]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Add initial version of test for linesearch in FE problem (step-44)
authorJean-Paul Pelteret <jppelteret@gmail.com>
Fri, 14 Sep 2018 15:31:39 +0000 (17:31 +0200)
committerDenis Davydov <davydden@gmail.com>
Mon, 17 Sep 2018 15:35:33 +0000 (17:35 +0200)
tests/optimization/prm/parameters-step-44-with_linesearch.prm [new file with mode: 0644]
tests/optimization/prm/parameters-step-44-with_linesearch_ptrb.prm [new file with mode: 0644]
tests/optimization/prm/parameters-step-44-without_linesearch.prm [new file with mode: 0644]
tests/optimization/step-44-with_line_search.cc [new file with mode: 0644]
tests/optimization/step-44-with_line_search.output [new file with mode: 0644]
tests/optimization/step-44-with_line_search_ptrb.cc [new file with mode: 0644]
tests/optimization/step-44-with_line_search_ptrb.output [new file with mode: 0644]
tests/optimization/step-44-without_line_search.cc [new file with mode: 0644]
tests/optimization/step-44-without_line_search.output [new file with mode: 0644]
tests/optimization/step-44.h [new file with mode: 0644]

diff --git a/tests/optimization/prm/parameters-step-44-with_linesearch.prm b/tests/optimization/prm/parameters-step-44-with_linesearch.prm
new file mode 100644 (file)
index 0000000..79a29e9
--- /dev/null
@@ -0,0 +1,81 @@
+# Listing of Parameters
+# ---------------------
+subsection Finite element system
+  # Displacement system polynomial order
+  set Polynomial degree = 1
+
+  # Gauss quadrature order
+  set Quadrature order  = 2
+end
+
+
+subsection Geometry
+  # Global refinement level
+  set Global refinement   = 2
+
+  # Global grid scaling factor
+  set Grid scale          = 1e-3
+
+  # Ratio of applied pressure to reference pressure
+  set Pressure ratio p/p0 = 100
+end
+
+
+subsection Linear solver
+  # Linear solver iterations (multiples of the system matrix size)
+  # In 2-d, this value is best set at 2. In 3-d, a value of 1 work fine.
+  set Max iteration multiplier = 2
+
+  # Linear solver residual (scaled by residual norm)
+  set Residual                 = 1e-6
+
+  # Use static condensation and solve a 1-block system, or solve
+  # the full 3-block system using Linear Operators and the Schur
+  # complement
+  set Use static condensation = true
+
+  # Preconditioner type
+  set Preconditioner type  = ssor
+
+  # Preconditioner relaxation value
+  set Preconditioner relaxation  = 0.65
+
+  # Type of solver used to solve the linear system
+  set Solver type              = CG
+end
+
+
+subsection Material properties
+  # Poisson's ratio
+  set Poisson's ratio = 0.4999
+
+  # Shear modulus
+  set Shear modulus   = 80.194e6
+end
+
+
+subsection Nonlinear solver
+  # Number of Newton-Raphson iterations allowed
+  set Max iterations Newton-Raphson        = 10
+
+  # Displacement error tolerance
+  set Tolerance displacement               = 1.0e-6
+
+  # Force residual tolerance
+  set Tolerance force                      = 1.0e-9
+  
+  # Use line-search minimization algorithm
+  set Use line search                      = true
+  
+  # Use an approximation for the gradient during line search
+  set Use line search approximate gradient = false
+end
+
+
+subsection Time
+  # End time
+  set End time       = 1
+
+  # Time step size
+  set Time step size = 0.5
+end
diff --git a/tests/optimization/prm/parameters-step-44-with_linesearch_ptrb.prm b/tests/optimization/prm/parameters-step-44-with_linesearch_ptrb.prm
new file mode 100644 (file)
index 0000000..042f1a8
--- /dev/null
@@ -0,0 +1,81 @@
+# Listing of Parameters
+# ---------------------
+subsection Finite element system
+  # Displacement system polynomial order
+  set Polynomial degree = 1
+
+  # Gauss quadrature order
+  set Quadrature order  = 2
+end
+
+
+subsection Geometry
+  # Global refinement level
+  set Global refinement   = 2
+
+  # Global grid scaling factor
+  set Grid scale          = 1e-3
+
+  # Ratio of applied pressure to reference pressure
+  set Pressure ratio p/p0 = 100
+end
+
+
+subsection Linear solver
+  # Linear solver iterations (multiples of the system matrix size)
+  # In 2-d, this value is best set at 2. In 3-d, a value of 1 work fine.
+  set Max iteration multiplier = 2
+
+  # Linear solver residual (scaled by residual norm)
+  set Residual                 = 1e-6
+
+  # Use static condensation and solve a 1-block system, or solve
+  # the full 3-block system using Linear Operators and the Schur
+  # complement
+  set Use static condensation = true
+
+  # Preconditioner type
+  set Preconditioner type  = ssor
+
+  # Preconditioner relaxation value
+  set Preconditioner relaxation  = 0.65
+
+  # Type of solver used to solve the linear system
+  set Solver type              = CG
+end
+
+
+subsection Material properties
+  # Poisson's ratio
+  set Poisson's ratio = 0.4999
+
+  # Shear modulus
+  set Shear modulus   = 80.194e6
+end
+
+
+subsection Nonlinear solver
+  # Number of Newton-Raphson iterations allowed
+  set Max iterations Newton-Raphson        = 10
+
+  # Displacement error tolerance
+  set Tolerance displacement               = 1.0e-6
+
+  # Force residual tolerance
+  set Tolerance force                      = 1.0e-9
+  
+  # Use line-search minimization algorithm
+  set Use line search                      = true
+  
+  # Use an approximation for the gradient during line search
+  set Use line search approximate gradient = true
+end
+
+
+subsection Time
+  # End time
+  set End time       = 1
+
+  # Time step size
+  set Time step size = 0.5
+end
diff --git a/tests/optimization/prm/parameters-step-44-without_linesearch.prm b/tests/optimization/prm/parameters-step-44-without_linesearch.prm
new file mode 100644 (file)
index 0000000..72f908c
--- /dev/null
@@ -0,0 +1,81 @@
+# Listing of Parameters
+# ---------------------
+subsection Finite element system
+  # Displacement system polynomial order
+  set Polynomial degree = 1
+
+  # Gauss quadrature order
+  set Quadrature order  = 2
+end
+
+
+subsection Geometry
+  # Global refinement level
+  set Global refinement   = 2
+
+  # Global grid scaling factor
+  set Grid scale          = 1e-3
+
+  # Ratio of applied pressure to reference pressure
+  set Pressure ratio p/p0 = 100
+end
+
+
+subsection Linear solver
+  # Linear solver iterations (multiples of the system matrix size)
+  # In 2-d, this value is best set at 2. In 3-d, a value of 1 work fine.
+  set Max iteration multiplier = 2
+
+  # Linear solver residual (scaled by residual norm)
+  set Residual                 = 1e-6
+
+  # Use static condensation and solve a 1-block system, or solve
+  # the full 3-block system using Linear Operators and the Schur
+  # complement
+  set Use static condensation = true
+
+  # Preconditioner type
+  set Preconditioner type  = ssor
+
+  # Preconditioner relaxation value
+  set Preconditioner relaxation  = 0.65
+
+  # Type of solver used to solve the linear system
+  set Solver type              = CG
+end
+
+
+subsection Material properties
+  # Poisson's ratio
+  set Poisson's ratio = 0.4999
+
+  # Shear modulus
+  set Shear modulus   = 80.194e6
+end
+
+
+subsection Nonlinear solver
+  # Number of Newton-Raphson iterations allowed
+  set Max iterations Newton-Raphson = 10
+
+  # Displacement error tolerance
+  set Tolerance displacement        = 1.0e-6
+
+  # Force residual tolerance
+  set Tolerance force               = 1.0e-9
+  
+  # Use line-search minimization algorithm
+  set Use line search               = false
+  
+  # Use an approximation for the gradient during line search
+  set Use line search approximate gradient = false
+end
+
+
+subsection Time
+  # End time
+  set End time       = 1
+
+  # Time step size
+  set Time step size = 0.5
+end
diff --git a/tests/optimization/step-44-with_line_search.cc b/tests/optimization/step-44-with_line_search.cc
new file mode 100644 (file)
index 0000000..f164b72
--- /dev/null
@@ -0,0 +1,67 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+// A reduced version of step-44 (based off of git rev 3f7e617) that utilizes
+// line-search to select the optimal step-size at each Newton iteration.
+// The chosen parameters dictate that the exact value of the gradient
+// for the function to be minimized is computed.
+
+#include "../tests.h"
+#include "step-44.h"
+
+int
+main(int argc, char **argv)
+{
+  initlog(true);
+
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(
+    argc, argv, testing_max_num_threads());
+
+  using namespace dealii;
+  using namespace Step44;
+  try
+    {
+      const unsigned int dim = 3;
+      Solid<dim>         solid(SOURCE_DIR
+                       "/prm/parameters-step-44-with_linesearch.prm");
+      solid.run();
+    }
+  catch (std::exception &exc)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Exception on processing: " << std::endl
+                << exc.what() << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  catch (...)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Unknown exception!" << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  return 0;
+}
diff --git a/tests/optimization/step-44-with_line_search.output b/tests/optimization/step-44-with_line_search.output
new file mode 100644 (file)
index 0000000..4c17c7f
--- /dev/null
@@ -0,0 +1,3 @@
+
+DEAL::Timestep 1: 0.00000 -0.000509022 0.00000
+DEAL::Timestep 2: 0.00000 -0.000789713 0.00000
diff --git a/tests/optimization/step-44-with_line_search_ptrb.cc b/tests/optimization/step-44-with_line_search_ptrb.cc
new file mode 100644 (file)
index 0000000..884c7e4
--- /dev/null
@@ -0,0 +1,68 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+// A reduced version of step-44 (based off of git rev 3f7e617) that utilizes
+// line-search to select the optimal step-size at each Newton iteration.
+// This is the same as optimization/step-44-with_line_search.cc, except that
+// a perturbation method is used to compute the gradient of the function to
+// be minimized.
+
+#include "../tests.h"
+#include "step-44.h"
+
+int
+main(int argc, char **argv)
+{
+  initlog(true);
+
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(
+    argc, argv, testing_max_num_threads());
+
+  using namespace dealii;
+  using namespace Step44;
+  try
+    {
+      const unsigned int dim = 3;
+      Solid<dim>         solid(SOURCE_DIR
+                       "/prm/parameters-step-44-with_linesearch_ptrb.prm");
+      solid.run();
+    }
+  catch (std::exception &exc)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Exception on processing: " << std::endl
+                << exc.what() << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  catch (...)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Unknown exception!" << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  return 0;
+}
diff --git a/tests/optimization/step-44-with_line_search_ptrb.output b/tests/optimization/step-44-with_line_search_ptrb.output
new file mode 100644 (file)
index 0000000..4c17c7f
--- /dev/null
@@ -0,0 +1,3 @@
+
+DEAL::Timestep 1: 0.00000 -0.000509022 0.00000
+DEAL::Timestep 2: 0.00000 -0.000789713 0.00000
diff --git a/tests/optimization/step-44-without_line_search.cc b/tests/optimization/step-44-without_line_search.cc
new file mode 100644 (file)
index 0000000..f5437b7
--- /dev/null
@@ -0,0 +1,66 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+// A reduced version of step-44 (based off of git rev 3f7e617) that does not
+// employ line-search. This serves as a compartive result for
+// optimization/step-44-with_line_search.cc .
+
+#include "../tests.h"
+#include "step-44.h"
+
+int
+main(int argc, char **argv)
+{
+  initlog();
+
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(
+    argc, argv, testing_max_num_threads());
+
+  using namespace dealii;
+  using namespace Step44;
+  try
+    {
+      const unsigned int dim = 3;
+      Solid<dim>         solid(SOURCE_DIR
+                       "/prm/parameters-step-44-without_linesearch.prm");
+      solid.run();
+    }
+  catch (std::exception &exc)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Exception on processing: " << std::endl
+                << exc.what() << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  catch (...)
+    {
+      std::cerr << std::endl
+                << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Unknown exception!" << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+  return 0;
+}
diff --git a/tests/optimization/step-44-without_line_search.output b/tests/optimization/step-44-without_line_search.output
new file mode 100644 (file)
index 0000000..4c17c7f
--- /dev/null
@@ -0,0 +1,3 @@
+
+DEAL::Timestep 1: 0.00000 -0.000509022 0.00000
+DEAL::Timestep 2: 0.00000 -0.000789713 0.00000
diff --git a/tests/optimization/step-44.h b/tests/optimization/step-44.h
new file mode 100644 (file)
index 0000000..649d203
--- /dev/null
@@ -0,0 +1,2247 @@
+// ---------------------------------------------------------------------
+//
+// 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 &parameters)
+    {
+      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

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