core_smoothers.h

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/*
 * Copyright (c) 2010-2015:  G-CSC, Goethe University Frankfurt
 * Author: Martin Rupp
 * 
 * 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__CPU_ALGEBRA__CORE_SMOOTHERS__
#define __H__UG__CPU_ALGEBRA__CORE_SMOOTHERS__
 
namespace ug
{
 
 
//  gs_step_LL
template<typename Matrix_type, typename Vector_type>
bool gs_step_LL(const Matrix_type &A, Vector_type &x, const Vector_type &b)
{
  // gs LL has preconditioning matrix
  // (D-L)^{-1}
 
  typename Vector_type::value_type s;
 
  for(size_t i=0; i < x.size(); i++)
  {
    s = b[i];
 
    for(typename Matrix_type::const_row_iterator it = A.begin_row(i); it != A.end_row(i) && it.index() < i; ++it)
      // s -= it.value() * x[it.index()];
      MatMultAdd(s, 1.0, s, -1.0, it.value(), x[it.index()]);
 
    // x[i] = s/A(i,i)
    InverseMatMult(x[i], 1.0, A(i,i), s);
  }
 
  return true;
}
 
//  gs_step_UR
template<typename Matrix_type, typename Vector_type>
bool gs_step_UR(const Matrix_type &A, Vector_type &x, const Vector_type &b)
{
  // gs UR has preconditioning matrix
  // (D-U)^{-1}
  typename Vector_type::value_type s;
 
  if(x.size() == 0) return true;
  size_t i = x.size()-1;
  do
  {
    s = b[i];
    typename Matrix_type::const_row_iterator diag = A.get_connection(i, i);
    
    typename Matrix_type::const_row_iterator it = diag; ++it;
    for(; it != A.end_row(i); ++it)
      // s -= it.value() * x[it.index()];
      MatMultAdd(s, 1.0, s, -1.0, it.value(), x[it.index()]);
 
    // x[i] = s/A(i,i)
    InverseMatMult(x[i], 1.0, diag.value(), s);
  } while(i-- != 0);
 
  return true;
}
 
//  sgs_step
template<typename Matrix_type, typename Vector_type>
bool sgs_step(const Matrix_type &A, Vector_type &x, const Vector_type &b)
{
  // sgs has preconditioning matrix
  // (D-U)^{-1} D (D-L)^{-1}
 
  // x1 = (D-L)^{-1} b
  gs_step_LL(A, x, b);
 
  // x2 = D x1
  for(size_t i = 0; i<x.size(); i++)
    MatMult(x[i], 1.0, A(i, i), x[i]);
 
  // x3 = (D-U)^{-1} x2
  gs_step_UR(A, x, x);
 
  return true;
}
 
//  diag_step
template<typename Matrix_type, typename Vector_type>
bool diag_step(const Matrix_type& A, Vector_type& x, const Vector_type& b, number damp)
{
  //exit(3);
  UG_ASSERT(x.size() == b.size() && x.size() == A.num_rows(), x << ", " << b << " and " << A << " need to have same size.");
 
  for(size_t i=0; i < x.size(); i++)
    // x[i] = damp * b[i]/A(i,i)
    InverseMatMult(x[i], damp, A(i,i), b[i]);
 
  return true;
}
 
}
#endif // __H__UG__CPU_ALGEBRA__CORE_SMOOTHERS__