BiCGStabSolver.H

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#ifdef CH_LANG_CC
/*
 *      _______              __
 *     / ___/ /  ___  __ _  / /  ___
 *    / /__/ _ \/ _ \/  V \/ _ \/ _ \
 *    \___/_//_/\___/_/_/_/_.__/\___/
 *    Please refer to Copyright.txt, in Chombo's root directory.
 */
#endif

// BVS, June 18, 2003

#ifndef _BICGSTABSOLVER_H_
#define _BICGSTABSOLVER_H_

#include "LinearSolver.H"
#include "parstream.H"
#include "CH_Timer.H"
#include "NamespaceHeader.H"

///
/**
   Elliptic solver using the BiCGStab algorithm.
 */
template <class T>
class BiCGStabSolver : public LinearSolver<T>
{
public:

  BiCGStabSolver();

  virtual ~BiCGStabSolver();

  virtual void setHomogeneous(bool a_homogeneous)
  {
    m_homogeneous = a_homogeneous;
  }

  ///
  /**
     define the solver.   a_op is the linear operator.
     a_homogeneous is whether the solver uses homogeneous boundary
     conditions.
   */
  virtual void define(LinearOp<T>* a_op, bool a_homogeneous);

  ///solve the equation.
  virtual void solve(T& a_phi, const T& a_rhs);

  ///
  virtual void setConvergenceMetrics(Real a_metric,
                                     Real a_tolerance);

  ///
  /**
     public member data: whether the solver is restricted to
     homogeneous boundary conditions
   */
  bool m_homogeneous;

  ///
  /**
     public member data: operator to solve.
   */
  LinearOp<T>* m_op;

  ///
  /**
     public member data:  maximum number of iterations
   */
  int m_imax;

  ///
  /**
     public member data:  how much screen out put the user wants.
     set = 0 for no output.
   */
  int m_verbosity;

  ///
  /**
     public member data:  solver tolerance
   */
  Real m_eps;

  ///
  /**
     public member data:  relative solver tolerance
   */
  Real m_reps;

  ///
  /**
     public member data: solver convergence metric -- if negative, use
     initial residual; if positive, then use m_convergenceMetric
  */
  Real m_convergenceMetric;

  ///
  /**
     public member data:  minium norm of solution should change per iterations
   */
  Real m_hang;

  ///
  /**
     public member data:
     set = -1 if solver exited for an unknown reason
     set =  1 if solver converged to tolerance
     set =  2 if rho = 0
     set =  3 if max number of restarts was reached
   */
  int m_exitStatus;

  ///
  /**
     public member data:  what the algorithm should consider "close to zero"
   */
  Real m_small;

  ///
  /**
     public member data:  number of times the algorithm can restart
   */
  int m_numRestarts;

  ///
  /**
     public member data:  norm to be used when evaluation convergence.
     0 is max norm, 1 is L(1), 2 is L(2) and so on.
   */
  int m_normType;

};

// *******************************************************
// BiCGStabSolver Implementation
// *******************************************************

// For large elliptic problem, bottom smoother needed 67 iterations.
// Bumping imax to 80.  (ndk)
template <class T>
BiCGStabSolver<T>::BiCGStabSolver()
  :m_homogeneous(false),
   m_op(NULL),
   m_imax(80),
   m_verbosity(3),
   m_eps(1.0E-6),
   m_reps(1.0E-12),
   m_convergenceMetric(-1.0),
   m_hang(1E-8),
   m_exitStatus(-1),
   m_small(1.0E-30),
   m_numRestarts(5),
   m_normType(2)
{
}

template <class T>
BiCGStabSolver<T>::~BiCGStabSolver()
{
  m_op = NULL;
}

template <class T>
void BiCGStabSolver<T>::define(LinearOp<T>* a_operator, bool a_homogeneous)
{
  m_homogeneous = a_homogeneous;
  m_op = a_operator;
}

template <class T>
void BiCGStabSolver<T>::solve(T& a_phi, const T& a_rhs)
{
  CH_TIMERS("BiCGStabSolver::solve");

  CH_TIMER("BiCGStabSolver::solve::Initialize",timeInitialize);
  CH_TIMER("BiCGStabSolver::solve::MainLoop",timeMainLoop);
  CH_TIMER("BiCGStabSolver::solve::Cleanup",timeCleanup);

  CH_START(timeInitialize);

  T r, r_tilde, e, p, p_tilde, s_tilde, t, v;

  m_op->create(r,       a_rhs);
  m_op->create(r_tilde, a_rhs);
  m_op->create(e,       a_phi);
  m_op->create(p,       a_rhs);
  m_op->create(p_tilde, a_phi);
  m_op->create(s_tilde, a_phi);
  m_op->create(t,       a_rhs);
  m_op->create(v,       a_rhs);

  int recount = 0;

  CH_assert(m_op != NULL);
  m_op->setToZero(r); // added by petermc, 26 Nov 2013, to zero out ghosts

  m_op->residual(r, a_phi, a_rhs, m_homogeneous);

  m_op->assignLocal(r_tilde, r);
  m_op->setToZero(e);
  // (DFM 2/1/07) these next two need to be set to zero to prevent
  // problems in the multilevel case
  m_op->setToZero(p_tilde);
  m_op->setToZero(s_tilde);

  int i = 0;

  // rho[0] = r_i , rho[1] = r_(i-1), etc.
  Real rho[4]=
  {
    0,0,0,0
  };
  Real norm[2];
  norm[0] = m_op->norm(r, m_normType);
  Real initial_norm = norm[0];
  Real initial_rnorm = norm[0];
  norm[1] = norm[0];

  Real alpha[2] =
  {
    0,0
  };
  Real  beta[2] =
  {
    0,0
  };
  Real omega[2] =
  {
    0,0
  };

  bool init = true;
  int restarts = 0;

  if (m_verbosity >= 5)
    {
      pout() << "      BiCGStab:: initial Residual norm = "
             << initial_norm << "\n";
    }

  // if a convergence metric has been supplied, replace initial residual
  // with the supplied convergence metric...
  if (m_convergenceMetric > 0)
    {
      initial_norm = m_convergenceMetric;
    }

  CH_STOP(timeInitialize);

  CH_START(timeMainLoop);
  while ((i<m_imax && norm[0] > m_eps*norm[1]) && (norm[1] > 0))
    {
      i++;

      norm[1] = norm[0];
      alpha[1]= alpha[0];
      beta[1] = beta[0];
      omega[1]= omega[0];

      if (m_verbosity >= 5)
        {
          pout() << "      BiCGStab::       norm[0]  = "  << norm[0] << ", "
                 <<                        "norm[1]  = "  << norm[1]
                 << "\n";
          pout() << "      BiCGStab::       alpha[0] = "  << alpha[0] << ", "
                 <<                        "alpha[1] = "  << alpha[1]
                 << "\n";
          pout() << "      BiCGStab::       beta[0]  = "  << beta[0] << ", "
                 <<                        "beta[1]  = "  << beta[1]
                 << "\n";
          pout() << "      BiCGStab::       omega[0] = "  << omega[0] << ", "
                 <<                        "omega[1] = "  << omega[1]
                 << "\n";
        }

      rho[3] = rho[2];
      rho[2] = rho[1];
      rho[1] = m_op->dotProduct(r_tilde, r);

      if (m_verbosity >= 5)
        {
          pout() << "      BiCGStab::       rho[1] = "  << rho[1] << ", "
                 <<                        "rho[2] = "  << rho[2] << ", "
                 <<                        "rho[3] = "  << rho[3]
                 << "\n";
        }

      if (rho[1] == 0.0)
        {
          // we are finished, we will not converge anymore
          m_op->incr(a_phi, e, 1.0);

          if (m_verbosity >= 5)
            {
              pout() << "      BiCGStab:: rho = 0, returning"
                     << " -- Residual norm = "
                     << norm[0] << "\n";
            }

          CH_STOP(timeMainLoop);

          CH_START(timeCleanup);

          m_exitStatus = 2;
          // need to call clear just in case
          // this is not ideal -- maybe change the return
          // to exit
          m_op->clear(r);
          m_op->clear(r_tilde);
          m_op->clear(e);
          m_op->clear(p);
          m_op->clear(p_tilde);
          m_op->clear(s_tilde);
          m_op->clear(t);
          m_op->clear(v);

          CH_STOP(timeCleanup);

          return;
        }

      if (init)
        {
          m_op->assignLocal(p, r);
          init = false;
        }
      else
        {
          beta[1] = (rho[1]/rho[2])*(alpha[1]/omega[1]);
          m_op->scale(p, beta[1]);
          m_op->incr(p, v, -beta[1]*omega[1]);
          m_op->incr(p, r, 1.0);
        }

      if (m_verbosity >= 5)
        {
          pout() << "      BiCGStab::       beta[1]  = "  << beta[1]
                 << "\n";
        }

      m_op->preCond(p_tilde, p);
      m_op->setToZero(v); // added by petermc, 27 Nov 2013, to zero out ghosts
      m_op->applyOp(v, p_tilde, true);
      Real m = m_op->dotProduct(r_tilde, v);
      alpha[0] = rho[1]/m;

      if (m_verbosity >= 5)
        {
          pout() << "      BiCGStab::       rho[1] = "  << rho[1]   << ", "
                 <<                             "m = "  << m        << ", "
                 <<                      "alpha[0] = "  << alpha[0]
                 << "\n";
        }

      if (Abs(m) > m_small*Abs(rho[1]))
        {
          m_op->incr(r, v, -alpha[0]);
          norm[0] = m_op->norm(r, m_normType);
          m_op->incr(e, p_tilde, alpha[0]);
        }
      else
        {
          m_op->setToZero(r);
          norm[0] = 0.0;
        }

      if (m_verbosity >= 4)
      {
        pout() << "norm[0] = " << norm[0]
               << " initial_norm = " << initial_norm
               << " initial_rnorm = " << initial_rnorm << endl;
      }

      if (norm[0] > m_eps*initial_norm && norm[0] > m_reps*initial_rnorm)
        {
          m_op->preCond(s_tilde, r);
          m_op->setToZero(t); // added by petermc, 27 Nov 2013, to zero out ghosts
          m_op->applyOp(t, s_tilde, true);
          omega[0] = m_op->dotProduct(t, r)/m_op->dotProduct(t, t);
          m_op->incr(e, s_tilde, omega[0]);
          m_op->incr(r, t,      -omega[0]);
          norm[0] = m_op->norm(r, m_normType);
        }

      if (m_verbosity >= 4)
        {
          pout() << "      BiCGStab::     iteration = "  << i        << ", error norm = " << norm[0] << ", rate = " << norm[1]/norm[0] << "\n";
        }

      if (norm[0] <= m_eps*initial_norm || norm[0] <= m_reps*initial_rnorm)
        {
          // converged to tolerance
          m_exitStatus = 1;
          break;
        }

      if (omega[0] == 0.0 || norm[0] > (1-m_hang)*norm[1])
        {
          if (recount == 0)
            {
              recount = 1;
            }
          else
            {
              recount = 0;
              m_op->incr(a_phi, e, 1.0);

              if (restarts == m_numRestarts)
                {
                  if (m_verbosity >= 4)
                    {
                      pout() << "      BiCGStab: max restarts reached" << endl;
                      pout() << "                init  norm = " << initial_norm << endl;
                      pout() << "                final norm = " << norm[0] << endl;
                    }

                  CH_STOP(timeMainLoop);

                  CH_START(timeCleanup);

                  m_exitStatus = 3;

                  // need to call clear just in case
                  // this is not ideal -- maybe change the return
                  // to exit
                  m_op->clear(r);
                  m_op->clear(r_tilde);
                  m_op->clear(e);
                  m_op->clear(p);
                  m_op->clear(p_tilde);
                  m_op->clear(s_tilde);
                  m_op->clear(t);
                  m_op->clear(v);

                  CH_STOP(timeCleanup);

                  return;
                }

              {
                CH_TIME("BiCGStabSolver::solve::Restart");

                m_op->residual(r, a_phi, a_rhs, m_homogeneous);
                norm[0] = m_op->norm(r, m_normType);
                rho[1]=0.0; rho[1]=0.0; rho[2]=0.0; rho[3]=0.0;
                alpha[0]=0; beta[0]=0; omega[0]=0;
                m_op->assignLocal(r_tilde, r);
                m_op->setToZero(e);

                restarts++;
              }

              if (m_verbosity >= 4)
                {
                  pout() << "      BiCGStab::   restart =  " << restarts << "\n";
                }

              init = true;
            }
        }
    }
  CH_STOP(timeMainLoop);

  CH_START(timeCleanup);

  if (m_verbosity >= 4)
    {
      pout() << "      BiCGStab:: " << i << " iterations, final Residual norm = "
             << norm[0] << "\n";
    }

  m_op->incr(a_phi, e, 1.0);

  m_op->clear(r);
  m_op->clear(r_tilde);
  m_op->clear(e);
  m_op->clear(p);
  m_op->clear(p_tilde);
  m_op->clear(s_tilde);
  m_op->clear(t);
  m_op->clear(v);

  CH_STOP(timeCleanup);
}

template <class T>
void BiCGStabSolver<T>::setConvergenceMetrics(Real a_metric,
                                              Real a_tolerance)
{
  m_convergenceMetric = a_metric;
  m_eps = a_tolerance;
}

#include "NamespaceFooter.H"
#endif /*_BICGSTABSOLVER_H_*/