+ void
+ copy_local_to_global_rhs(const PerTaskData_RHS &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
+ update_qph_incremental(const BlockVector<double> &solution_delta,
+ const bool print = true);
+ void
+ update_qph_incremental_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_UQPH & scratch,
+ PerTaskData_UQPH & data);
+ void
+ copy_local_to_global_UQPH(const PerTaskData_UQPH & /*data*/)
+ {}
+ 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;
+ AffineConstraints<double> 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;
+ double
+ compute_vol_current() const;
+ static void
+ print_conv_header();
+ void
+ print_conv_footer();
+ };
+ template <int dim>
+ Solid<dim>::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>
+ Solid<dim>::~Solid()
+ {
+ dof_handler_ref.clear();
+ }
+ template <int dim>
+ void
+ Solid<dim>::run()
+ {
+ make_grid();
+ system_setup();
+ {
+ AffineConstraints<double> 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>
+ struct Solid<dim>::PerTaskData_K
+ {
+ FullMatrix<double> cell_matrix;
+ std::vector<types::global_dof_index> local_dof_indices;
+ BlockSparseMatrix<double> * tangent_matrix;
+ PerTaskData_K(const unsigned int dofs_per_cell,
+ BlockSparseMatrix<double> &tangent_matrix)
+ : cell_matrix(dofs_per_cell, dofs_per_cell)
+ , local_dof_indices(dofs_per_cell)
+ , tangent_matrix(&tangent_matrix)
+ {}
+ void
+ reset()
+ {
+ cell_matrix = 0.0;
+ }
+ };
+ template <int dim>
+ struct Solid<dim>::ScratchData_K
+ {
+ FEValues<dim> fe_values_ref;
+ std::vector<std::vector<double>> Nx;
+ std::vector<std::vector<Tensor<2, dim>>> grad_Nx;
+ std::vector<std::vector<SymmetricTensor<2, dim>>> symm_grad_Nx;
+ ScratchData_K(const FiniteElement<dim> &fe_cell,
+ const QGauss<dim> & qf_cell,
+ const UpdateFlags uf_cell)
+ : fe_values_ref(fe_cell, qf_cell, uf_cell)
+ , Nx(qf_cell.size(), std::vector<double>(fe_cell.dofs_per_cell))
+ , grad_Nx(qf_cell.size(),
+ std::vector<Tensor<2, dim>>(fe_cell.dofs_per_cell))
+ , symm_grad_Nx(qf_cell.size(),
+ std::vector<SymmetricTensor<2, dim>>(
+ fe_cell.dofs_per_cell))
+ {}
+ ScratchData_K(const ScratchData_K &rhs)
+ : fe_values_ref(rhs.fe_values_ref.get_fe(),
+ rhs.fe_values_ref.get_quadrature(),
+ rhs.fe_values_ref.get_update_flags())
+ , Nx(rhs.Nx)
+ , grad_Nx(rhs.grad_Nx)
+ , symm_grad_Nx(rhs.symm_grad_Nx)
+ {}
+ void
+ reset()
+ {
+ const unsigned int n_q_points = Nx.size();
+ const unsigned int n_dofs_per_cell = Nx[0].size();
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ Assert(Nx[q_point].size() == n_dofs_per_cell, ExcInternalError());
+ Assert(grad_Nx[q_point].size() == n_dofs_per_cell,
+ ExcInternalError());
+ Assert(symm_grad_Nx[q_point].size() == n_dofs_per_cell,
+ ExcInternalError());
+ for (unsigned int k = 0; k < n_dofs_per_cell; ++k)
+ {
+ Nx[q_point][k] = 0.0;
+ grad_Nx[q_point][k] = 0.0;
+ symm_grad_Nx[q_point][k] = 0.0;
+ }
+ }
+ }
+ };
+ template <int dim>
+ struct Solid<dim>::PerTaskData_RHS
+ {
+ Vector<double> cell_rhs;
+ std::vector<types::global_dof_index> local_dof_indices;
+ BlockVector<double> * system_rhs;
+ PerTaskData_RHS(const unsigned int dofs_per_cell,
+ BlockVector<double> &system_rhs)
+ : cell_rhs(dofs_per_cell)
+ , local_dof_indices(dofs_per_cell)
+ , system_rhs(&system_rhs)
+ {}
+ void
+ reset()
+ {
+ cell_rhs = 0.0;
+ }
+ };
+ template <int dim>
+ struct Solid<dim>::ScratchData_RHS
+ {
+ FEValues<dim> fe_values_ref;
+ FEFaceValues<dim> fe_face_values_ref;
+ std::vector<std::vector<double>> Nx;
+ std::vector<std::vector<SymmetricTensor<2, dim>>> symm_grad_Nx;
+ ScratchData_RHS(const FiniteElement<dim> &fe_cell,
+ const QGauss<dim> & qf_cell,
+ const UpdateFlags uf_cell,
+ const QGauss<dim - 1> & qf_face,
+ const UpdateFlags uf_face)
+ : fe_values_ref(fe_cell, qf_cell, uf_cell)
+ , fe_face_values_ref(fe_cell, qf_face, uf_face)
+ , Nx(qf_cell.size(), std::vector<double>(fe_cell.dofs_per_cell))
+ , symm_grad_Nx(qf_cell.size(),
+ std::vector<SymmetricTensor<2, dim>>(
+ fe_cell.dofs_per_cell))
+ {}
+ ScratchData_RHS(const ScratchData_RHS &rhs)
+ : 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())
+ , Nx(rhs.Nx)
+ , symm_grad_Nx(rhs.symm_grad_Nx)
+ {}
+ void
+ reset()
+ {
+ const unsigned int n_q_points = Nx.size();
+ const unsigned int n_dofs_per_cell = Nx[0].size();
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ Assert(Nx[q_point].size() == n_dofs_per_cell, ExcInternalError());
+ Assert(symm_grad_Nx[q_point].size() == n_dofs_per_cell,
+ ExcInternalError());
+ for (unsigned int k = 0; k < n_dofs_per_cell; ++k)
+ {
+ Nx[q_point][k] = 0.0;
+ symm_grad_Nx[q_point][k] = 0.0;
+ }
+ }
+ }
+ };
+ template <int dim>
+ struct Solid<dim>::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>
+ struct Solid<dim>::ScratchData_SC
+ {
+ void
+ reset()
+ {}
+ };
+ template <int dim>
+ struct Solid<dim>::PerTaskData_UQPH
+ {
+ void
+ reset()
+ {}
+ };
+ template <int dim>
+ struct Solid<dim>::ScratchData_UQPH
+ {
+ const BlockVector<double> & solution_total;
+ std::vector<Tensor<2, dim>> solution_grads_u_total;
+ std::vector<double> solution_values_p_total;
+ std::vector<double> solution_values_J_total;
+ FEValues<dim> fe_values_ref;
+ ScratchData_UQPH(const FiniteElement<dim> & fe_cell,
+ const QGauss<dim> & qf_cell,
+ const UpdateFlags uf_cell,
+ const BlockVector<double> &solution_total)
+ : solution_total(solution_total)
+ , solution_grads_u_total(qf_cell.size())
+ , solution_values_p_total(qf_cell.size())
+ , solution_values_J_total(qf_cell.size())
+ , fe_values_ref(fe_cell, qf_cell, uf_cell)
+ {}
+ ScratchData_UQPH(const ScratchData_UQPH &rhs)
+ : solution_total(rhs.solution_total)
+ , solution_grads_u_total(rhs.solution_grads_u_total)
+ , solution_values_p_total(rhs.solution_values_p_total)
+ , solution_values_J_total(rhs.solution_values_J_total)
+ , fe_values_ref(rhs.fe_values_ref.get_fe(),
+ rhs.fe_values_ref.get_quadrature(),
+ rhs.fe_values_ref.get_update_flags())
+ {}
+ void
+ reset()
+ {
+ const unsigned int n_q_points = solution_grads_u_total.size();
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ solution_grads_u_total[q] = 0.0;
+ solution_values_p_total[q] = 0.0;
+ solution_values_J_total[q] = 0.0;
+ }
+ }
+ };
+ template <int dim>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::update_qph_incremental(const BlockVector<double> &solution_delta,
+ const bool print)
+ {
+ timer.enter_subsection("Update QPH data");
+ if (print)
+ std::cout << " UQPH " << std::flush;
+ const BlockVector<double> solution_total(
+ get_total_solution(solution_delta));
+ const UpdateFlags uf_UQPH(update_values | update_gradients);
+ PerTaskData_UQPH per_task_data_UQPH;
+ ScratchData_UQPH scratch_data_UQPH(fe, qf_cell, uf_UQPH, solution_total);
+ WorkStream::run(dof_handler_ref.begin_active(),
+ dof_handler_ref.end(),
+ *this,
+ &Solid::update_qph_incremental_one_cell,
+ &Solid::copy_local_to_global_UQPH,
+ scratch_data_UQPH,
+ per_task_data_UQPH);
+ timer.leave_subsection();
+ }
+ template <int dim>
+ void
+ Solid<dim>::update_qph_incremental_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_UQPH & scratch,
+ PerTaskData_UQPH & /*data*/)
+ {
+ const std::vector<std::shared_ptr<PointHistory<dim>>> lqph =
+ quadrature_point_history.get_data(cell);
+ Assert(lqph.size() == n_q_points, ExcInternalError());
+ Assert(scratch.solution_grads_u_total.size() == n_q_points,
+ ExcInternalError());
+ Assert(scratch.solution_values_p_total.size() == n_q_points,
+ ExcInternalError());
+ Assert(scratch.solution_values_J_total.size() == n_q_points,
+ ExcInternalError());
+ scratch.reset();
+ scratch.fe_values_ref.reinit(cell);
+ scratch.fe_values_ref[u_fe].get_function_gradients(
+ scratch.solution_total, scratch.solution_grads_u_total);
+ scratch.fe_values_ref[p_fe].get_function_values(
+ scratch.solution_total, scratch.solution_values_p_total);
+ scratch.fe_values_ref[J_fe].get_function_values(
+ scratch.solution_total, scratch.solution_values_J_total);
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ lqph[q_point]->update_values(scratch.solution_grads_u_total[q_point],
+ scratch.solution_values_p_total[q_point],
+ scratch.solution_values_J_total[q_point]);
+ }
+ template <int dim>
+ void
+ Solid<dim>::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;
+ tangent_matrix = 0.0;
+ system_rhs = 0.0;
+ assemble_system_rhs(system_rhs);
+ 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();
+ break;
+ }
+ assemble_system_tangent(this->tangent_matrix);
+ make_constraints(newton_iteration);
+ constraints.condense(tangent_matrix, system_rhs);
+ const std::pair<unsigned int, double> lin_solver_output =
+ solve_linear_system(newton_update);
+
+ // Here (in a most inefficient way) we check the effect of
+ // taking the proposed Newton step, and adjust it using
+ // the line-search algorith.
+
+ // Previous step residual
+ BlockVector<double> residual_0 = this->system_rhs;
+ residual_0 *= -1.0; // Residual = -RHS
+ constraints.set_zero(residual_0);
+ const double tang_mtrx_norm_old =
+ tangent_matrix.block(0, 0).frobenius_norm();
+
+ // Minimization function (exact)
+ auto ls_minimization_function =
+ [this,
+ &residual_0,
+ &solution_delta,
+ &newton_update,
+ &tang_mtrx_norm_old](const double ss /*step size*/) {
+ // Ensure that the constraints for the Dirichlet BC's are correct,
+ // irrespective of the chosen step size.
+ BlockVector<double> solution_delta_trial(newton_update);
+ solution_delta_trial *= ss;
+ this->constraints.distribute(solution_delta_trial);
+ // Now add the constribution from the previously accepted solution
+ // history.
+ solution_delta_trial += solution_delta;
+
+ // Compute residual for proposed step
+ this->update_qph_incremental(solution_delta_trial, false);
+ this->assemble_system_rhs(this->system_rhs, false);
+ this->assemble_system_tangent(this->tangent_matrix, false);
+ constraints.condense(this->tangent_matrix, this->system_rhs);
+ BlockVector<double> residual_trial = this->system_rhs;
+ residual_trial *= -1.0; // Residual = -RHS
+
+
+ const double tang_mtrx_norm_new =
+ tangent_matrix.block(0, 0).frobenius_norm();
+
+ if (ss != 0.0)
+ Assert(tang_mtrx_norm_new != tang_mtrx_norm_old,
+ ExcInternalError());
+
+ // Negelect the constrained entries in the consideration
+ this->constraints.set_zero(residual_trial);
+
+ // Wriggers p159 eq 5.11
+ const double f = 0.5 * (residual_trial * residual_trial); // Value
+ // Wriggers p159 eq 5.14 is wrong...
+ // const double g = -(residual_0*residual_trial); // Gradient
+ // This should be g = G(V + alpha*delta)*[ K(V + alpha*delta)*delta
+ // ]
+ BlockVector<double> tmp(newton_update);
+ tangent_matrix.vmult(tmp, newton_update);
+ const double g = tmp * residual_trial; // Gradient
+
+ return std::make_pair(f, g);
+ };
+
+ // Minimization function (perturbation method, to confirm result
+ // of exact minimization function's gradient -- this verifies
+ // that Wriggers 5.14 is incorrect)
+ auto ls_minimization_function_ptrb =
+ [&ls_minimization_function](const double ss) {
+ const double ptrb = 0.005 * 1e-2;
+ const auto f_m = ls_minimization_function(ss);
+ const auto f_minus = ls_minimization_function(ss - ptrb);
+ const auto f_plus = ls_minimization_function(ss + ptrb);
+ return std::make_pair(f_m.first,
+ (f_plus.first - f_minus.first) / (2. * ptrb));
+ };
+
+ // Invoke line search
+ const bool use_ptrb = parameters.use_line_search_ptrb;
+ auto perform_linesearch = [&ls_minimization_function,
+ &ls_minimization_function_ptrb,
+ &use_ptrb]() {
+ const auto res_0 = (use_ptrb ? ls_minimization_function_ptrb(0.0) :
+ ls_minimization_function(0.0));
+ Assert(res_0.second < 0.0,
+ ExcMessage("Gradient should be negative. Current value: " +
+ std::to_string(res_0.second)));
+ const auto res_1 = (use_ptrb ? ls_minimization_function_ptrb(1.0) :
+ ls_minimization_function(1.0));
+
+ // Wriggers discussion after 5.14
+ if (res_0.second * res_1.second > 0.0)
+ return 1.0;
+
+ // The values for eta, mu are chosen such that
+ // more strict convergence conditions are enforced.
+ const double a1 = 1.0;
+ const double eta = 0.5;
+ const double mu = 0.49;
+ const double a_max = 1.25;
+ const double max_evals = 20;
+ const bool debug_linesearch = false;
+ const auto res = (use_ptrb ? LineMinimization::line_search<double>(
+ ls_minimization_function_ptrb,
+ res_0.first,
+ res_0.second,
+ LineMinimization::poly_fit<double>,
+ a1,
+ eta,
+ mu,
+ a_max,
+ max_evals,
+ debug_linesearch) :
+ LineMinimization::line_search<double>(
+ ls_minimization_function,
+ res_0.first,
+ res_0.second,
+ LineMinimization::poly_fit<double>,
+ a1,
+ eta,
+ mu,
+ a_max,
+ max_evals,
+ debug_linesearch));
+
+ return res.first; // Final stepsize
+ };
+ const double linesearch_step_size =
+ (parameters.use_line_search ? perform_linesearch() : 1.0);
+
+ 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);
+ if (linesearch_step_size != 1.0)
+ newton_update *= linesearch_step_size;
+ solution_delta += newton_update;
+ update_qph_incremental(solution_delta);
+ std::cout << " | " << std::fixed << std::setprecision(3) << std::setw(7)
+ << std::scientific << lin_solver_output.first << " "
+ << lin_solver_output.second << " " << linesearch_step_size
+ << " " << 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>
+ void
+ Solid<dim>::print_conv_header()
+ {
+ static const unsigned int l_width = 166;
+ for (unsigned int i = 0; i < l_width; ++i)
+ std::cout << "_";
+ std::cout << std::endl;
+ std::cout << " SOLVER STEP "
+ << " | LIN_IT LIN_RES LS_STP_SZ 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>
+ void
+ Solid<dim>::print_conv_footer()
+ {
+ static const unsigned int l_width = 166;
+ 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();
+ 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>
+ double
+ Solid<dim>::compute_vol_current() const
+ {
+ double vol_current = 0.0;
+ FEValues<dim> fe_values_ref(fe, qf_cell, update_JxW_values);
+ for (typename Triangulation<dim>::active_cell_iterator cell =
+ triangulation.begin_active();
+ cell != triangulation.end();
+ ++cell)
+ {
+ fe_values_ref.reinit(cell);
+ 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 = lqph[q_point]->get_det_F();
+ const double JxW = fe_values_ref.JxW(q_point);
+ vol_current += det_F_qp * JxW;
+ }
+ }
+ Assert(vol_current > 0.0, ExcInternalError());
+ return vol_current;
+ }
+ template <int dim>
+ std::pair<double, double>
+ Solid<dim>::get_error_dilation() const
+ {
+ double dil_L2_error = 0.0;
+ FEValues<dim> fe_values_ref(fe, qf_cell, update_JxW_values);
+ for (typename Triangulation<dim>::active_cell_iterator cell =
+ triangulation.begin_active();
+ cell != triangulation.end();
+ ++cell)
+ {
+ fe_values_ref.reinit(cell);
+ 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 = lqph[q_point]->get_det_F();
+ const double J_tilde_qp = lqph[q_point]->get_J_tilde();
+ 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;
+ }
+ }
+ return std::make_pair(std::sqrt(dil_L2_error),
+ compute_vol_current() / vol_reference);
+ }
+ template <int dim>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ BlockVector<double>
+ Solid<dim>::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>
+ void
+ Solid<dim>::assemble_system_tangent(BlockSparseMatrix<double> &tangent_matrix,
+ const bool print)
+ {
+ timer.enter_subsection("Assemble tangent matrix");
+ if (print)
+ std::cout << " ASM_K " << std::flush;
+ tangent_matrix = 0.0;
+ const UpdateFlags uf_cell(update_values | update_gradients |
+ update_JxW_values);
+ PerTaskData_K per_task_data(dofs_per_cell, tangent_matrix);
+ ScratchData_K scratch_data(fe, qf_cell, uf_cell);
+ WorkStream::run(dof_handler_ref.begin_active(),
+ dof_handler_ref.end(),
+ std::bind(&Solid<dim>::assemble_system_tangent_one_cell,
+ this,
+ std::placeholders::_1,
+ std::placeholders::_2,
+ std::placeholders::_3),
+ std::bind(&Solid<dim>::copy_local_to_global_K,
+ this,
+ std::placeholders::_1),
+ scratch_data,
+ per_task_data);
+ timer.leave_subsection();
+ }
+ template <int dim>
+ void
+ Solid<dim>::copy_local_to_global_K(const PerTaskData_K &data)
+ {
+ BlockSparseMatrix<double> &tangent_matrix = *data.tangent_matrix;
+ 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>
+ void
+ Solid<dim>::assemble_system_tangent_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_K & scratch,
+ PerTaskData_K & 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());
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const Tensor<2, dim> F_inv = lqph[q_point]->get_F_inv();
+ for (unsigned int k = 0; k < dofs_per_cell; ++k)
+ {
+ const unsigned int k_group = fe.system_to_base_index(k).first.first;
+ if (k_group == u_dof)
+ {
+ scratch.grad_Nx[q_point][k] =
+ scratch.fe_values_ref[u_fe].gradient(k, q_point) * F_inv;
+ scratch.symm_grad_Nx[q_point][k] =
+ symmetrize(scratch.grad_Nx[q_point][k]);
+ }
+ else if (k_group == p_dof)
+ scratch.Nx[q_point][k] =
+ scratch.fe_values_ref[p_fe].value(k, q_point);
+ else if (k_group == J_dof)
+ scratch.Nx[q_point][k] =
+ scratch.fe_values_ref[J_fe].value(k, q_point);
+ else
+ Assert(k_group <= J_dof, ExcInternalError());
+ }
+ }
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const Tensor<2, dim> tau = lqph[q_point]->get_tau();
+ const SymmetricTensor<4, dim> Jc = lqph[q_point]->get_Jc();
+ const double d2Psi_vol_dJ2 = lqph[q_point]->get_d2Psi_vol_dJ2();
+ const double det_F = lqph[q_point]->get_det_F();
+ const std::vector<double> & N = scratch.Nx[q_point];
+ const std::vector<SymmetricTensor<2, dim>> &symm_grad_Nx =
+ scratch.symm_grad_Nx[q_point];
+ const std::vector<Tensor<2, dim>> &grad_Nx = scratch.grad_Nx[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 component_i =
+ fe.system_to_component_index(i).first;
+ const unsigned int i_group = fe.system_to_base_index(i).first.first;
+ for (unsigned int j = 0; j <= i; ++j)
+ {
+ const unsigned int component_j =
+ fe.system_to_component_index(j).first;
+ const unsigned int j_group =
+ fe.system_to_base_index(j).first.first;
+ if ((i_group == j_group) && (i_group == u_dof))
+ {
+ data.cell_matrix(i, j) += symm_grad_Nx[i] *
+ Jc // The material contribution:
+ * symm_grad_Nx[j] * JxW;
+ if (component_i ==
+ component_j) // geometrical stress contribution
+ data.cell_matrix(i, j) += grad_Nx[i][component_i] * tau *
+ grad_Nx[j][component_j] * JxW;
+ }
+ else if ((i_group == p_dof) && (j_group == u_dof))
+ {
+ data.cell_matrix(i, j) +=
+ N[i] * det_F *
+ (symm_grad_Nx[j] * StandardTensors<dim>::I) * JxW;
+ }
+ else if ((i_group == J_dof) && (j_group == p_dof))
+ data.cell_matrix(i, j) -= N[i] * N[j] * JxW;
+ else if ((i_group == j_group) && (i_group == J_dof))
+ data.cell_matrix(i, j) += N[i] * d2Psi_vol_dJ2 * N[j] * JxW;
+ else
+ Assert((i_group <= J_dof) && (j_group <= J_dof),
+ ExcInternalError());
+ }
+ }
+ }
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ for (unsigned int j = i + 1; j < dofs_per_cell; ++j)
+ data.cell_matrix(i, j) = data.cell_matrix(j, i);
+ }
+ template <int dim>
+ void
+ Solid<dim>::assemble_system_rhs(BlockVector<double> &system_rhs,
+ const bool print)
+ {
+ timer.enter_subsection("Assemble system right-hand side");
+ if (print)
+ std::cout << " ASM_R " << std::flush;
+
+ system_rhs = 0.0;
+ const UpdateFlags uf_cell(update_values | update_gradients |
+ update_JxW_values);
+ const UpdateFlags uf_face(update_values | update_normal_vectors |
+ update_JxW_values);
+ PerTaskData_RHS per_task_data(dofs_per_cell, system_rhs);
+ ScratchData_RHS scratch_data(fe, qf_cell, uf_cell, qf_face, uf_face);
+ WorkStream::run(dof_handler_ref.begin_active(),
+ dof_handler_ref.end(),
+ std::bind(&Solid<dim>::assemble_system_rhs_one_cell,
+ this,
+ std::placeholders::_1,
+ std::placeholders::_2,
+ std::placeholders::_3),
+ std::bind(&Solid<dim>::copy_local_to_global_rhs,
+ this,
+ std::placeholders::_1),
+ scratch_data,
+ per_task_data);
+ timer.leave_subsection();
+ }
+ template <int dim>
+ void
+ Solid<dim>::copy_local_to_global_rhs(const PerTaskData_RHS &data)
+ {
+ BlockVector<double> &system_rhs = *data.system_rhs;
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ system_rhs(data.local_dof_indices[i]) += data.cell_rhs(i);
+ }
+ template <int dim>
+ void
+ Solid<dim>::assemble_system_rhs_one_cell(
+ const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_RHS & scratch,
+ PerTaskData_RHS & 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());
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const Tensor<2, dim> F_inv = lqph[q_point]->get_F_inv();
+ for (unsigned int k = 0; k < dofs_per_cell; ++k)
+ {
+ const unsigned int k_group = fe.system_to_base_index(k).first.first;
+ if (k_group == u_dof)
+ scratch.symm_grad_Nx[q_point][k] = symmetrize(
+ scratch.fe_values_ref[u_fe].gradient(k, q_point) * F_inv);
+ else if (k_group == p_dof)
+ scratch.Nx[q_point][k] =
+ scratch.fe_values_ref[p_fe].value(k, q_point);
+ else if (k_group == J_dof)
+ scratch.Nx[q_point][k] =
+ scratch.fe_values_ref[J_fe].value(k, q_point);
+ else
+ Assert(k_group <= J_dof, ExcInternalError());
+ }
+ }
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const SymmetricTensor<2, dim> tau = lqph[q_point]->get_tau();
+ const double det_F = lqph[q_point]->get_det_F();
+ const double J_tilde = lqph[q_point]->get_J_tilde();
+ const double p_tilde = lqph[q_point]->get_p_tilde();
+ const double dPsi_vol_dJ = lqph[q_point]->get_dPsi_vol_dJ();
+ const std::vector<double> & N = scratch.Nx[q_point];
+ const std::vector<SymmetricTensor<2, dim>> &symm_grad_Nx =
+ scratch.symm_grad_Nx[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)
+ data.cell_rhs(i) -= (symm_grad_Nx[i] * tau) * JxW;
+ else if (i_group == p_dof)
+ data.cell_rhs(i) -= N[i] * (det_F - J_tilde) * JxW;
+ else if (i_group == J_dof)
+ data.cell_rhs(i) -= N[i] * (dPsi_vol_dJ - p_tilde) * 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);
+ data.cell_rhs(i) += (Ni * traction[component_i]) * JxW;
+ }
+ }
+ }
+ }
+ }
+ template <int dim>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ void
+ Solid<dim>::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>
+ std::pair<unsigned int, double>
+ Solid<dim>::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>
+ void
+ Solid<dim>::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