--- /dev/null
+/* ---------------------------------------------------------------------
+ * Copyright (C) 2017 by the deal.II authors and
+ * Jean-Paul Pelteret
+ *
+ * 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.
+ *
+ * ---------------------------------------------------------------------
+ */
+
+/*
+ * Authors: Jean-Paul Pelteret, University of Erlangen-Nuremberg, 2017
+ */
+
+#include <deal.II/base/mpi.h>
+#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/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/base/quadrature_point_data.h>
+#include <deal.II/grid/filtered_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_in.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_boundary_lib.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/lac/block_sparsity_pattern.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/solver_selector.h>
+#include <deal.II/lac/trilinos_block_sparse_matrix.h>
+#include <deal.II/lac/trilinos_block_vector.h>
+#include <deal.II/lac/trilinos_precondition.h>
+#include <deal.II/lac/trilinos_sparsity_pattern.h>
+#include <deal.II/lac/trilinos_sparse_matrix.h>
+#include <deal.II/lac/trilinos_vector.h>
+#include <deal.II/lac/linear_operator.h>
+#include <deal.II/lac/packaged_operation.h>
+#include <deal.II/lac/trilinos_linear_operator.h>
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/physics/transformations.h>
+#include <deal.II/physics/elasticity/kinematics.h>
+#include <deal.II/physics/elasticity/standard_tensors.h>
+#include <iostream>
+#include <fstream>
+#include <numeric>
+
+#include <deal.II/grid/grid_out.h>
+
+namespace ViscoElasStripHole
+{
+ using namespace dealii;
+ namespace LA = TrilinosWrappers;
+ namespace Parameters
+ {
+ struct BoundaryConditions
+ {
+ BoundaryConditions();
+
+ std::string driver;
+ double stretch;
+ double pressure;
+ double load_time;
+
+ const types::boundary_id boundary_id_minus_X;
+ const types::boundary_id boundary_id_plus_X;
+ const types::boundary_id boundary_id_minus_Y;
+ const types::boundary_id boundary_id_plus_Y;
+ const types::boundary_id boundary_id_minus_Z;
+ const types::boundary_id boundary_id_plus_Z;
+ const types::boundary_id boundary_id_hole;
+ const types::manifold_id manifold_id_hole;
+
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ BoundaryConditions::BoundaryConditions()
+ :
+ driver ("Neumann"),
+ stretch (2.0),
+ pressure(0.0),
+ load_time(2.5),
+ boundary_id_minus_X (1),
+ boundary_id_plus_X (2),
+ boundary_id_minus_Y (3),
+ boundary_id_plus_Y (4),
+ boundary_id_minus_Z (5),
+ boundary_id_plus_Z (6),
+ boundary_id_hole (10),
+ manifold_id_hole (10)
+ { }
+ void BoundaryConditions::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Boundary conditions");
+ {
+ prm.declare_entry("Driver", "Dirichlet",
+ Patterns::Selection("Dirichlet|Neumann"),
+ "Driver boundary condition for the problem");
+ prm.declare_entry("Final stretch", "2.0",
+ Patterns::Double(1.0),
+ "Positive stretch applied length-ways to the strip");
+ prm.declare_entry("Applied pressure", "0.0",
+ Patterns::Double(-1e3,1e3),
+ "Hydrostatic pressure applied (in the referential configuration) to the interior surface of the hole");
+ prm.declare_entry("Load time", "2.5",
+ Patterns::Double(0.0),
+ "Total time over which the stretch/pressure is ramped up");
+ }
+ prm.leave_subsection();
+ }
+ void BoundaryConditions::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Boundary conditions");
+ {
+ driver = prm.get("Driver");
+ stretch = prm.get_double("Final stretch");
+ pressure = prm.get_double("Applied pressure");
+ load_time = prm.get_double("Load time");
+ }
+ prm.leave_subsection();
+ }
+ 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
+ {
+ double length;
+ double width;
+ double thickness;
+ double hole_diameter;
+ double hole_division_fraction;
+ unsigned int n_repetitions_xy;
+ unsigned int n_repetitions_z;
+ unsigned int global_refinement;
+ double scale;
+ static void
+ declare_parameters(ParameterHandler &prm);
+ void
+ parse_parameters(ParameterHandler &prm);
+ };
+ void Geometry::declare_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Geometry");
+ {
+ prm.declare_entry("Length", "100.0",
+ Patterns::Double(0.0),
+ "Total sample length");
+ prm.declare_entry("Width", "50.0",
+ Patterns::Double(0.0),
+ "Total sample width");
+ prm.declare_entry("Thickness", "5.0",
+ Patterns::Double(0.0),
+ "Total sample thickness");
+ prm.declare_entry("Hole diameter", "20.0",
+ Patterns::Double(0.0),
+ "Hole diameter");
+ prm.declare_entry("Hole division fraction", "0.5",
+ Patterns::Double(0.0,1.0),
+ "A geometric factor affecting the discretisation near the hole");
+ prm.declare_entry("Number of subdivisions in cross-section", "2",
+ Patterns::Integer(1.0),
+ "A factor defining the number of initial grid subdivisions in the cross-section");
+ prm.declare_entry("Number of subdivisions thickness", "6",
+ Patterns::Integer(1.0),
+ "A factor defining the number of initial grid subdivisions through the thickness");
+ 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.leave_subsection();
+ }
+ void Geometry::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Geometry");
+ {
+ length = prm.get_double("Length");
+ width = prm.get_double("Width");
+ thickness = prm.get_double("Thickness");
+ hole_diameter = prm.get_double("Hole diameter");
+ hole_division_fraction = prm.get_double("Hole division fraction");
+ n_repetitions_xy = prm.get_integer("Number of subdivisions in cross-section");
+ n_repetitions_z = prm.get_integer("Number of subdivisions thickness");
+ global_refinement = prm.get_integer("Global refinement");
+ scale = prm.get_double("Grid scale");
+ }
+ prm.leave_subsection();
+ }
+ struct Materials
+ {
+ double nu_e;
+ double mu_e;
+ double mu_v;
+ double tau_v;
+ 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("Elastic shear modulus", "80.194e6",
+ Patterns::Double(0.0),
+ "Elastic shear modulus");
+ prm.declare_entry("Viscous shear modulus", "80.194e6",
+ Patterns::Double(0.0),
+ "Viscous shear modulus");
+ prm.declare_entry("Viscous relaxation time", "2.0",
+ Patterns::Double(0.0),
+ "Viscous relaxation time");
+ }
+ prm.leave_subsection();
+ }
+ void Materials::parse_parameters(ParameterHandler &prm)
+ {
+ prm.enter_subsection("Material properties");
+ {
+ nu_e = prm.get_double("Poisson's ratio");
+ mu_e = prm.get_double("Elastic shear modulus");
+ mu_v = prm.get_double("Viscous shear modulus");
+ tau_v = prm.get_double("Viscous relaxation time");
+ }
+ prm.leave_subsection();
+ }
+ struct LinearSolver
+ {
+ std::string type_lin;
+ double tol_lin;
+ double max_iterations_lin;
+ 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(SolverSelector<LA::Vector>::get_solver_names()),
+ "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(1.0),
+ "Linear solver iterations (multiples of the system matrix size)");
+ }
+ 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");
+ }
+ 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 displacement", "1.0e-6",
+ Patterns::Double(0.0),
+ "Displacement error tolerance");
+ prm.declare_entry("Tolerance force", "1.0e-9",
+ Patterns::Double(0.0),
+ "Force residual 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 BoundaryConditions,
+ 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)
+ {
+ BoundaryConditions::declare_parameters(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)
+ {
+ BoundaryConditions::parse_parameters(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);
+ }
+ }
+ 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_Three_Field_Linear_Viscoelastic
+ {
+ public:
+ Material_Compressible_Three_Field_Linear_Viscoelastic(const double mu_e,
+ const double nu_e,
+ const double mu_v,
+ const double tau_v,
+ const Time &time)
+ :
+ kappa((2.0 * mu_e * (1.0 + nu_e)) / (3.0 * (1.0 - 2.0 * nu_e))),
+ mu_e(mu_e),
+ mu_v(mu_v),
+ tau_v(tau_v),
+ time(time),
+ Q_n_t(Physics::Elasticity::StandardTensors<dim>::I),
+ Q_t1(Physics::Elasticity::StandardTensors<dim>::I)
+ {
+ Assert(kappa > 0, ExcInternalError());
+ }
+ ~Material_Compressible_Three_Field_Linear_Viscoelastic()
+ {}
+
+ SymmetricTensor<2,dim>
+ get_tau(const Tensor<2,dim> &F,
+ const double &p_tilde) const
+ {
+ return get_tau_iso(F) + get_tau_vol(F,p_tilde);
+ }
+ SymmetricTensor<4,dim> get_Jc(const Tensor<2,dim> &F,
+ const double &p_tilde) const
+ {
+ return get_Jc_iso(F) + get_Jc_vol(F,p_tilde);
+ }
+ double
+ get_dPsi_vol_dJ(const double &J_tilde) const
+ {
+ return (kappa / 2.0) * (J_tilde - 1.0 / J_tilde);
+ }
+ double
+ get_d2Psi_vol_dJ2(const double &J_tilde) const
+ {
+ return ( (kappa / 2.0) * (1.0 + 1.0 / (J_tilde * J_tilde)));
+ }
+ void
+ update_internal_equilibrium(const Tensor<2, dim> &F,
+ const double &p_tilde,
+ const double &J_tilde)
+ {
+ const double det_F = determinant(F);
+ const SymmetricTensor<2,dim> C_bar = std::pow(det_F, -2.0 / dim) * Physics::Elasticity::Kinematics::C(F);
+ // Linder2011 eq 54
+ // Assumes first-oder backward Euler time discretisation
+ Q_n_t = (1.0/(1.0 + time.get_delta_t()/tau_v))*(Q_t1 + (time.get_delta_t()/tau_v)*invert(C_bar));
+ }
+ void
+ update_end_timestep()
+ {
+ Q_t1 = Q_n_t;
+ }
+
+ protected:
+ const double kappa;
+ const double mu_e;
+ const double mu_v;
+ const double tau_v;
+ const Time &time;
+ SymmetricTensor<2,dim> Q_n_t; // Value of internal variable at this Newton step and timestep
+ SymmetricTensor<2,dim> Q_t1; // Value of internal variable at the previous timestep
+
+ SymmetricTensor<2, dim>
+ get_tau_vol(const Tensor<2,dim> &F,
+ const double &p_tilde) const
+ {
+ const double det_F = determinant(F);
+
+ return p_tilde * det_F * Physics::Elasticity::StandardTensors<dim>::I;
+ }
+ SymmetricTensor<2, dim>
+ get_tau_iso(const Tensor<2,dim> &F) const
+ {
+ return Physics::Elasticity::StandardTensors<dim>::dev_P * get_tau_bar(F);
+ }
+ SymmetricTensor<2, dim>
+ get_tau_bar(const Tensor<2,dim> &F) const
+ {
+ const double det_F = determinant(F);
+ const Tensor<2,dim> F_bar = std::pow(det_F, -1.0 / dim) * F;
+ const SymmetricTensor<2,dim> b_bar = std::pow(det_F, -2.0 / dim) * symmetrize(F * transpose(F));
+ // Elastic Neo-Hookean + Linder2011 eq 47
+ return mu_e * b_bar
+ + mu_v * symmetrize(F_bar*static_cast<Tensor<2,dim> >(Q_n_t)*transpose(F_bar));
+ }
+ SymmetricTensor<4, dim> get_Jc_vol(const Tensor<2,dim> &F,
+ const double &p_tilde) const
+ {
+ const double det_F = determinant(F);
+ return p_tilde * det_F
+ * ( Physics::Elasticity::StandardTensors<dim>::IxI
+ - (2.0 * Physics::Elasticity::StandardTensors<dim>::S) );
+ }
+ SymmetricTensor<4, dim> get_Jc_iso(const Tensor<2,dim> &F) const
+ {
+ const SymmetricTensor<2, dim> tau_bar = get_tau_bar(F);
+ const SymmetricTensor<2, dim> tau_iso = get_tau_iso(F);
+ const SymmetricTensor<4, dim> tau_iso_x_I
+ = outer_product(tau_iso,
+ Physics::Elasticity::StandardTensors<dim>::I);
+ const SymmetricTensor<4, dim> I_x_tau_iso
+ = outer_product(Physics::Elasticity::StandardTensors<dim>::I,
+ tau_iso);
+ const SymmetricTensor<4, dim> c_bar = get_c_bar(F);
+ return (2.0 / dim) * trace(tau_bar)
+ * Physics::Elasticity::StandardTensors<dim>::dev_P
+ - (2.0 / dim) * (tau_iso_x_I + I_x_tau_iso)
+ + Physics::Elasticity::StandardTensors<dim>::dev_P * c_bar
+ * Physics::Elasticity::StandardTensors<dim>::dev_P;
+ }
+ SymmetricTensor<4, dim> get_c_bar(const Tensor<2,dim> &F) const
+ {
+ // Elastic Neo-Hookean + Linder2011 eq 56
+ return -2.0*mu_v*((time.get_delta_t()/tau_v)/(1.0 + time.get_delta_t()/tau_v))*Physics::Elasticity::StandardTensors<dim>::S;
+ }
+ };
+ template <int dim>
+ class PointHistory
+ {
+ public:
+ PointHistory()
+ {}
+ virtual ~PointHistory()
+ {}
+ void
+ setup_lqp (const Parameters::AllParameters ¶meters,
+ const Time &time)
+ {
+ material.reset(new Material_Compressible_Three_Field_Linear_Viscoelastic<dim>(
+ parameters.mu_e, parameters.nu_e,
+ parameters.mu_v, parameters.tau_v,
+ time));
+ }
+
+ SymmetricTensor<2, dim>
+ get_tau(const Tensor<2, dim> &F,
+ const double &p_tilde) const
+ {
+ return material->get_tau(F, p_tilde);
+ }
+ SymmetricTensor<4, dim>
+ get_Jc(const Tensor<2, dim> &F,
+ const double &p_tilde) const
+ {
+ return material->get_Jc(F, p_tilde);
+ }
+ double
+ get_dPsi_vol_dJ(const double &J_tilde) const
+ {
+ return material->get_dPsi_vol_dJ(J_tilde);
+ }
+ double
+ get_d2Psi_vol_dJ2(const double &J_tilde) const
+ {
+ return material->get_d2Psi_vol_dJ2(J_tilde);
+ }
+ void
+ update_internal_equilibrium(const Tensor<2, dim> &F,
+ const double &p_tilde,
+ const double &J_tilde)
+ {
+ material->update_internal_equilibrium(F,p_tilde,J_tilde);
+ }
+ void
+ update_end_timestep()
+ {
+ material->update_end_timestep();
+ }
+ private:
+ std_cxx11::shared_ptr< Material_Compressible_Three_Field_Linear_Viscoelastic<dim> > material;
+ };
+ template <int dim>
+ class Solid
+ {
+ public:
+ Solid(const std::string &input_file);
+ virtual
+ ~Solid();
+ void
+ run();
+ private:
+ struct PerTaskData_ASM;
+ struct ScratchData_ASM;
+ void
+ make_grid();
+ void
+ make_2d_quarter_plate_with_hole(Triangulation<2> &tria_2d,
+ const double half_length,
+ const double half_width,
+ const double hole_radius,
+ const unsigned int n_repetitions_xy = 1,
+ const double hole_division_fraction = 0.25);
+ void
+ setup_system(LA::MPI::BlockVector &solution_delta);
+ void
+ determine_component_extractors();
+ void
+ assemble_system(const LA::MPI::BlockVector &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
+ make_constraints(const int &it_nr);
+ void
+ setup_qph();
+ void
+ solve_nonlinear_timestep(LA::MPI::BlockVector &solution_delta);
+ std::pair<unsigned int, double>
+ solve_linear_system(LA::MPI::BlockVector &newton_update);
+ LA::MPI::BlockVector
+ get_solution_total(const LA::MPI::BlockVector &solution_delta) const;
+ void
+ update_end_timestep();
+ void
+ output_results(const unsigned int timestep,
+ const double current_time) const;
+ void
+ compute_vertex_positions(std::vector<double> &real_time,
+ std::vector<std::vector<Point<dim> > > &tracked_vertices,
+ const LA::MPI::BlockVector &solution_total) const;
+
+ // Parallel communication
+ MPI_Comm mpi_communicator;
+ const unsigned int n_mpi_processes;
+ const unsigned int this_mpi_process;
+ mutable ConditionalOStream pcout;
+
+ Parameters::AllParameters parameters;
+ 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;
+ 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_block = 0,
+ p_block = 1,
+ J_block = 2
+ };
+ // Block data
+ std::vector<unsigned int> block_component;
+
+ // DoF index data
+ std::vector<IndexSet> all_locally_owned_dofs;
+ IndexSet locally_owned_dofs;
+ IndexSet locally_relevant_dofs;
+ std::vector<IndexSet> locally_owned_partitioning;
+ std::vector<IndexSet> locally_relevant_partitioning;
+ 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;
+ LA::BlockSparseMatrix tangent_matrix;
+ LA::MPI::BlockVector system_rhs;
+ LA::MPI::BlockVector 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 LA::MPI::BlockVector &newton_update,
+ Errors &error_update);
+ std::pair<double, std::pair<double,double> >
+ get_error_dilation(const LA::MPI::BlockVector &solution_total) const;
+ void
+ print_conv_header();
+ void
+ print_conv_footer(const LA::MPI::BlockVector &solution_delta);
+ };
+ template <int dim>
+ Solid<dim>::Solid(const std::string &input_file)
+ :
+ mpi_communicator(MPI_COMM_WORLD),
+ n_mpi_processes (Utilities::MPI::n_mpi_processes(mpi_communicator)),
+ this_mpi_process (Utilities::MPI::this_mpi_process(mpi_communicator)),
+ pcout(std::cout, this_mpi_process == 0),
+ parameters(input_file),
+ triangulation(Triangulation<dim>::maximum_smoothing),
+ time(parameters.end_time, parameters.delta_t),
+ timer(mpi_communicator,
+ pcout,
+ TimerOutput::summary,
+ 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(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.clear();
+ }
+ template <int dim>
+ void Solid<dim>::run()
+ {
+ LA::MPI::BlockVector solution_delta;
+
+ make_grid();
+ setup_system(solution_delta);
+ {
+ ConstraintMatrix constraints;
+ constraints.close();
+ const ComponentSelectFunction<dim>
+ J_mask (J_component, n_components);
+ VectorTools::project (dof_handler,
+ constraints,
+ QGauss<dim>(degree+2),
+ J_mask,
+ solution_n);
+ }
+ output_results(time.get_timestep(), time.current());
+ time.increment();
+
+ // Some points for post-processing
+ std::vector<double> real_time;
+ real_time.push_back(0);
+ std::vector<std::vector<Point<dim> > > tracked_vertices (4);
+ {
+ Point<dim> p;
+ p[1] = parameters.length/2.0;
+ tracked_vertices[0].push_back(p*parameters.scale);
+ }
+ {
+ Point<dim> p;
+ p[1] = parameters.hole_diameter/2.0;
+ tracked_vertices[1].push_back(p*parameters.scale);
+ }
+ {
+ Point<dim> p;
+ p[0] = parameters.hole_diameter/2.0;
+ tracked_vertices[2].push_back(p*parameters.scale);
+ }
+ {
+ Point<dim> p;
+ p[0] = parameters.width/2.0;
+ tracked_vertices[3].push_back(p*parameters.scale);
+ }
+
+ while (time.current() < time.end()+0.01*time.get_delta_t())
+ {
+ solve_nonlinear_timestep(solution_delta);
+ solution_n += solution_delta;
+ solution_delta = 0.0;
+ output_results(time.get_timestep(), time.current());
+ compute_vertex_positions(real_time,
+ tracked_vertices,
+ get_solution_total(solution_delta));
+ update_end_timestep();
+ time.increment();
+ }
+
+ pcout << "\n\n*** Spatial position history for tracked vertices ***" << std::endl;
+ for (unsigned int t=0; t<real_time.size(); ++t)
+ {
+ if (t == 0)
+ {
+ pcout << "Time,";
+ for (unsigned int p=0; p<tracked_vertices.size(); ++p)
+ {
+ for (unsigned int d=0; d<dim; ++d)
+ {
+ pcout << "Point " << p << " [" << d << "]";
+ if (!(p == tracked_vertices.size()-1 & d == dim-1))
+ pcout << ",";
+ }
+ }
+ pcout << std::endl;
+ }
+
+ pcout << std::setprecision(6);
+ pcout << real_time[t] << ",";
+ for (unsigned int p=0; p<tracked_vertices.size(); ++p)
+ {
+ Assert(tracked_vertices[p].size() == real_time.size(),
+ ExcMessage("Vertex not tracked at each timestep"));
+ for (unsigned int d=0; d<dim; ++d)
+ {
+ pcout << tracked_vertices[p][t][d];
+ if (!(p == tracked_vertices.size()-1 & d == dim-1))
+ pcout << ",";
+ }
+ }
+ pcout << std::endl;
+ }
+ }
+ template <int dim>
+ struct Solid<dim>::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>
+ struct Solid<dim>::ScratchData_ASM
+ {
+ const LA::MPI::BlockVector &solution_total;
+
+ // Integration helper
+ FEValues<dim> fe_values_ref;
+ FEFaceValues<dim> fe_face_values_ref;
+
+ // Quadrature point solution
+ std::vector<Tensor<2, dim> > solution_grads_u_total;
+ std::vector<double> solution_values_p_total;
+ std::vector<double> solution_values_J_total;
+
+ // Shape function values and gradients
+ 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_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 LA::MPI::BlockVector &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),
+ solution_grads_u_total(qf_cell.size()),
+ solution_values_p_total(qf_cell.size()),
+ solution_values_J_total(qf_cell.size()),
+ 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_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()),
+ 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),
+ Nx(rhs.Nx),
+ grad_Nx(rhs.grad_Nx),
+ symm_grad_Nx(rhs.symm_grad_Nx)
+ {}
+ void reset()
+ {
+ const unsigned int n_q_points = solution_grads_u_total.size();
+ const unsigned int n_dofs_per_cell = Nx[0].size();
+
+ Assert(solution_grads_u_total.size() == n_q_points,
+ ExcInternalError());
+ Assert(solution_values_p_total.size() == n_q_points,
+ ExcInternalError());
+ Assert(solution_values_J_total.size() == n_q_points,
+ ExcInternalError());
+ Assert(Nx.size() == n_q_points,
+ ExcInternalError());
+ Assert(grad_Nx.size() == n_q_points,
+ ExcInternalError());
+ Assert(symm_grad_Nx.size() == n_q_points,
+ ExcInternalError());
+
+ 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());
+
+ solution_grads_u_total[q_point] = 0.0;
+ solution_values_p_total[q_point] = 0.0;
+ solution_values_J_total[q_point] = 0.0;
+ 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 <>
+ void Solid<2>::make_grid()
+ {
+ const int dim = 2;
+ const double tol = 1e-12;
+ make_2d_quarter_plate_with_hole(triangulation,
+ parameters.length/2.0,
+ parameters.width/2.0,
+ parameters.hole_diameter/2.0,
+ parameters.n_repetitions_xy,
+ parameters.hole_division_fraction);
+
+ // Clear boundary ID's
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ {
+ for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ {
+ cell->face(face)->set_all_boundary_ids(0);
+ }
+ }
+
+ // Set boundary IDs and and manifolds
+ const Point<dim> centre (0,0);
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ {
+ for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ {
+ // Set boundary IDs
+ if (std::abs(cell->face(face)->center()[0] - 0.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_minus_X);
+ }
+ else if (std::abs(cell->face(face)->center()[0] - parameters.width/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_plus_X);
+ }
+ else if (std::abs(cell->face(face)->center()[1] - 0.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_minus_Y);
+ }
+ else if (std::abs(cell->face(face)->center()[1] - parameters.length/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_plus_Y);
+ }
+ else
+ {
+ for (unsigned int vertex=0; vertex<GeometryInfo<dim>::vertices_per_face; ++vertex)
+ if (std::abs(cell->vertex(vertex).distance(centre) - parameters.hole_diameter/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_hole);
+ break;
+ }
+ }
+
+ // Set manifold IDs
+ for (unsigned int vertex=0; vertex<GeometryInfo<dim>::vertices_per_face; ++vertex)
+ if (std::abs(cell->vertex(vertex).distance(centre) - parameters.hole_diameter/2.0) < tol)
+ {
+ cell->face(face)->set_manifold_id(parameters.manifold_id_hole);
+ break;
+ }
+ }
+ }
+ static SphericalManifold<dim> spherical_manifold (centre);
+ triangulation.set_manifold(parameters.manifold_id_hole,spherical_manifold);
+ triangulation.refine_global(parameters.global_refinement);
+ GridTools::scale(parameters.scale,triangulation);
+ }
+ template <>
+ void Solid<3>::make_grid()
+ {
+ const int dim = 3;
+ const double tol = 1e-12;
+ Triangulation<2> tria_2d;
+ make_2d_quarter_plate_with_hole(tria_2d,
+ parameters.length/2.0,
+ parameters.width/2.0,
+ parameters.hole_diameter/2.0,
+ parameters.n_repetitions_xy,
+ parameters.hole_division_fraction);
+ GridGenerator::extrude_triangulation(tria_2d,
+ parameters.n_repetitions_z+1,
+ parameters.thickness/2.0,
+ triangulation);
+
+ // Clear boundary ID's
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ {
+ for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ {
+ cell->face(face)->set_all_boundary_ids(0);
+ }
+ }
+
+ // Set boundary IDs and and manifolds
+ const Point<dim> direction (0,0,1);
+ const Point<dim> centre (0,0,0);
+ for (typename Triangulation<dim>::active_cell_iterator
+ cell = triangulation.begin_active();
+ cell != triangulation.end(); ++cell)
+ {
+ for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ {
+ // Set boundary IDs
+ if (std::abs(cell->face(face)->center()[0] - 0.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_minus_X);
+ }
+ else if (std::abs(cell->face(face)->center()[0] - parameters.width/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_plus_X);
+ }
+ else if (std::abs(cell->face(face)->center()[1] - 0.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_minus_Y);
+ }
+ else if (std::abs(cell->face(face)->center()[1] - parameters.length/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_plus_Y);
+ }
+ else if (std::abs(cell->face(face)->center()[2] - 0.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_minus_Z);
+ }
+ else if (std::abs(cell->face(face)->center()[2] - parameters.thickness/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_plus_Z);
+ }
+ else
+ {
+ for (unsigned int vertex=0; vertex<GeometryInfo<dim>::vertices_per_face; ++vertex)
+ {
+ // Project the cell vertex to the XY plane and
+ // test the distance from the cylinder axis
+ Point<dim> vertex_proj = cell->vertex(vertex);
+ vertex_proj[2] = 0.0;
+ if (std::abs(vertex_proj.distance(centre) - parameters.hole_diameter/2.0) < tol)
+ {
+ cell->face(face)->set_boundary_id(parameters.boundary_id_hole);
+ break;
+ }
+ }
+ }
+
+ // Set manifold IDs
+ for (unsigned int vertex=0; vertex<GeometryInfo<dim>::vertices_per_face; ++vertex)
+ {
+ // Project the cell vertex to the XY plane and
+ // test the distance from the cylinder axis
+ Point<dim> vertex_proj = cell->vertex(vertex);
+ vertex_proj[2] = 0.0;
+ if (std::abs(vertex_proj.distance(centre) - parameters.hole_diameter/2.0) < 1e-12)
+ {
+ // Set manifold ID on face and edges
+ cell->face(face)->set_all_manifold_ids(parameters.manifold_id_hole);
+ break;
+ }
+ }
+ }
+ }
+ static CylindricalManifold<dim> cylindrical_manifold (direction,centre);
+ triangulation.set_manifold(parameters.manifold_id_hole,cylindrical_manifold);
+ triangulation.refine_global(parameters.global_refinement);
+ GridTools::scale(parameters.scale,triangulation);
+ }
+ template <int dim>
+ void Solid<dim>::make_2d_quarter_plate_with_hole(Triangulation<2> &tria_2d,
+ const double half_length,
+ const double half_width,
+ const double hole_radius,
+ const unsigned int n_repetitions_xy,
+ const double hole_division_fraction)
+ {
+ const double length = 2.0*half_length;
+ const double width = 2.0*half_width;
+ const double hole_diameter = 2.0*hole_radius;
+
+ const double internal_width = hole_diameter + hole_division_fraction*(width - hole_diameter);
+ Triangulation<2> tria_quarter_plate_hole;
+ {
+ Triangulation<2> tria_plate_hole;
+ GridGenerator::hyper_cube_with_cylindrical_hole (tria_plate_hole,
+ hole_diameter/2.0,
+ internal_width/2.0);
+
+ std::set<typename Triangulation<2>::active_cell_iterator > cells_to_remove;
+ for (typename Triangulation<2>::active_cell_iterator
+ cell = tria_plate_hole.begin_active();
+ cell != tria_plate_hole.end(); ++cell)
+ {
+ // Remove all cells that are not in the first quadrant
+ if (cell->center()[0] < 0.0 || cell->center()[1] < 0.0)
+ cells_to_remove.insert(cell);
+ }
+ Assert(cells_to_remove.size() > 0, ExcInternalError());
+ Assert(cells_to_remove.size() != tria_plate_hole.n_active_cells(), ExcInternalError());
+ GridGenerator::create_triangulation_with_removed_cells(tria_plate_hole,cells_to_remove,tria_quarter_plate_hole);
+ }
+
+ Triangulation<2> tria_cut_plate;
+ {
+ Triangulation<2> tria_plate;
+ // Subdivide the plate so that we're left one
+ // cell to remove (we'll replace this with the
+ // plate with the hole) and then make the
+ // rest of the subdivisions so that we're left
+ // with cells with a decent aspect ratio
+ std::vector<std::vector<double> > step_sizes;
+ {
+ std::vector<double> subdivision_width;
+ subdivision_width.push_back(internal_width/2.0);
+ const double width_remaining = (width - internal_width)/2.0;
+ const unsigned int n_subs = std::max(1.0,std::ceil(width_remaining/(internal_width/2.0)));
+ Assert(n_subs>0, ExcInternalError());
+ for (unsigned int s=0; s<n_subs; ++s)
+ subdivision_width.push_back(width_remaining/n_subs);
+ step_sizes.push_back(subdivision_width);
+
+ const double sum_half_width = std::accumulate(subdivision_width.begin(), subdivision_width.end(), 0.0);
+ Assert(std::abs(sum_half_width-width/2.0) < 1e-12, ExcInternalError());
+ }
+ {
+ std::vector<double> subdivision_length;
+ subdivision_length.push_back(internal_width/2.0);
+ const double length_remaining = (length - internal_width)/2.0;
+ const unsigned int n_subs = std::max(1.0,std::ceil(length_remaining/(internal_width/2.0)));
+ Assert(n_subs>0, ExcInternalError());
+ for (unsigned int s=0; s<n_subs; ++s)
+ subdivision_length.push_back(length_remaining/n_subs);
+ step_sizes.push_back(subdivision_length);
+
+ const double sum_half_length = std::accumulate(subdivision_length.begin(), subdivision_length.end(), 0.0);
+ Assert(std::abs(sum_half_length-length/2.0) < 1e-12, ExcInternalError());
+ }
+
+ GridGenerator::subdivided_hyper_rectangle(tria_plate,
+ step_sizes,
+ Point<2>(0.0, 0.0),
+ Point<2>(width/2.0, length/2.0));
+
+ std::set<typename Triangulation<2>::active_cell_iterator > cells_to_remove;
+ for (typename Triangulation<2>::active_cell_iterator
+ cell = tria_plate.begin_active();
+ cell != tria_plate.end(); ++cell)
+ {
+ // Remove all cells that are in the first quadrant
+ if (cell->center()[0] < internal_width/2.0 && cell->center()[1] < internal_width/2.0)
+ cells_to_remove.insert(cell);
+ }
+ Assert(cells_to_remove.size() > 0, ExcInternalError());
+ Assert(cells_to_remove.size() != tria_plate.n_active_cells(), ExcInternalError());
+ GridGenerator::create_triangulation_with_removed_cells(tria_plate,cells_to_remove,tria_cut_plate);
+ }
+
+ Triangulation<2> tria_2d_not_flat;
+ GridGenerator::merge_triangulations(tria_quarter_plate_hole,
+ tria_cut_plate,
+ tria_2d_not_flat);
+
+ // Attach a manifold to the curved boundary and refine
+ // Note: We can only guarentee that the vertices sit on
+ // the curve, so we must test with their position instead
+ // of the cell centre.
+ const Point<2> centre_2d (0,0);
+ for (typename Triangulation<2>::active_cell_iterator
+ cell = tria_2d_not_flat.begin_active();
+ cell != tria_2d_not_flat.end(); ++cell)
+ {
+ for (unsigned int face=0; face<GeometryInfo<2>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ for (unsigned int vertex=0; vertex<GeometryInfo<2>::vertices_per_face; ++vertex)
+ if (std::abs(cell->vertex(vertex).distance(centre_2d) - hole_diameter/2.0) < 1e-12)
+ {
+ cell->face(face)->set_manifold_id(10);
+ break;
+ }
+ }
+ SphericalManifold<2> spherical_manifold_2d (centre_2d);
+ tria_2d_not_flat.set_manifold(10,spherical_manifold_2d);
+ tria_2d_not_flat.refine_global(std::max (1U, n_repetitions_xy));
+ tria_2d_not_flat.set_manifold(10); // Clear manifold
+
+ GridGenerator::flatten_triangulation(tria_2d_not_flat,tria_2d);
+ }
+ template <int dim>
+ void Solid<dim>::setup_system(LA::MPI::BlockVector &solution_delta)
+ {
+ timer.enter_subsection("Setup system");
+ pcout << "Setting up linear system..." << std::endl;
+
+ // Partition triangulation
+ GridTools::partition_triangulation (n_mpi_processes,
+ triangulation);
+
+ block_component = std::vector<unsigned int> (n_components, u_block); // Displacement
+ block_component[p_component] = p_block; // Pressure
+ block_component[J_component] = J_block; // Dilatation
+ dof_handler.distribute_dofs(fe);
+ DoFRenumbering::Cuthill_McKee(dof_handler);
+ DoFRenumbering::component_wise(dof_handler, block_component);
+
+ // Count DoFs in each block
+ dofs_per_block.clear();
+ dofs_per_block.resize(n_blocks);
+ DoFTools::count_dofs_per_block(dof_handler, dofs_per_block,
+ block_component);
+
+ all_locally_owned_dofs = DoFTools::locally_owned_dofs_per_subdomain (dof_handler);
+ std::vector<IndexSet> all_locally_relevant_dofs
+ = DoFTools::locally_relevant_dofs_per_subdomain (dof_handler);
+
+ locally_owned_dofs.clear();
+ locally_owned_partitioning.clear();
+ Assert(all_locally_owned_dofs.size() > this_mpi_process, ExcInternalError());
+ locally_owned_dofs = all_locally_owned_dofs[this_mpi_process];
+
+ locally_relevant_dofs.clear();
+ locally_relevant_partitioning.clear();
+ Assert(all_locally_relevant_dofs.size() > this_mpi_process, ExcInternalError());
+ locally_relevant_dofs = all_locally_relevant_dofs[this_mpi_process];
+
+ locally_owned_partitioning.reserve(n_blocks);
+ locally_relevant_partitioning.reserve(n_blocks);
+ for (unsigned int b=0; b<n_blocks; ++b)
+ {
+ const types::global_dof_index idx_begin
+ = std::accumulate(dofs_per_block.begin(),
+ std::next(dofs_per_block.begin(),b), 0);
+ const types::global_dof_index idx_end
+ = std::accumulate(dofs_per_block.begin(),
+ std::next(dofs_per_block.begin(),b+1), 0);
+ locally_owned_partitioning.push_back(locally_owned_dofs.get_view(idx_begin, idx_end));
+ locally_relevant_partitioning.push_back(locally_relevant_dofs.get_view(idx_begin, idx_end));
+ }
+
+ pcout
+ << " Number of active cells: " << triangulation.n_active_cells()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout
+ << (p==0 ? ' ' : '+')
+ << (GridTools::count_cells_with_subdomain_association (triangulation,p));
+ pcout << ")" << std::endl;
+
+ pcout
+ << " Number of degrees of freedom: " << dof_handler.n_dofs()
+ << " (by partition:";
+ for (unsigned int p=0; p<n_mpi_processes; ++p)
+ pcout
+ << (p==0 ? ' ' : '+')
+ << (DoFTools::count_dofs_with_subdomain_association (dof_handler,p));
+ pcout << ")" << std::endl;
+ pcout
+ << " Number of degrees of freedom per block: "
+ << "[n_u, n_p, n_J] = ["
+ << dofs_per_block[u_block] << ", "
+ << dofs_per_block[p_block] << ", "
+ << dofs_per_block[J_block] << "]"
+ << std::endl;
+
+
+ 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;
+
+ TrilinosWrappers::BlockSparsityPattern bsp (locally_owned_partitioning,
+ locally_owned_partitioning,
+ locally_relevant_partitioning,
+ mpi_communicator);
+ DoFTools::make_sparsity_pattern (dof_handler, bsp,
+ constraints, false,
+ this_mpi_process);
+ bsp.compress();
+ tangent_matrix.reinit (bsp);
+
+ // We then set up storage vectors
+ system_rhs.reinit(locally_owned_partitioning,
+ mpi_communicator);
+ solution_n.reinit(locally_owned_partitioning,
+ mpi_communicator);
+ solution_delta.reinit(locally_owned_partitioning,
+ mpi_communicator);
+ 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_block)
+ element_indices_u.push_back(k);
+ else if (k_group == p_block)
+ element_indices_p.push_back(k);
+ else if (k_group == J_block)
+ element_indices_J.push_back(k);
+ else
+ {
+ Assert(k_group <= J_block, ExcInternalError());
+ }
+ }
+ }
+ template <int dim>
+ void Solid<dim>::setup_qph()
+ {
+ pcout << "Setting up quadrature point data..." << std::endl;
+ quadrature_point_history.initialize(triangulation.begin_active(),
+ triangulation.end(),
+ n_q_points);
+ FilteredIterator<typename DoFHandler<dim>::active_cell_iterator>
+ cell (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.begin_active()),
+ endc (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.end());
+ for (; cell!=endc; ++cell)
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+ 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, time);
+ }
+ }
+ template <int dim>
+ void
+ Solid<dim>::solve_nonlinear_timestep(LA::MPI::BlockVector &solution_delta)
+ {
+ pcout << std::endl
+ << "Timestep " << time.get_timestep() << " @ "
+ << time.current() << "s of "
+ << time.end() << "s" << std::endl;
+ LA::MPI::BlockVector newton_update(locally_owned_partitioning,
+ mpi_communicator);
+ 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)
+ {
+ pcout << " " << 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) )
+ {
+ pcout << " 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;
+ newton_update = 0.0;
+ pcout << " | " << 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>
+ void Solid<dim>::print_conv_header()
+ {
+ pcout << std::string(132,'_') << std::endl;
+ pcout << " SOLVER STEP "
+ << " | LIN_IT LIN_RES RES_NORM "
+ << " RES_U RES_P RES_J NU_NORM "
+ << " NU_U NU_P NU_J " << std::endl;
+ pcout << std::string(132,'_') << std::endl;
+ }
+ template <int dim>
+ void Solid<dim>::print_conv_footer(const LA::MPI::BlockVector &solution_delta)
+ {
+ pcout << std::string(132,'_') << std::endl;
+ const std::pair<double,std::pair<double,double> > error_dil = get_error_dilation(get_solution_total(solution_delta));
+ pcout << "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.second << " / " << error_dil.second.first
+ << " = " << (error_dil.second.second/error_dil.second.first) << std::endl;
+ }
+ template <int dim>
+ std::pair<double,std::pair<double,double> >
+ Solid<dim>::get_error_dilation(const LA::MPI::BlockVector &solution_total) const
+ {
+ double vol_reference = 0.0;
+ 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());
+ FilteredIterator<typename DoFHandler<dim>::active_cell_iterator>
+ cell (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.begin_active()),
+ endc (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.end());
+ for (; cell != endc; ++cell)
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+ 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(Physics::Elasticity::Kinematics::F(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_reference += JxW;
+ vol_current += det_F_qp * JxW;
+ }
+ }
+ Assert(vol_current > 0.0, ExcInternalError());
+ // Sum across all porcessors
+ dil_L2_error = Utilities::MPI::sum(dil_L2_error,mpi_communicator);
+ vol_reference = Utilities::MPI::sum(vol_reference,mpi_communicator);
+ vol_current = Utilities::MPI::sum(vol_current,mpi_communicator);
+
+ return std::make_pair(std::sqrt(dil_L2_error),
+ std::make_pair(vol_reference,vol_current));
+ }
+ template <int dim>
+ void Solid<dim>::get_error_residual(Errors &error_residual)
+ {
+ // Construct a residual vector that has the values for all of its
+ // constrained DoFs set to zero.
+ LA::MPI::BlockVector error_res (system_rhs);
+ constraints.set_zero(error_res);
+ error_residual.norm = error_res.l2_norm();
+ error_residual.u = error_res.block(u_block).l2_norm();
+ error_residual.p = error_res.block(p_block).l2_norm();
+ error_residual.J = error_res.block(J_block).l2_norm();
+ }
+ template <int dim>
+ void Solid<dim>::get_error_update(const LA::MPI::BlockVector &newton_update,
+ Errors &error_update)
+ {
+ // Construct a update vector that has the values for all of its
+ // constrained DoFs set to zero.
+ LA::MPI::BlockVector error_ud (newton_update);
+ constraints.set_zero(error_ud);
+ error_update.norm = error_ud.l2_norm();
+ error_update.u = error_ud.block(u_block).l2_norm();
+ error_update.p = error_ud.block(p_block).l2_norm();
+ error_update.J = error_ud.block(J_block).l2_norm();
+ }
+ template <int dim>
+ LA::MPI::BlockVector
+ Solid<dim>::get_solution_total(const LA::MPI::BlockVector &solution_delta) const
+ {
+ // Cell interpolation -> Ghosted vector
+ LA::MPI::BlockVector solution_total (locally_owned_partitioning,
+ locally_relevant_partitioning,
+ mpi_communicator,
+ /*vector_writable = */ false);
+ LA::MPI::BlockVector tmp (solution_total);
+ solution_total = solution_n;
+ tmp = solution_delta;
+ solution_total += tmp;
+ return solution_total;
+ }
+ template <int dim>
+ void Solid<dim>::assemble_system(const LA::MPI::BlockVector &solution_delta)
+ {
+ timer.enter_subsection("Assemble system");
+ pcout << " ASM_SYS " << std::flush;
+ tangent_matrix = 0.0;
+ system_rhs = 0.0;
+ const LA::MPI::BlockVector solution_total(get_solution_total(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);
+
+ FilteredIterator<typename DoFHandler<dim>::active_cell_iterator>
+ cell (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.begin_active()),
+ endc (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.end());
+ for (; cell != endc; ++cell)
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+ assemble_system_one_cell(cell, scratch_data, per_task_data);
+ copy_local_to_global_system(per_task_data);
+ }
+ tangent_matrix.compress(VectorOperation::add);
+ system_rhs.compress(VectorOperation::add);
+ timer.leave_subsection();
+ }
+ template <int dim>
+ void Solid<dim>::copy_local_to_global_system(const PerTaskData_ASM &data)
+ {
+ constraints.distribute_local_to_global(data.cell_matrix, data.cell_rhs,
+ data.local_dof_indices,
+ tangent_matrix, system_rhs);
+ }
+ template <int dim>
+ void
+ Solid<dim>::assemble_system_one_cell(const typename DoFHandler<dim>::active_cell_iterator &cell,
+ ScratchData_ASM &scratch,
+ PerTaskData_ASM &data) const
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+
+ 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());
+
+ // Update quadrature point solution
+ 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);
+
+ // Update shape functions and their gradients (push-forward)
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const Tensor<2, dim> F = Physics::Elasticity::Kinematics::F(scratch.solution_grads_u_total[q_point]);
+ const Tensor<2, dim> F_inv = invert(F);
+
+ 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_block)
+ {
+ 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_block)
+ scratch.Nx[q_point][k] = scratch.fe_values_ref[p_fe].value(k,
+ q_point);
+ else if (k_group == J_block)
+ scratch.Nx[q_point][k] = scratch.fe_values_ref[J_fe].value(k,
+ q_point);
+ else
+ Assert(k_group <= J_block, ExcInternalError());
+ }
+ }
+ for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+ {
+ const SymmetricTensor<2, dim> &I = Physics::Elasticity::StandardTensors<dim>::I;
+ const Tensor<2, dim> F = Physics::Elasticity::Kinematics::F(scratch.solution_grads_u_total[q_point]);
+ const double det_F = determinant(F);
+ const double &p_tilde = scratch.solution_values_p_total[q_point];
+ const double &J_tilde = scratch.solution_values_J_total[q_point];
+ Assert(det_F > 0, ExcInternalError());
+
+ {
+ PointHistory<dim> *lqph_q_point_nc = const_cast<PointHistory<dim>*>(lqph[q_point].get());
+ lqph_q_point_nc->update_internal_equilibrium(F,p_tilde,J_tilde);
+ }
+
+ const SymmetricTensor<2, dim> tau = lqph[q_point]->get_tau(F,p_tilde);
+ const Tensor<2, dim> tau_ns (tau);
+ const SymmetricTensor<4, dim> Jc = lqph[q_point]->get_Jc(F,p_tilde);
+ const double dPsi_vol_dJ = lqph[q_point]->get_dPsi_vol_dJ(J_tilde);
+ const double d2Psi_vol_dJ2 = lqph[q_point]->get_d2Psi_vol_dJ2(J_tilde);
+
+ const std::vector<double> &Nx = scratch.Nx[q_point];
+ const std::vector<Tensor<2, dim> > &grad_Nx = scratch.grad_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 component_i = fe.system_to_component_index(i).first;
+ const unsigned int i_group = fe.system_to_base_index(i).first.first;
+ if (i_group == u_block)
+ data.cell_rhs(i) -= (symm_grad_Nx[i] * tau) * JxW;
+ else if (i_group == p_block)
+ data.cell_rhs(i) -= Nx[i] * (det_F - J_tilde) * JxW;
+ else if (i_group == J_block)
+ data.cell_rhs(i) -= Nx[i] * (dPsi_vol_dJ - p_tilde) * JxW;
+ else
+ Assert(i_group <= J_block, ExcInternalError());
+
+ 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 == u_block) && (j_group == u_block))
+ {
+ 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_ns
+ * grad_Nx[j][component_j] * JxW;
+ }
+ else if ((i_group == u_block) && (j_group == p_block))
+ {
+ data.cell_matrix(i, j) += (symm_grad_Nx[i] * I)
+ * Nx[j] * det_F
+ * JxW;
+ }
+ else if ((i_group == p_block) && (j_group == u_block))
+ {
+ data.cell_matrix(i, j) += Nx[i] * det_F
+ * (symm_grad_Nx[j] * I)
+ * JxW;
+ }
+ else if ((i_group == p_block) && (j_group == J_block))
+ data.cell_matrix(i, j) -= Nx[i] * Nx[j] * JxW;
+ else if ((i_group == J_block) && (j_group == p_block))
+ data.cell_matrix(i, j) -= Nx[i] * Nx[j] * JxW;
+ else if ((i_group == J_block) && (j_group == J_block))
+ data.cell_matrix(i, j) += Nx[i] * d2Psi_vol_dJ2 * Nx[j] * JxW;
+ else
+ Assert((i_group <= J_block) && (j_group <= J_block),
+ 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);
+
+ if (parameters.driver == "Neumann")
+ for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell;
+ ++face)
+ if (cell->face(face)->at_boundary() == true
+ && cell->face(face)->boundary_id() == parameters.boundary_id_plus_Y)
+ {
+ 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 pressure_nom = parameters.pressure
+ / (parameters.scale * parameters.scale);
+ const double time_ramp = (time.current() < parameters.load_time ?
+ time.current() / parameters.load_time : 1.0);
+ const double pressure = -pressure_nom * 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_block)
+ {
+ 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)
+ {
+ pcout << " 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 = parameters.boundary_id_minus_X;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(x_displacement));
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(x_displacement));
+ }
+ {
+ const int boundary_id = parameters.boundary_id_minus_Y;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ 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 = parameters.boundary_id_minus_Z;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ }
+ {
+ const int boundary_id = parameters.boundary_id_plus_Z;
+ if (apply_dirichlet_bc == true)
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(z_displacement));
+ }
+ }
+ if (parameters.driver == "Dirichlet")
+ {
+ const int boundary_id = parameters.boundary_id_plus_Y;
+ if (apply_dirichlet_bc == true)
+ {
+
+ if (time.current() < parameters.load_time+0.01*time.get_delta_t())
+ {
+ const double delta_length = parameters.length*(parameters.stretch - 1.0)*parameters.scale;
+ const unsigned int n_stretch_steps = parameters.load_time/time.get_delta_t();
+ const double delta_u_y = delta_length/2.0/n_stretch_steps;
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ConstantFunction<dim>(delta_u_y,n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ }
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ }
+ else
+ VectorTools::interpolate_boundary_values(dof_handler,
+ boundary_id,
+ ZeroFunction<dim>(n_components),
+ constraints,
+ fe.component_mask(y_displacement));
+ }
+ constraints.close();
+ }
+ template <int dim>
+ std::pair<unsigned int, double>
+ Solid<dim>::solve_linear_system(LA::MPI::BlockVector &newton_update)
+ {
+ unsigned int lin_it = 0;
+ double lin_res = 0.0;
+
+ timer.enter_subsection("Linear solver");
+ pcout << " SLV " << std::flush;
+
+ const LA::MPI::Vector &f_u = system_rhs.block(u_block);
+ const LA::MPI::Vector &f_p = system_rhs.block(p_block);
+ const LA::MPI::Vector &f_J = system_rhs.block(J_block);
+ LA::MPI::Vector &d_u = newton_update.block(u_block);
+ LA::MPI::Vector &d_p = newton_update.block(p_block);
+ LA::MPI::Vector &d_J = newton_update.block(J_block);
+ const auto K_uu = linear_operator<LA::MPI::Vector>(tangent_matrix.block(u_block, u_block));
+ const auto K_up = linear_operator<LA::MPI::Vector>(tangent_matrix.block(u_block, p_block));
+ const auto K_pu = linear_operator<LA::MPI::Vector>(tangent_matrix.block(p_block, u_block));
+ const auto K_Jp = linear_operator<LA::MPI::Vector>(tangent_matrix.block(J_block, p_block));
+ const auto K_JJ = linear_operator<LA::MPI::Vector>(tangent_matrix.block(J_block, J_block));
+
+ LA::PreconditionJacobi preconditioner_K_Jp_inv;
+ preconditioner_K_Jp_inv.initialize(
+ tangent_matrix.block(J_block, p_block),
+ LA::PreconditionJacobi::AdditionalData());
+ ReductionControl solver_control_K_Jp_inv (
+ tangent_matrix.block(J_block, p_block).m() * parameters.max_iterations_lin,
+ 1.0e-30, 1e-6);
+ dealii::SolverCG<LA::MPI::Vector> solver_K_Jp_inv (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;
+
+ LA::PreconditionAMG preconditioner_K_con_inv;
+ preconditioner_K_con_inv.initialize(
+ tangent_matrix.block(u_block, u_block),
+ LA::PreconditionAMG::AdditionalData(
+ true /*elliptic*/,
+ (parameters.poly_degree > 1 /*higher_order_elements*/)) );
+ ReductionControl solver_control_K_con_inv (
+ tangent_matrix.block(u_block, u_block).m() * parameters.max_iterations_lin,
+ 1.0e-30, parameters.tol_lin);
+ dealii::SolverSelector<LA::MPI::Vector> solver_K_con_inv;
+ solver_K_con_inv.select(parameters.type_lin);
+ 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));
+ lin_it = solver_control_K_con_inv.last_step();
+ lin_res = solver_control_K_con_inv.last_value();
+ timer.leave_subsection();
+
+ timer.enter_subsection("Linear solver postprocessing");
+ d_J = K_pJ_inv*(f_p - K_pu*d_u);
+ d_p = K_Jp_inv*(f_J - K_JJ*d_J);
+ timer.leave_subsection();
+
+ constraints.distribute(newton_update);
+ return std::make_pair(lin_it, lin_res);
+ }
+ template <int dim>
+ void
+ Solid<dim>::update_end_timestep ()
+ {
+ FilteredIterator<typename DoFHandler<dim>::active_cell_iterator>
+ cell (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.begin_active()),
+ endc (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.end());
+ for (; cell != endc; ++cell)
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+ 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]->update_end_timestep();
+ }
+ }
+
+ template<int dim, class DH=DoFHandler<dim> >
+ class FilteredDataOut : public DataOut<dim, DH>
+ {
+ public:
+ FilteredDataOut (const unsigned int subdomain_id)
+ :
+ subdomain_id (subdomain_id)
+ {}
+
+ virtual ~FilteredDataOut() {}
+
+ virtual typename DataOut<dim, DH>::cell_iterator
+ first_cell ()
+ {
+ typename DataOut<dim, DH>::active_cell_iterator
+ cell = this->dofs->begin_active();
+ while ((cell != this->dofs->end()) &&
+ (cell->subdomain_id() != subdomain_id))
+ ++cell;
+ return cell;
+ }
+
+ virtual typename DataOut<dim, DH>::cell_iterator
+ next_cell (const typename DataOut<dim, DH>::cell_iterator &old_cell)
+ {
+ if (old_cell != this->dofs->end())
+ {
+ const IteratorFilters::SubdomainEqualTo predicate(subdomain_id);
+ return
+ ++(FilteredIterator
+ <typename DataOut<dim, DH>::active_cell_iterator>
+ (predicate,old_cell));
+ }
+ else
+ return old_cell;
+ }
+
+ private:
+ const unsigned int subdomain_id;
+ };
+
+ template <int dim>
+ void Solid<dim>::output_results(const unsigned int timestep,
+ const double current_time) const
+ {
+ // Output -> Ghosted vector
+ LA::MPI::BlockVector solution_total (locally_owned_partitioning,
+ locally_relevant_partitioning,
+ mpi_communicator,
+ /*vector_writable = */ false);
+ LA::MPI::BlockVector residual (locally_owned_partitioning,
+ locally_relevant_partitioning,
+ mpi_communicator,
+ /*vector_writable = */ false);
+ solution_total = solution_n;
+ residual = system_rhs;
+ residual *= -1.0;
+
+ // --- Additional data ---
+ Vector<double> material_id;
+ Vector<double> polynomial_order;
+ material_id.reinit(triangulation.n_active_cells());
+ polynomial_order.reinit(triangulation.n_active_cells());
+ std::vector<types::subdomain_id> partition_int (triangulation.n_active_cells());
+
+ FilteredDataOut<dim> data_out(this_mpi_process);
+ 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);
+
+ GridTools::get_subdomain_association (triangulation, partition_int);
+
+ // Can't use filtered iterators here because the cell
+ // count "c" is incorrect for the parallel case
+ unsigned int c = 0;
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ for (; cell!=endc; ++cell, ++c)
+ {
+ if (cell->subdomain_id() != this_mpi_process) continue;
+
+ material_id(c) = static_cast<int>(cell->material_id());
+ }
+
+ std::vector<std::string> solution_name(n_components, "solution_");
+ std::vector<std::string> residual_name(n_components, "residual_");
+ for (unsigned int c=0; c<n_components; ++c)
+ {
+ if (block_component[c] == u_block)
+ {
+ solution_name[c] += "u";
+ residual_name[c] += "u";
+ }
+ else if (block_component[c] == p_block)
+ {
+ solution_name[c] += "p";
+ residual_name[c] += "p";
+ }
+ else if (block_component[c] == J_block)
+ {
+ solution_name[c] += "J";
+ residual_name[c] += "J";
+ }
+ else
+ {
+ Assert(c <= J_block, ExcInternalError());
+ }
+ }
+
+ data_out.attach_dof_handler(dof_handler);
+ data_out.add_data_vector(solution_total,
+ solution_name,
+ DataOut<dim>::type_dof_data,
+ data_component_interpretation);
+ data_out.add_data_vector(residual,
+ residual_name,
+ DataOut<dim>::type_dof_data,
+ data_component_interpretation);
+ const Vector<double> partitioning(partition_int.begin(),
+ partition_int.end());
+ data_out.add_data_vector (material_id, "material_id");
+ data_out.add_data_vector (partitioning, "partitioning");
+ data_out.build_patches(degree);
+
+ struct Filename
+ {
+ static std::string get_filename_vtu (unsigned int process,
+ unsigned int timestep,
+ const unsigned int n_digits = 4)
+ {
+ std::ostringstream filename_vtu;
+ filename_vtu
+ << "solution-"
+ << (std::to_string(dim) + "d")
+ << "."
+ << Utilities::int_to_string (process, n_digits)
+ << "."
+ << Utilities::int_to_string(timestep, n_digits)
+ << ".vtu";
+ return filename_vtu.str();
+ }
+
+ static std::string get_filename_pvtu (unsigned int timestep,
+ const unsigned int n_digits = 4)
+ {
+ std::ostringstream filename_vtu;
+ filename_vtu
+ << "solution-"
+ << (std::to_string(dim) + "d")
+ << "."
+ << Utilities::int_to_string(timestep, n_digits)
+ << ".pvtu";
+ return filename_vtu.str();
+ }
+
+ static std::string get_filename_pvd (void)
+ {
+ std::ostringstream filename_vtu;
+ filename_vtu
+ << "solution-"
+ << (std::to_string(dim) + "d")
+ << ".pvd";
+ return filename_vtu.str();
+ }
+ };
+
+ // Write out main data file
+ const std::string filename_vtu = Filename::get_filename_vtu(this_mpi_process, timestep);
+ std::ofstream output(filename_vtu.c_str());
+ data_out.write_vtu(output);
+
+ // Collection of files written in parallel
+ // This next set of steps should only be performed
+ // by master process
+ if (this_mpi_process == 0)
+ {
+ // List of all files written out at this timestep by all processors
+ std::vector<std::string> parallel_filenames_vtu;
+ for (unsigned int p=0; p < n_mpi_processes; ++p)
+ {
+ parallel_filenames_vtu.push_back(Filename::get_filename_vtu(p, timestep));
+ }
+
+ const std::string filename_pvtu (Filename::get_filename_pvtu(timestep));
+ std::ofstream pvtu_master(filename_pvtu.c_str());
+ data_out.write_pvtu_record(pvtu_master,
+ parallel_filenames_vtu);
+
+ // Time dependent data master file
+ static std::vector<std::pair<double,std::string> > time_and_name_history;
+ time_and_name_history.push_back (std::make_pair (current_time,
+ filename_pvtu));
+ const std::string filename_pvd (Filename::get_filename_pvd());
+ std::ofstream pvd_output (filename_pvd.c_str());
+ DataOutBase::write_pvd_record (pvd_output, time_and_name_history);
+ }
+ }
+ template <int dim>
+ void Solid<dim>::compute_vertex_positions(std::vector<double> &real_time,
+ std::vector<std::vector<Point<dim> > > &tracked_vertices,
+ const LA::MPI::BlockVector &solution_total) const
+ {
+ real_time.push_back(time.current());
+
+ std::vector<bool> vertex_found (tracked_vertices.size(), false);
+ std::vector<Tensor<1,dim> > vertex_update (tracked_vertices.size());
+
+ FilteredIterator<typename DoFHandler<dim>::active_cell_iterator>
+ cell (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.begin_active()),
+ endc (IteratorFilters::SubdomainEqualTo(this_mpi_process),
+ dof_handler.end());
+ for (; cell != endc; ++cell)
+ {
+ Assert(cell->subdomain_id()==this_mpi_process, ExcInternalError());
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ {
+ for (unsigned int p=0; p<tracked_vertices.size(); ++p)
+ {
+ if (vertex_found[p] == true) continue;
+
+ const Point<dim> pt_ref = tracked_vertices[p][0];
+ if (cell->vertex(v).distance(pt_ref) < 1e-6*parameters.scale)
+ {
+ for (unsigned int d=0; d<dim; ++d)
+ vertex_update[p][d] = solution_total(cell->vertex_dof_index(v,u_block+d));
+
+ vertex_found[p] = true;
+ }
+ }
+ }
+ }
+
+ for (unsigned int p=0; p<tracked_vertices.size(); ++p)
+ {
+ const int found_on_n_processes = Utilities::MPI::sum(int(vertex_found[p]), mpi_communicator);
+ Assert(found_on_n_processes>0, ExcMessage("Vertex not found on any processor"));
+ Tensor<1,dim> update;
+ for (unsigned int d=0; d<dim; ++d)
+ update[d] = Utilities::MPI::sum(vertex_update[p][d], mpi_communicator);
+ update /= found_on_n_processes;
+ tracked_vertices[p].push_back(tracked_vertices[p][0] + update);
+ }
+
+ }
+}
+int main (int argc, char *argv[])
+{
+ using namespace dealii;
+ using namespace ViscoElasStripHole;
+
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv);
+
+ try
+ {
+ const unsigned int dim = 2; // Works in both 2d and 3d
+ Solid<dim> solid("parameters.prm");
+ solid.run();
+ }
+ catch (std::exception &exc)
+ {
+ if (Utilities::MPI::this_mpi_process(MPI_COMM_WORLD) == 0)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl << exc.what()
+ << std::endl << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ }
+ catch (...)
+ {
+ if (Utilities::MPI::this_mpi_process(MPI_COMM_WORLD) == 0)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl << "Aborting!"
+ << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ }
+ return 0;
+}
projects / code-gallery.git / commitdiff
