pcr_ilut.h

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/*
 * Copyright (c) 2013-2014:  G-CSC, Goethe University Frankfurt
 * Authors: Martin Rupp, Christian Wehner
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
 
#ifndef __H__UG__PLUGINS__NAVIER_STOKES__INCOMPRESSIBLE__FVCR__PCRILUT__
#define __H__UG__PLUGINS__NAVIER_STOKES__INCOMPRESSIBLE__FVCR__PCRILUT__
 
#include "lib_algebra/operator/interface/operator.h"
#include "lib_algebra/operator/interface/preconditioner.h"
#ifdef UG_PARALLEL
  #include "lib_algebra/parallelization/parallelization.h"
#endif
 
namespace ug{
  
/*  Threshold ILU method
*
*   parallelization equivalent to ILU parallelization (see ilu.h)
*
* The matrix entries can be devided into four sectors: 
* velocity-velocity, velocity-pressure, pressure-velocity, pressure-pressure
* Threshold tolerance depends on sector of new entry
* (given by parameters m_eps_vv, m_eps_vp, m_eps_pv, m_eps_pp)    
* Type of entry a_ij is determined by diagonal entry of rows i and j
*   if a_ii=0 i is a pressure index, else a velocity index
*
*/
template <typename TAlgebra>
class PCRILUTPreconditioner : public IPreconditioner<TAlgebra>
{
  public:
  //  Algebra type
    typedef TAlgebra algebra_type;
 
  //  Vector type
    typedef typename TAlgebra::vector_type vector_type;
 
  //  Matrix type
    typedef typename TAlgebra::matrix_type matrix_type;
 
    typedef typename IPreconditioner<TAlgebra>::matrix_operator_type matrix_operator_type;
 
  private:
    typedef typename matrix_type::value_type block_type;
    using IPreconditioner<TAlgebra>::debug_writer;
    using IPreconditioner<TAlgebra>::set_debug;
 
  public:
  //  Constructor
    PCRILUTPreconditioner(double eps=1e-6) :
      m_eps(eps), m_eps_vv(eps), m_eps_vp(eps), m_eps_pv(eps), m_eps_pp(eps)
    {
      m_info = false;
    };
 
    PCRILUTPreconditioner(number threshvv,number thresh_vp_pv_pp)
    {
      set_threshold(threshvv,thresh_vp_pv_pp);
      m_info = false;
    }
 
    PCRILUTPreconditioner(number threshvv,number threshvp,number threshpv,number threshpp)
    {
      set_threshold(threshvv,threshvp,threshpv,threshpp);
      m_info = false;
    };
 
    PCRILUTPreconditioner(double eps,bool info) :
    m_eps(eps), m_eps_vv(eps), m_eps_vp(eps), m_eps_pv(eps), m_eps_pp(eps), m_info(info)
    {
    }
 
    PCRILUTPreconditioner(number threshvv,number thresh_vp_pv_pp,bool info)
    {
      set_threshold(threshvv,thresh_vp_pv_pp);
      m_info = info;
    }
 
    PCRILUTPreconditioner(number threshvv,number threshvp,number threshpv,number threshpp,bool info)
    {
      set_threshold(threshvv,threshvp,threshpv,threshpp);
      m_info = info;
    }
 
  //  Clone
  
  SmartPtr<ILinearIterator<vector_type> > clone()
  {
    SmartPtr<PCRILUTPreconditioner<algebra_type> > newInst(new PCRILUTPreconditioner<algebra_type>(m_eps));
    newInst->set_debug(debug_writer());
    newInst->set_damp(this->damping());
    newInst->set_threshold(this->m_eps_vv,this->m_eps_vp,this->m_eps_pv,this->m_eps_pp);
    newInst->set_info(this->m_info);
    return newInst;
  }
 
  //  Destructor
    virtual ~PCRILUTPreconditioner()
    {
    };
 
    virtual bool supports_parallel() const {return true;}
 
  void set_threshold(number threshvv,number threshvp,number threshpv,number threshpp)
  {
    m_eps_vv = threshvv;
    m_eps_vp = threshvp;
    m_eps_pv = threshpv;
    m_eps_pp = threshpp;
    m_eps = std::min(std::min(m_eps_vv,m_eps_vp),std::min(m_eps_pv,m_eps_pp));
  }
  
  void set_threshold(number threshvv,number thresh_vp_pv_pp)
  {
    m_eps_vv = threshvv;
    m_eps_vp = thresh_vp_pv_pp;
    m_eps_pv = thresh_vp_pv_pp;
    m_eps_pp = thresh_vp_pv_pp;
    m_eps = std::min(m_eps_vv,m_eps_vp);
  }
 
  void set_threshold(number thresh)
  {
    m_eps_vv = thresh;
    m_eps_vp = thresh;
    m_eps_pv = thresh;
    m_eps_pp = thresh;
    m_eps = thresh;
  }
  
  void set_info(bool info)
  {
    m_info = info;
  }
    
  
protected:
  //  Name of preconditioner
  virtual const char* name() const {return "PCRILUTPreconditioner";}
  
  //  Preprocess routine
  virtual bool preprocess(SmartPtr<MatrixOperator<matrix_type, vector_type> > pOp)
  {
    STATIC_ASSERT(matrix_type::rows_sorted, Matrix_has_to_have_sorted_rows);
    matrix_type& mat = *pOp;
 
#ifdef  UG_PARALLEL
    //  copy original matrix
    // commented-out function seems to be broken (A.Vogel)
    //      MakeConsistent(mat, m_ILUT);
 
    // we use new instead (A.Vogel)
    m_A = mat;
    MatAddSlaveRowsToMasterRowOverlap0(m_A);
 
    //  set zero on slaves
    std::vector<IndexLayout::Element> vIndex;
    CollectUniqueElements(vIndex,  m_A.layouts()->slave());
    SetDirichletRow(m_A, vIndex);
#else
    //  copy original matrix
    m_A = mat;
#endif
    typedef typename matrix_type::connection connection;
    m_L.resize_and_clear(m_A.num_rows(), m_A.num_cols());
    m_U.resize_and_clear(m_A.num_rows(), m_A.num_cols());
    
    // con is the current line of L/U
    std::vector<typename matrix_type::connection> con;
    con.reserve(300);
    con.resize(0);
    
    static const size_t velocity=0;
    static const size_t pressure=1; 
    
    // init row 0 of U
    for(typename matrix_type::row_iterator i_it = m_A.begin_row(0); i_it != m_A.end_row(0); ++i_it)
      con.push_back(connection(i_it.index(), i_it.value()));
    m_U.set_matrix_row(0, &con[0], con.size());
    
    size_t totalentries=0;
    size_t maxentries=0;
    
    for(size_t i=1; i<m_A.num_rows(); i++)
    {       
      size_t itype;
      if (m_A(i,i)!=0) itype=velocity; else itype=pressure;
      
      con.resize(0);
      size_t u_part=0;
      
      // get the row A(i, .) into con
      double dmax=0;
      m_remove_zeros = false;
      if (m_remove_zeros==false){
        for(typename matrix_type::row_iterator i_it = m_A.begin_row(i); i_it != m_A.end_row(i); ++i_it)
        {
          con.push_back(connection(i_it.index(), i_it.value()));
          if(dmax < BlockNorm(i_it.value()))
            dmax = BlockNorm(i_it.value());
        }
      } else {
        typename matrix_type::row_iterator i_it = m_A.begin_row(i);
        con.push_back(connection(i_it.index(), i_it.value()));
        ++i_it;
        for(; i_it != m_A.end_row(i); ++i_it)
        {
          if (i_it.value()==0) continue;
          con.push_back(connection(i_it.index(), i_it.value()));
          if(dmax < BlockNorm(i_it.value()))
            dmax = BlockNorm(i_it.value());
        }
      }
      // eliminate all entries A(i, k) with k<i with rows U(k, .) and k<i
      for(size_t i_it = 0; i_it < con.size(); ++i_it)
      {
        size_t k = con[i_it].iIndex;
        if(k >= i)
        {
          // safe where U begins / L ends in con
          u_part = i_it;
          break;
        }
        if(con[i_it].dValue == 0.0) continue;
        UG_ASSERT(m_U.num_connections(k) != 0 && m_U.begin_row(k).index() == k, "");
        block_type &ukk = m_U.begin_row(k).value();
        
        // add row k to row i by A(i, .) -= U(k,.)  A(i,k) / U(k,k)
        // so that A(i,k) is zero.
        // safe A(i,k)/U(k,k) in con, (later L(i,k) )
        block_type &d = con[i_it].dValue = con[i_it].dValue / ukk;
        
        typename matrix_type::row_iterator k_it = m_U.begin_row(k); // upper row iterator
        ++k_it; // skip diag
        size_t j = i_it+1;
        while(k_it != m_U.end_row(k) && j < con.size())
        {
          
          // (since con and U[k] is sorted, we can do sth like a merge on the two lists)
          if(k_it.index() == con[j].iIndex)
          {
            // match
            con[j].dValue -= k_it.value() * d;
            ++k_it; ++j;
          }
          else if(k_it.index() < con[j].iIndex)
          {
            // we have a value in U(k, (*k_it).iIndex), but not in A.
            // check tolerance criteria
            
            typename matrix_type::connection 
            c(k_it.index(), k_it.value() * d * -1.0);
            
            if(BlockNorm(c.dValue) > dmax * m_eps){
              
              size_t kitType;
              if (m_A(k_it.index(),k_it.index())!=0) kitType=velocity; else kitType=pressure;
            
            if ((itype==velocity)&&(kitType==velocity)){
              if(BlockNorm(c.dValue) > dmax * m_eps_vv)
              {
                // insert sorted
                con.insert(con.begin()+j, c);
                ++j;
              }
            }
            if ((itype==velocity)&&(kitType==pressure)){
              if(BlockNorm(c.dValue) > dmax * m_eps_vp)
              {
                // insert sorted
                con.insert(con.begin()+j, c);
                ++j;
              }
            }
            if ((itype==pressure)&&(kitType==velocity)){
              if(BlockNorm(c.dValue) > dmax * m_eps_pv)
              {
                // insert sorted
                con.insert(con.begin()+j, c);
                ++j;
              }
            }
            if ((itype==pressure)&&(kitType==pressure)){
              if(BlockNorm(c.dValue) > dmax * m_eps_pp)
              {
                // insert sorted
                con.insert(con.begin()+j, c);
                ++j;
              }
            } 
            }
            // else do some lumping
            ++k_it;
          }
          else
          {
            // we have a value in A(k, con[j].iIndex), but not in U.
            ++j;
          }
        }
        // insert new connections after last connection of row i
        if (k_it!=m_U.end_row(k)){
          for (;k_it!=m_U.end_row(k);++k_it){
            typename matrix_type::connection c(k_it.index(),-k_it.value()*d);
            if(BlockNorm(c.dValue) > dmax * m_eps){
              size_t kitType;
              if (m_A(k_it.index(),k_it.index())!=0) kitType=velocity; else kitType=pressure;
              if ((itype==velocity)&&(kitType==velocity)){
                if(BlockNorm(c.dValue) > dmax * m_eps_vv)
                {
                  con.push_back(c);
                }
              } else {
                if ((itype==velocity)&&(kitType==pressure)){
                  if(BlockNorm(c.dValue) > dmax * m_eps_vp)
                  {
                    con.push_back(c);
                  }
                } else {
                  if ((itype==pressure)&&(kitType==velocity)){
                    if(BlockNorm(c.dValue) > dmax * m_eps_pv)
                    {
                      con.push_back(c);
                    }
                  } else {
                //    if ((itype==pressure)&&(kitType==pressure)){
                      if(BlockNorm(c.dValue) > dmax * m_eps_pp)
                      {
                        con.push_back(c); 
                      }
                //    } 
                  }
                }
              }
 
            };
          }
        };
      }
      
      totalentries+=con.size();
      if(maxentries < con.size()) maxentries = con.size();
      
      // safe L and U
      m_L.set_matrix_row(i, &con[0], u_part);
      m_U.set_matrix_row(i, &con[u_part], con.size()-u_part);
      
    }
    
    m_L.defragment();
    m_U.defragment();
    m_A.defragment();
    
    if (m_info==true){
      UG_LOG("\n  PCRILUT storage information:\n");
      UG_LOG("  A nr of connections: " << m_A.total_num_connections()  << "\n");
      UG_LOG("  L+U nr of connections: " << m_L.total_num_connections()+m_U.total_num_connections() << "\n");
      UG_LOG("  Increase factor: " << (float)(m_L.total_num_connections() + m_U.total_num_connections() )/m_A.total_num_connections() << "\n");
    }
    
    return true;
  }
  
  //  Stepping routine
  virtual bool step(SmartPtr<MatrixOperator<matrix_type, vector_type> > pOp, vector_type& c, const vector_type& d)
  {
#ifdef  UG_PARALLEL
    SmartPtr<vector_type> spDtmp = d.clone();
    spDtmp->change_storage_type(PST_UNIQUE);
    // apply iterator: c = LU^{-1}*d (damp is not used)
    // L
    for(size_t i=0; i < m_L.num_rows(); i++)
    {
      // c[i] = d[i] - m_L[i]*c;
      c[i] = (*spDtmp)[i];
      for(typename matrix_type::row_iterator it = m_L.begin_row(i); it != m_L.end_row(i); ++it)
        MatMultAdd(c[i], 1.0, c[i], -1.0, it.value(), c[it.index()] );
      // lii = 1.0.
    }
    // U
    //
    // last row diagonal U entry might be close to zero with corresponding zero rhs 
    // when solving Navier Stokes system, therefore handle separately
    {
      size_t i=m_U.num_rows()-1;
      typename matrix_type::row_iterator it = m_U.begin_row(i);
      UG_ASSERT(it.index() == i, "");
      block_type &uii = it.value();
      typename vector_type::value_type s = c[i];
      // check if close to zero
      if (BlockNorm(uii)<m_small_lower){
        // set correction to zero
        c[i] = 0;
        if (BlockNorm(s)>m_small_upper){
          UG_LOG("Warning: zero entry in last row of U with corresponding non-zero rhs entry (" << BlockNorm(s) << ")\n");
        }
      } else {
        // c[i] = s/uii;
        InverseMatMult(c[i], 1.0, uii, s);
      }
    }
    // handle all other rows
    for(size_t i=m_U.num_rows()-2; ; i--)
    {
      typename matrix_type::row_iterator it = m_U.begin_row(i);
      UG_ASSERT(it.index() == i, "");
      block_type &uii = it.value();
      
      typename vector_type::value_type s = c[i];
      ++it; // skip diag
      for(; it != m_U.end_row(i); ++it)
        // s -= it.value() * c[it.index()];
        MatMultAdd(s, 1.0, s, -1.0, it.value(), c[it.index()] );
      
      // c[i] = s/uii;
      InverseMatMult(c[i], 1.0, uii, s);
      
      if(i==0) break;
    }
    //  Correction is always consistent
    c.set_storage_type(PST_ADDITIVE);
    c.change_storage_type(PST_CONSISTENT);
#else
    // apply iterator: c = LU^{-1}*d (damp is not used)
    // L
    for(size_t i=0; i < m_L.num_rows(); i++)
    {
      // c[i] = d[i] - m_L[i]*c;
      c[i] = d[i];
      for(typename matrix_type::row_iterator it = m_L.begin_row(i); it != m_L.end_row(i); ++it)
        MatMultAdd(c[i], 1.0, c[i], -1.0, it.value(), c[it.index()] );
      // lii = 1.0.
    }
    // U
    //
    // last row diagonal U entry might be close to zero with corresponding zero rhs
    // when solving Navier Stokes system, therefore handle separately
    {
      size_t i=m_U.num_rows()-1;
      typename matrix_type::row_iterator it = m_U.begin_row(i);
      UG_ASSERT(it.index() == i, "");
      block_type &uii = it.value();
      typename vector_type::value_type s = c[i];
      // check if close to zero
      if (BlockNorm(uii)<m_small_lower){
        // set correction to zero
        c[i] = 0;
        if (BlockNorm(s)>m_small_upper){
          UG_LOG("Warning: zero entry in last row of U with corresponding non-zero rhs entry (" << BlockNorm(s) << ")\n");
        }
      } else {
        // c[i] = s/uii;
        InverseMatMult(c[i], 1.0, uii, s);
      }
    }
    // handle all other rows
    for(size_t i=m_U.num_rows()-2; ; i--)
    {
      typename matrix_type::row_iterator it = m_U.begin_row(i);
      UG_ASSERT(it.index() == i, "");
      block_type &uii = it.value();
 
      typename vector_type::value_type s = c[i];
      ++it; // skip diag
      for(; it != m_U.end_row(i); ++it)
        // s -= it.value() * c[it.index()];
        MatMultAdd(s, 1.0, s, -1.0, it.value(), c[it.index()] );
 
      // c[i] = s/uii;
      InverseMatMult(c[i], 1.0, uii, s);
 
      if(i==0) break;
    }
#endif
    return true;
  }
  
  //  Postprocess routine
  virtual bool postprocess() {return true;}
  
protected:
  matrix_type m_L;
  matrix_type m_U;
  matrix_type m_A;
  number m_eps;
  number m_eps_vv;
  number m_eps_vp;
  number m_eps_pv;
  number m_eps_pp;
  bool m_info;
  bool m_remove_zeros;
  static const number m_small_lower;
  static const number m_small_upper;
};
  
template <typename TAlgebra>
const number PCRILUTPreconditioner<TAlgebra>::m_small_lower = 1e-9;
template <typename TAlgebra>
const number PCRILUTPreconditioner<TAlgebra>::m_small_upper = 1e-6;
 
} // end namespace ug
 
#endif