pseudo_elastic_preconditioner.cc

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// LIC// ====================================================================
// LIC// This file forms part of oomph-lib, the object-oriented,
// LIC// multi-physics finite-element library, available
// LIC// at http://www.oomph-lib.org.
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// LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
// LIC//
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// LIC// License as published by the Free Software Foundation; either
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#include "pseudo_elastic_preconditioner.h"
 
namespace oomph
{
  //=============================================================================
  /// Functions to create instances of optimal subsidiary operators for
  /// the PseudoElasticPreconditioner
  //=============================================================================
  namespace Pseudo_Elastic_Preconditioner_Subsidiary_Operator_Helper
  {
#ifdef OOMPH_HAS_HYPRE
 
    /// AMG w/ GS smoothing for the augmented elastic subsidiary linear
    /// systems
    Preconditioner* get_elastic_preconditioner_hypre()
    {
      HyprePreconditioner* hypre_preconditioner_pt =
        new HyprePreconditioner("Hypre for diagonal blocks in pseudo-solid");
      hypre_preconditioner_pt->set_amg_iterations(2);
      hypre_preconditioner_pt->amg_using_simple_smoothing();
      if (MPI_Helpers::communicator_pt()->nproc() > 1)
      {
        // Jacobi in parallel
        hypre_preconditioner_pt->amg_simple_smoother() = 0;
      }
      else
      {
        // Gauss Seidel in serial (was 3 actually...)
        hypre_preconditioner_pt->amg_simple_smoother() = 1;
      }
      hypre_preconditioner_pt->hypre_method() = HyprePreconditioner::BoomerAMG;
      hypre_preconditioner_pt->amg_damping() = 1.0;
      hypre_preconditioner_pt->amg_coarsening() = 6;
      return hypre_preconditioner_pt;
    }
 
 
    /// AMG w/ GS smoothing for the augmented elastic subsidiary linear
    /// systems -- calls Hypre version to stay consistent with previous default
    Preconditioner* get_elastic_preconditioner()
    {
      return get_elastic_preconditioner_hypre();
    }
 
#endif
 
#ifdef OOMPH_HAS_TRILINOS
 
    /// TrilinosML smoothing for the augmented elastic
    /// subsidiary linear systems
    Preconditioner* get_elastic_preconditioner_trilinos_ml()
    {
      TrilinosMLPreconditioner* trilinos_prec_pt = new TrilinosMLPreconditioner;
      return trilinos_prec_pt;
    }
 
    /// CG with diagonal preconditioner for the lagrange multiplier
    /// subsidiary linear systems.
    Preconditioner* get_lagrange_multiplier_preconditioner()
    {
      InnerIterationPreconditioner<TrilinosAztecOOSolver,
                                   MatrixBasedDiagPreconditioner>* prec_pt =
        new InnerIterationPreconditioner<TrilinosAztecOOSolver,
                                         MatrixBasedDiagPreconditioner>;
      // Note: This makes CG a proper "inner iteration" for
      // which GMRES (may) no longer converge. We should really
      // use FGMRES or GMRESR for this. However, here the solver
      // is so good that it'll converge very quickly anyway
      // so there isn't much to be gained by limiting the number
      // of iterations...
      // prec_pt->max_iter() = 4;
      prec_pt->solver_pt()->solver_type() = TrilinosAztecOOSolver::CG;
      prec_pt->solver_pt()->disable_doc_time();
      return prec_pt;
    }
#endif
  } // namespace Pseudo_Elastic_Preconditioner_Subsidiary_Operator_Helper
 
 
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
 
 
  //=============================================================================
  // Setup method for the PseudoElasticPreconditioner.
  //=============================================================================
  void PseudoElasticPreconditioner::setup()
  {
    // clean
    this->clean_up_memory();
 
#ifdef PARANOID
    // paranoid check that meshes have been set
    if (Elastic_mesh_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "The elastic mesh must be set.";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
    if (Lagrange_multiplier_mesh_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "The Lagrange multiplier mesh must be set.";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // set the meshes
    this->set_nmesh(2);
    this->set_mesh(0, Elastic_mesh_pt);
    this->set_mesh(1, Lagrange_multiplier_mesh_pt);
 
    // Figure out number of dof types
    unsigned n_solid_dof_types = 0;
    unsigned n_dof_types = 0;
 
    if (this->is_master_block_preconditioner())
    {
      // get the number of solid dof types from the first element
      n_solid_dof_types = this->ndof_types_in_mesh(0);
 
      // get the total number of dof types
      n_dof_types = n_solid_dof_types + this->ndof_types_in_mesh(1);
    }
    else
    {
      n_dof_types = this->ndof_types();
      n_solid_dof_types = n_dof_types - (n_dof_types / 3);
    }
#ifdef PARANOID
    if (n_dof_types % 3 != 0)
    {
      std::ostringstream error_message;
      error_message << "This preconditioner requires DIM*3 types of DOF";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // determine the dimension
    Dim = n_dof_types / 3;
 
#ifdef PARANOID
    // Recast Jacobian matrix to CRDoubleMatrix
    CRDoubleMatrix* cr_matrix_pt = dynamic_cast<CRDoubleMatrix*>(matrix_pt());
 
    if (cr_matrix_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "FSIPreconditioner only works with"
                    << " CRDoubleMatrix matrices" << std::endl;
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // Setup the dof_list scheme for block_setup.
    // The natural DOF types order is (in 3D):
    // 0 1 2 3  4  5  6  7  8  <- natural DOF type index
    // x y z xc yc zc lx ly lz <- DOf type
    //
    // We need to group the directional displacements together:
    // 0 1  2 3  4  5  6  7  8  <- block index
    // x xc y yc xz zc lx ly lz <- DOF type
    //
    // The mapping required is:
    // 0 2 4 1 3 5 6 7 8
    //
    // In general we want:
    //
    //   dof_to_block_map[DOF type] = block type
    Vector<unsigned> dof_list_for_block_setup(n_dof_types);
    for (unsigned dim_i = 0; dim_i < Dim; dim_i++)
    {
      // bulk solid dof types
      dof_list_for_block_setup[dim_i] = 2 * dim_i;
 
      // constrained solid dof types
      dof_list_for_block_setup[dim_i + Dim] = 2 * dim_i + 1;
 
      // lagr dof types
      dof_list_for_block_setup[dim_i + 2 * Dim] = 2 * Dim + dim_i;
    }
 
    // Setup the block ordering. We have the following:
    // Block types [0, 2*Dim) are the solid blocks.
    // Block types [2*Dim, 3*Dim) are the Lagrange multiplier blocks.
    //
    // For d = 0, 1, 2,
    // Bulk solid doftypes: 2*d
    // Constrained solid doftypes: 2*d+1
    // Lgr doftyoes: 2*Dim + d
    this->block_setup(dof_list_for_block_setup);
 
    // Create dof_list for subsidiary preconditioner. This will be used later
    // in turn_into_subsidiary_block_preconditioner(...)
    Vector<unsigned> dof_list_for_subsidiary_prec(n_solid_dof_types);
 
    // The dof types are currently in the order (in 3D):
    // 0 1 2 3  4  5  6  7  8  <- DOF index
    // x y z xc yc zc lx ly lz <- DOF type
    //
    // We need to group the directional displacements together:
    // x xc y yc xz zc
    //
    // The mapping required is:
    // 0 3 1 4 2 5
    //
    // In general we want:
    //    dof_list[subsidiary DOF type] = master DOF type
    for (unsigned dim_i = 0; dim_i < Dim; dim_i++)
    {
      // bulk solid dof
      dof_list_for_subsidiary_prec[2 * dim_i] = dim_i;
 
      // constrained solid dof
      dof_list_for_subsidiary_prec[2 * dim_i + 1] = dim_i + Dim;
    }
 
    // Get the solid blocks
    DenseMatrix<CRDoubleMatrix*> solid_matrix_pt(
      n_solid_dof_types, n_solid_dof_types, 0);
 
    for (unsigned row_i = 0; row_i < n_solid_dof_types; row_i++)
    {
      for (unsigned col_i = 0; col_i < n_solid_dof_types; col_i++)
      {
        solid_matrix_pt(row_i, col_i) = new CRDoubleMatrix;
        this->get_block(row_i, col_i, *solid_matrix_pt(row_i, col_i));
      }
    }
 
    // compute the scaling (if required)
    if (Use_inf_norm_of_s_scaling)
    {
      Scaling = CRDoubleMatrixHelpers::inf_norm(solid_matrix_pt);
    }
    else
    {
      Scaling = 1.0;
    }
 
    // Add the scaled identify matrix to the constrained solid blocks.
    for (unsigned d = 0; d < Dim; d++)
    {
      // Where is the constrained block located?
      unsigned block_i = 2 * d + 1;
 
      // Data from the constrained block.
      double* s_values = solid_matrix_pt(block_i, block_i)->value();
      int* s_column_index = solid_matrix_pt(block_i, block_i)->column_index();
      int* s_row_start = solid_matrix_pt(block_i, block_i)->row_start();
      int s_nrow_local = solid_matrix_pt(block_i, block_i)->nrow_local();
      int s_first_row = solid_matrix_pt(block_i, block_i)->first_row();
 
      // Loop through the diagonal entries and add the scaling.
      for (int i = 0; i < s_nrow_local; i++)
      {
        bool found = false;
        for (int j = s_row_start[i]; j < s_row_start[i + 1] && !found; j++)
        {
          if (s_column_index[j] == i + s_first_row)
          {
            s_values[j] += Scaling;
            found = true;
          } // if
        } // for row start
 
        // Check if the diagonal entry is found.
        if (!found)
        {
          std::ostringstream error_message;
          error_message << "The diagonal entry for the constained block("
                        << block_i << "," << block_i << ")\n"
                        << "on local row " << i << " does not exist."
                        << std::endl;
          throw OomphLibError(error_message.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
        }
      } // for nrow_local
    } // for Dim
 
 
    // setup the solid subsidiary preconditioner
    // //////////////////////////////// this preconditioner uses the full S
    // matrix
    if (E_preconditioner_type == Exact_block_preconditioner)
    {
      ExactBlockPreconditioner<CRDoubleMatrix>* s_prec_pt =
        new ExactBlockPreconditioner<CRDoubleMatrix>;
 
      // Add mesh (not actually used since this only acts as a subsidiary
      // preconditioner...
      // s_prec_pt->add_mesh(Elastic_mesh_pt);
 
      Vector<Vector<unsigned>> doftype_to_doftype_map(n_solid_dof_types,
                                                      Vector<unsigned>(1, 0));
 
      for (unsigned i = 0; i < n_solid_dof_types; i++)
      {
        doftype_to_doftype_map[i][0] = i;
      }
 
      s_prec_pt->turn_into_subsidiary_block_preconditioner(
        this, dof_list_for_subsidiary_prec, doftype_to_doftype_map);
 
      if (Elastic_subsidiary_preconditioner_function_pt != 0)
      {
        s_prec_pt->set_subsidiary_preconditioner_function(
          Elastic_subsidiary_preconditioner_function_pt);
      }
 
      // Set the replacement blocks.
      for (unsigned d = 0; d < Dim; d++)
      {
        // The dof-block located in the block-ordering.
        unsigned block_i = 2 * d + 1;
 
        // The dof-block located in the dof-ordering.
        unsigned dof_block_i = Dim + d;
        this->set_replacement_dof_block(
          dof_block_i, dof_block_i, solid_matrix_pt(block_i, block_i));
      }
 
      s_prec_pt->Preconditioner::setup(matrix_pt());
      Elastic_preconditioner_pt = s_prec_pt;
    }
    // otherwise it is a block based preconditioner
    else
    {
      GeneralPurposeBlockPreconditioner<CRDoubleMatrix>* s_prec_pt = 0;
 
      // set the block preconditioning method
      switch (E_preconditioner_type)
      {
        case Block_diagonal_preconditioner:
        {
          s_prec_pt = new BlockDiagonalPreconditioner<CRDoubleMatrix>;
        }
        break;
        case Block_upper_triangular_preconditioner:
        {
          BlockTriangularPreconditioner<CRDoubleMatrix>*
            block_triangular_prec_pt =
              new BlockTriangularPreconditioner<CRDoubleMatrix>;
          block_triangular_prec_pt->upper_triangular();
 
          s_prec_pt = block_triangular_prec_pt;
        }
        break;
        case Block_lower_triangular_preconditioner:
        {
          BlockTriangularPreconditioner<CRDoubleMatrix>*
            block_triangular_prec_pt =
              new BlockTriangularPreconditioner<CRDoubleMatrix>;
          block_triangular_prec_pt->lower_triangular();
 
          s_prec_pt = block_triangular_prec_pt;
        }
        break;
        default:
        {
          std::ostringstream error_msg;
          error_msg
            << "There is no such block based preconditioner.\n"
            << "Candidates are:\n"
            << "PseudoElasticPreconditioner::Block_diagonal_preconditioner\n"
            << "PseudoElasticPreconditioner::Block_upper_triangular_"
               "preconditioner\n"
            << "PseudoElasticPreconditioner::Block_lower_triangular_"
               "preconditioner\n";
          throw OomphLibError(
            error_msg.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
        }
        break;
      }
 
 
      // Add mesh (not actually used since this only acts as a subsidiary
      // preconditioner...
      // s_prec_pt->add_mesh(Elastic_mesh_pt);
 
      // The block to block map
      Vector<Vector<unsigned>> doftype_to_doftype_map(Dim,
                                                      Vector<unsigned>(2, 0));
      Vector<unsigned> s_prec_dof_to_block_map(Dim, 0);
 
      unsigned tmp_index = 0;
      for (unsigned d = 0; d < Dim; d++)
      {
        s_prec_dof_to_block_map[d] = d;
        doftype_to_doftype_map[d][0] = tmp_index++;
        doftype_to_doftype_map[d][1] = tmp_index++;
      }
 
      s_prec_pt->turn_into_subsidiary_block_preconditioner(
        this, dof_list_for_subsidiary_prec, doftype_to_doftype_map);
 
      if (Elastic_subsidiary_preconditioner_function_pt != 0)
      {
        s_prec_pt->set_subsidiary_preconditioner_function(
          Elastic_subsidiary_preconditioner_function_pt);
      }
 
      // Set the replacement blocks.
      for (unsigned d = 0; d < Dim; d++)
      {
        // The dof-block located in the block-ordering.
        unsigned block_i = 2 * d + 1;
 
        // Then dof-block located in the dof-ordering.
        unsigned dof_block_i = Dim + d;
        this->set_replacement_dof_block(
          dof_block_i, dof_block_i, solid_matrix_pt(block_i, block_i));
      }
 
      s_prec_pt->set_dof_to_block_map(s_prec_dof_to_block_map);
      s_prec_pt->Preconditioner::setup(matrix_pt());
 
      Elastic_preconditioner_pt = s_prec_pt;
    }
 
    // No longer require the solid blocks
    for (unsigned row_i = 0; row_i < n_solid_dof_types; row_i++)
    {
      for (unsigned col_i = 0; col_i < n_solid_dof_types; col_i++)
      {
        delete solid_matrix_pt(row_i, col_i);
        solid_matrix_pt(row_i, col_i) = 0;
      }
    }
 
    // next setup the lagrange multiplier preconditioners
    Lagrange_multiplier_preconditioner_pt.resize(Dim);
    for (unsigned d = 0; d < Dim; d++)
    {
      CRDoubleMatrix* b_pt = new CRDoubleMatrix;
      this->get_block(2 * Dim + d, 2 * d + 1, *b_pt);
 
      // if a non default preconditioner is specified create
      // the preconditioners
      if (Lagrange_multiplier_subsidiary_preconditioner_function_pt != 0)
      {
        Lagrange_multiplier_preconditioner_pt[d] =
          (*Lagrange_multiplier_subsidiary_preconditioner_function_pt)();
      }
      // else use default superlu preconditioner
      else
      {
        Lagrange_multiplier_preconditioner_pt[d] =
          ExactPreconditionerFactory::create_exact_preconditioner();
      }
 
      // and setup
      Lagrange_multiplier_preconditioner_pt[d]->setup(b_pt);
      delete b_pt;
      b_pt = 0;
    }
  }
 
  //=============================================================================
  /// Apply the elastic subsidiary preconditioner.
  //=============================================================================
  void PseudoElasticPreconditioner::elastic_preconditioner_solve(
    const DoubleVector& r, DoubleVector& z)
  {
    // apply the solid preconditioner
    Elastic_preconditioner_pt->preconditioner_solve(r, z);
  }
 
  //=============================================================================
  /// Apply the lagrange multiplier subsidiary preconditioner.
  //=============================================================================
  void PseudoElasticPreconditioner::lagrange_multiplier_preconditioner_solve(
    const DoubleVector& r, DoubleVector& z)
  {
    // apply the lagrange multiplier preconditioner
    for (unsigned d = 0; d < Dim; d++)
    {
      DoubleVector x;
      this->get_block_vector(Dim * 2 + d, r, x);
      DoubleVector y;
      Lagrange_multiplier_preconditioner_pt[d]->preconditioner_solve(x, y);
      Lagrange_multiplier_preconditioner_pt[d]->preconditioner_solve(y, x);
      unsigned nrow_local = x.nrow_local();
      double* x_pt = x.values_pt();
      for (unsigned i = 0; i < nrow_local; i++)
      {
        x_pt[i] = x_pt[i] * Scaling;
      }
      this->return_block_vector(Dim * 2 + d, x, z);
    }
  }
 
  //=============================================================================
  /// Clears the memory.
  //=============================================================================
  void PseudoElasticPreconditioner::clean_up_memory()
  {
    // clean the block preconditioner base class memory
    this->clear_block_preconditioner_base();
 
    // delete the solid preconditioner
    delete Elastic_preconditioner_pt;
    Elastic_preconditioner_pt = 0;
 
    // delete the lagrange multiplier preconditioner pt
    unsigned sz = Lagrange_multiplier_preconditioner_pt.size();
    for (unsigned i = 0; i < sz; i++)
    {
      delete Lagrange_multiplier_preconditioner_pt[i];
      Lagrange_multiplier_preconditioner_pt[i] = 0;
    }
  }
 
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
 
  //=============================================================================
  // Setup method for the PseudoElasticPreconditioner.
  //=============================================================================
  void PseudoElasticPreconditionerOld::setup()
  {
    // clean
    this->clean_up_memory();
 
#ifdef PARANOID
    // paranoid check that meshes have been set
    if (Elastic_mesh_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "The elastic mesh must be set.";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
    if (Lagrange_multiplier_mesh_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "The Lagrange multiplier mesh must be set.";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // set the mesh
    unsigned n_solid_dof_types = 0;
    unsigned n_dof_types = 0;
    this->set_mesh(0, Elastic_mesh_pt);
    this->set_mesh(1, Lagrange_multiplier_mesh_pt);
    if (this->is_master_block_preconditioner())
    {
      // get the number of solid dof types from the first element
      n_solid_dof_types = this->ndof_types_in_mesh(0);
 
      // get the total number of dof types
      n_dof_types = n_solid_dof_types + this->ndof_types_in_mesh(1);
    }
    else
    {
      n_dof_types = this->ndof_types();
      n_solid_dof_types = n_dof_types - (n_dof_types / 3);
    }
#ifdef PARANOID
    if (n_dof_types % 3 != 0)
    {
      std::ostringstream error_message;
      error_message << "This preconditioner requires DIM*3 types of DOF";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // determine the dimension
    Dim = n_dof_types / 3;
 
    // Recast Jacobian matrix to CRDoubleMatrix
    CRDoubleMatrix* cr_matrix_pt = dynamic_cast<CRDoubleMatrix*>(matrix_pt());
 
#ifdef PARANOID
    if (cr_matrix_pt == 0)
    {
      std::ostringstream error_message;
      error_message << "FSIPreconditioner only works with"
                    << " CRDoubleMatrix matrices" << std::endl;
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // Setup the block ordering.
    this->block_setup();
 
    // Create dof_list for subsidiary preconditioner. This will be used later
    // in turn_into_subsidiary_block_preconditioner(...)
    Vector<unsigned> dof_list_for_subsidiary_prec(n_solid_dof_types);
    for (unsigned i = 0; i < n_solid_dof_types; i++)
    {
      dof_list_for_subsidiary_prec[i] = i;
    }
 
    // compute the scaling (if required)
    if (Use_inf_norm_of_s_scaling)
    {
      Vector<unsigned> dof_list(n_solid_dof_types);
      for (unsigned i = 0; i < n_solid_dof_types; i++)
      {
        dof_list[i] = i;
      }
 
      PseudoElasticPreconditionerScalingHelperOld* helper_pt =
        new PseudoElasticPreconditionerScalingHelperOld(
          this, cr_matrix_pt, dof_list, Elastic_mesh_pt, comm_pt());
      Scaling = helper_pt->s_inf_norm();
      delete helper_pt;
      helper_pt = 0;
    }
    else
    {
      Scaling = 1.0;
    }
 
 
    // setup the solid subsidiary preconditioner
    // //////////////////////////////// this preconditioner uses the full S
    // matrix
    if (E_preconditioner_type == Exact_block_preconditioner)
    {
      PseudoElasticPreconditionerSubsidiaryPreconditionerOld* s_prec_pt =
        new PseudoElasticPreconditionerSubsidiaryPreconditionerOld;
      Vector<unsigned> dof_list(n_solid_dof_types);
      for (unsigned i = 0; i < n_solid_dof_types; i++)
      {
        dof_list[i] = i;
      }
      s_prec_pt->turn_into_subsidiary_block_preconditioner(this, dof_list);
      if (Elastic_subsidiary_preconditioner_function_pt != 0)
      {
        s_prec_pt->set_subsidiary_preconditioner_function(
          Elastic_subsidiary_preconditioner_function_pt);
      }
      s_prec_pt->scaling() = Scaling;
      s_prec_pt->Preconditioner::setup(matrix_pt());
      Elastic_preconditioner_pt = s_prec_pt;
    }
 
    // otherwise it is a block based preconditioner
    else
    {
      // create the preconditioner
      PseudoElasticPreconditionerSubsidiaryBlockPreconditionerOld* s_prec_pt =
        new PseudoElasticPreconditionerSubsidiaryBlockPreconditionerOld;
      Vector<unsigned> dof_list(n_solid_dof_types);
      for (unsigned i = 0; i < n_solid_dof_types; i++)
      {
        dof_list[i] = i;
      }
      s_prec_pt->turn_into_subsidiary_block_preconditioner(this, dof_list);
 
      // set the subsidiary solve method
      if (Elastic_subsidiary_preconditioner_function_pt != 0)
      {
        s_prec_pt->set_subsidiary_preconditioner_function(
          Elastic_subsidiary_preconditioner_function_pt);
      }
 
      // set the scaling
      s_prec_pt->scaling() = Scaling;
 
      // set the block preconditioning method
      switch (E_preconditioner_type)
      {
        case Block_diagonal_preconditioner:
          s_prec_pt->use_block_diagonal_approximation();
          break;
        case Block_upper_triangular_preconditioner:
          s_prec_pt->use_upper_triangular_approximation();
          break;
        case Block_lower_triangular_preconditioner:
          s_prec_pt->use_lower_triangular_approximation();
          break;
        default:
          break;
      }
 
      // setup
      s_prec_pt->Preconditioner::setup(matrix_pt());
      Elastic_preconditioner_pt = s_prec_pt;
    }
 
    // next setup the lagrange multiplier preconditioners
    Lagrange_multiplier_preconditioner_pt.resize(Dim);
    for (unsigned d = 0; d < Dim; d++)
    {
      CRDoubleMatrix* b_pt = new CRDoubleMatrix;
      this->get_block(2 * Dim + d, Dim + d, *b_pt);
 
      // if a non default preconditioner is specified create
      // the preconditioners
      if (Lagrange_multiplier_subsidiary_preconditioner_function_pt != 0)
      {
        Lagrange_multiplier_preconditioner_pt[d] =
          (*Lagrange_multiplier_subsidiary_preconditioner_function_pt)();
      }
 
      // else use default superlu preconditioner
      else
      {
        Lagrange_multiplier_preconditioner_pt[d] =
          ExactPreconditionerFactory::create_exact_preconditioner();
      }
 
      // and setup
      Lagrange_multiplier_preconditioner_pt[d]->setup(b_pt);
      delete b_pt;
      b_pt = 0;
    }
  }
 
  //=============================================================================
  /// Apply the elastic subsidiary preconditioner.
  //=============================================================================
  void PseudoElasticPreconditionerOld::elastic_preconditioner_solve(
    const DoubleVector& r, DoubleVector& z)
  {
    // apply the solid preconditioner
    Elastic_preconditioner_pt->preconditioner_solve(r, z);
  }
 
 
  //=============================================================================
  /// Apply the lagrange multiplier subsidiary preconditioner.
  //=============================================================================
  void PseudoElasticPreconditionerOld::lagrange_multiplier_preconditioner_solve(
    const DoubleVector& r, DoubleVector& z)
  {
    // apply the lagrange multiplier preconditioner
    for (unsigned d = 0; d < Dim; d++)
    {
      DoubleVector x;
      this->get_block_vector(Dim * 2 + d, r, x);
      DoubleVector y;
      Lagrange_multiplier_preconditioner_pt[d]->preconditioner_solve(x, y);
      Lagrange_multiplier_preconditioner_pt[d]->preconditioner_solve(y, x);
      unsigned nrow_local = x.nrow_local();
      double* x_pt = x.values_pt();
      for (unsigned i = 0; i < nrow_local; i++)
      {
        x_pt[i] = x_pt[i] * Scaling;
      }
      this->return_block_vector(Dim * 2 + d, x, z);
    }
  }
 
  //=============================================================================
  /// Clears the memory.
  //=============================================================================
  void PseudoElasticPreconditionerOld::clean_up_memory()
  {
    // clean the block preconditioner base class memory
    this->clear_block_preconditioner_base();
 
    // delete the solid preconditioner
    delete Elastic_preconditioner_pt;
    Elastic_preconditioner_pt = 0;
 
    // delete the lagrange multiplier preconditioner pt
    unsigned sz = Lagrange_multiplier_preconditioner_pt.size();
    for (unsigned i = 0; i < sz; i++)
    {
      delete Lagrange_multiplier_preconditioner_pt[i];
      Lagrange_multiplier_preconditioner_pt[i] = 0;
    }
  }
 
 
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
 
 
  //=============================================================================
  /// Setup the preconditioner
  //=============================================================================
  void PseudoElasticPreconditionerSubsidiaryPreconditionerOld::setup()
  {
    // clean memory
    this->clean_up_memory();
 
#ifdef PARANOID
    // paranoid check that this preconditioner has an even number of DOF types
    if (this->ndof_types() % 2 != 0)
    {
      std::ostringstream error_message;
      error_message
        << "This SUBSIDIARY preconditioner requires an even number of "
        << "types of DOF";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // assemble dof_to_block_map
    unsigned ndof_types = this->ndof_types();
    Vector<unsigned> dof_to_block_map(ndof_types, 0);
    for (unsigned i = ndof_types / 2; i < ndof_types; i++)
    {
      dof_to_block_map[i] = 1;
    }
 
    this->block_setup(dof_to_block_map);
 
    // get block 11
    CRDoubleMatrix* s11_pt = new CRDoubleMatrix;
    this->get_block(1, 1, *s11_pt);
 
    // add the scaled identity matrix to block 11
    double* s11_values = s11_pt->value();
    int* s11_column_index = s11_pt->column_index();
    int* s11_row_start = s11_pt->row_start();
    int s11_nrow_local = s11_pt->nrow_local();
    int s11_first_row = s11_pt->first_row();
    for (int i = 0; i < s11_nrow_local; i++)
    {
      bool found = false;
      for (int j = s11_row_start[i]; j < s11_row_start[i + 1] && !found; j++)
      {
        if (s11_column_index[j] == i + s11_first_row)
        {
          s11_values[j] += Scaling;
          found = true;
        }
      }
    }
 
    VectorMatrix<BlockSelector> required_blocks(2, 2);
    const bool want_block = true;
    for (unsigned b_i = 0; b_i < 2; b_i++)
    {
      for (unsigned b_j = 0; b_j < 2; b_j++)
      {
        required_blocks[b_i][b_j].select_block(b_i, b_j, want_block);
      }
    }
 
    required_blocks[1][1].set_replacement_block_pt(s11_pt);
 
    CRDoubleMatrix s_prec_pt = this->get_concatenated_block(required_blocks);
 
    delete s11_pt;
    s11_pt = 0;
 
    // setup the preconditioner
    if (Subsidiary_preconditioner_function_pt != 0)
    {
      Preconditioner_pt = (*Subsidiary_preconditioner_function_pt)();
    }
    else
    {
      Preconditioner_pt =
        ExactPreconditionerFactory::create_exact_preconditioner();
    }
    Preconditioner_pt->setup(&s_prec_pt);
  }
 
  //=============================================================================
  /// Apply the preconditioner.
  //=============================================================================
  void PseudoElasticPreconditionerSubsidiaryPreconditionerOld::
    preconditioner_solve(const DoubleVector& r, DoubleVector& z)
  {
    DoubleVector x;
    this->get_block_ordered_preconditioner_vector(r, x);
    DoubleVector y;
    Preconditioner_pt->preconditioner_solve(x, y);
    this->return_block_ordered_preconditioner_vector(y, z);
  }
 
 
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
  ///////////////////////////////////////////////////////////////////////////////
 
 
  //=============================================================================
  /// clean up the memory
  //=============================================================================
  void PseudoElasticPreconditionerSubsidiaryBlockPreconditionerOld::
    clean_up_memory()
  {
    // number of block types
    unsigned n_block = Diagonal_block_preconditioner_pt.size();
 
    // delete diagonal blocks
    for (unsigned i = 0; i < n_block; i++)
    {
      delete Diagonal_block_preconditioner_pt[i];
      Diagonal_block_preconditioner_pt[i] = 0;
      if (Method == 1)
      {
        for (unsigned j = i + 1; j < n_block; j++)
        {
          delete Off_diagonal_matrix_vector_products(i, j);
          Off_diagonal_matrix_vector_products(i, j) = 0;
        }
      }
      else if (Method == 2)
      {
        for (unsigned j = 0; j < i; j++)
        {
          delete Off_diagonal_matrix_vector_products(i, j);
          Off_diagonal_matrix_vector_products(i, j) = 0;
        }
      }
    }
 
    // clean up the block preconditioner
    this->clear_block_preconditioner_base();
  }
 
  //=============================================================================
  /// Setup the preconditioner.
  //=============================================================================
  void PseudoElasticPreconditionerSubsidiaryBlockPreconditionerOld::setup()
  {
    // clean the memory
    this->clean_up_memory();
 
    // determine the number of DOF types
    unsigned n_dof_types = this->ndof_types();
 
#ifdef PARANOID
    // must be Dim*2 dof types
    if (n_dof_types % 2 != 0)
    {
      std::ostringstream error_message;
      error_message << "This preconditioner requires DIM*3 types of DOF";
      throw OomphLibError(
        error_message.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
    // store the dimension of the problem
    unsigned dim = n_dof_types / 2;
 
    // assemble the dof to block lookup scheme
    Vector<unsigned> dof_to_block_map(n_dof_types, 0);
    for (unsigned d = 0; d < dim; d++)
    {
      dof_to_block_map[d] = d;
      dof_to_block_map[d + dim] = d;
    }
 
    // setup the blocks look up schemes
    this->block_setup(dof_to_block_map);
 
    // Storage for the diagonal block preconditioners
    Diagonal_block_preconditioner_pt.resize(dim);
 
    // storage for the off diagonal matrix vector products
    Off_diagonal_matrix_vector_products.resize(dim, dim, 0);
 
    // setup the subsidiary preconditioners
    for (unsigned d = 0; d < dim; d++)
    {
      Vector<unsigned> dof_list(2);
      dof_list[0] = d;
      dof_list[1] = d + dim;
 
      Diagonal_block_preconditioner_pt[d] =
        new PseudoElasticPreconditionerSubsidiaryPreconditionerOld;
      Diagonal_block_preconditioner_pt[d]
        ->turn_into_subsidiary_block_preconditioner(this, dof_list);
      if (Subsidiary_preconditioner_function_pt != 0)
      {
        Diagonal_block_preconditioner_pt[d]
          ->set_subsidiary_preconditioner_function(
            Subsidiary_preconditioner_function_pt);
      }
      Diagonal_block_preconditioner_pt[d]->scaling() = Scaling;
 
      Diagonal_block_preconditioner_pt[d]->Preconditioner::setup(matrix_pt());
 
      // the preconditioning method.\n
      // 0 - block diagonal\n
      // 1 - upper triangular\n
      // 2 - lower triangular\n
      // next setup the off diagonal mat vec operators if required
      if (Method == 1 || Method == 2)
      {
        unsigned l = d + 1;
        unsigned u = dim;
        if (Method == 2)
        {
          l = 0;
          u = d;
        }
        for (unsigned j = l; j < u; j++)
        {
          CRDoubleMatrix* block_matrix_pt = new CRDoubleMatrix;
          this->get_block(d, j, *block_matrix_pt);
          Off_diagonal_matrix_vector_products(d, j) = new MatrixVectorProduct();
          //        Off_diagonal_matrix_vector_products(d,j)->setup(block_matrix_pt);
          this->setup_matrix_vector_product(
            Off_diagonal_matrix_vector_products(d, j), block_matrix_pt, j);
 
          delete block_matrix_pt;
          block_matrix_pt = 0;
        }
      }
    } // setup the subsidiary preconditioner.
  } // preconditioner setup
 
  //=============================================================================
  /// Apply preconditioner to r
  //=============================================================================
  void PseudoElasticPreconditionerSubsidiaryBlockPreconditionerOld::
    preconditioner_solve(const DoubleVector& res, DoubleVector& z)
  {
    // copy r
    DoubleVector r(res);
 
    unsigned n_block;
 
    // Cache umber of block types (also the spatial DIM)
    n_block = this->nblock_types();
 
    // loop parameters
    int start = n_block - 1;
    int end = -1;
    int step = -1;
    if (Method != 1)
    {
      start = 0;
      end = n_block;
      step = 1;
    }
 
    // the preconditioning method.
    // 0 - block diagonal
    // 1 - upper triangular
    // 2 - lower triangular
    //
    // loop over the DIM
    //
    // For Method = 0 or 2 (diagonal, lower)
    // start = 2, end = -1, step = -1
    // i = 2,1,0
    //
    // For Method = 1 (upper)
    // start = 0, end = 3 step = 1
    // i = 0, 1, 2
    for (int i = start; i != end; i += step)
    {
      // solve
      Diagonal_block_preconditioner_pt[i]->preconditioner_solve(r, z);
 
      // if upper or lower triangular
      if (Method != 0)
      {
        // substitute
        //
        for (int j = i + step; j != end; j += step)
        {
          DoubleVector x;
          this->get_block_vector(i, z, x);
          DoubleVector y;
          Off_diagonal_matrix_vector_products(j, i)->multiply(x, y);
          x.clear();
          this->get_block_vector(j, r, x);
          x -= y;
          this->return_block_vector(j, x, r);
        } // substitute
      } // if upper or lower
    } // for loop over DIM
  } // Block preconditioner solve
} // namespace oomph