solver_richardson.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 1999 - 2021 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.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_solver_richardson_h
#define dealii_solver_richardson_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/logstream.h>
#include <deal.II/base/signaling_nan.h>
 
#include <deal.II/lac/solver.h>
#include <deal.II/lac/solver_control.h>
 
DEAL_II_NAMESPACE_OPEN
 
 
template <class VectorType = Vector<double>>
class SolverRichardson : public SolverBase<VectorType>
{
public:
  struct AdditionalData
  {
    explicit AdditionalData(const double omega                       = 1,
                            const bool   use_preconditioned_residual = false);
 
    double omega;
 
    bool use_preconditioned_residual;
  };
 
  SolverRichardson(SolverControl &           cn,
                   VectorMemory<VectorType> &mem,
                   const AdditionalData &    data = AdditionalData());
 
  SolverRichardson(SolverControl &       cn,
                   const AdditionalData &data = AdditionalData());
 
  virtual ~SolverRichardson() override = default;
 
  template <typename MatrixType, typename PreconditionerType>
  void
  solve(const MatrixType &        A,
        VectorType &              x,
        const VectorType &        b,
        const PreconditionerType &preconditioner);
 
  template <typename MatrixType, typename PreconditionerType>
  void
  Tsolve(const MatrixType &        A,
         VectorType &              x,
         const VectorType &        b,
         const PreconditionerType &preconditioner);
 
  void
  set_omega(const double om = 1.);
 
  virtual void
  print_vectors(const unsigned int step,
                const VectorType & x,
                const VectorType & r,
                const VectorType & d) const;
 
protected:
  virtual typename VectorType::value_type
  criterion(const VectorType &r, const VectorType &d) const;
 
  AdditionalData additional_data;
};
 
/*----------------- Implementation of the Richardson Method ------------------*/
 
#ifndef DOXYGEN
 
template <class VectorType>
inline SolverRichardson<VectorType>::AdditionalData::AdditionalData(
  const double omega,
  const bool   use_preconditioned_residual)
  : omega(omega)
  , use_preconditioned_residual(use_preconditioned_residual)
{}
 
 
template <class VectorType>
SolverRichardson<VectorType>::SolverRichardson(SolverControl &           cn,
                                               VectorMemory<VectorType> &mem,
                                               const AdditionalData &    data)
  : SolverBase<VectorType>(cn, mem)
  , additional_data(data)
{}
 
 
 
template <class VectorType>
SolverRichardson<VectorType>::SolverRichardson(SolverControl &       cn,
                                               const AdditionalData &data)
  : SolverBase<VectorType>(cn)
  , additional_data(data)
{}
 
 
 
template <class VectorType>
template <typename MatrixType, typename PreconditionerType>
void
SolverRichardson<VectorType>::solve(const MatrixType &        A,
                                    VectorType &              x,
                                    const VectorType &        b,
                                    const PreconditionerType &preconditioner)
{
  SolverControl::State conv = SolverControl::iterate;
 
  double last_criterion = std::numeric_limits<double>::lowest();
 
  unsigned int iter = 0;
 
  // Memory allocation.
  // 'Vr' holds the residual, 'Vd' the preconditioned residual
  typename VectorMemory<VectorType>::Pointer Vr(this->memory);
  typename VectorMemory<VectorType>::Pointer Vd(this->memory);
 
  VectorType &r = *Vr;
  r.reinit(x);
 
  VectorType &d = *Vd;
  d.reinit(x);
 
  LogStream::Prefix prefix("Richardson");
 
  // Main loop
  while (conv == SolverControl::iterate)
    {
      // Do not use residual,
      // but do it in 2 steps
      A.vmult(r, x);
      r.sadd(-1., 1., b);
      preconditioner.vmult(d, r);
 
      // get the required norm of the (possibly preconditioned)
      // residual
      last_criterion = criterion(r, d);
      conv           = this->iteration_status(iter, last_criterion, x);
      if (conv != SolverControl::iterate)
        break;
 
      x.add(additional_data.omega, d);
      print_vectors(iter, x, r, d);
 
      ++iter;
    }
 
  // in case of failure: throw exception
  if (conv != SolverControl::success)
    AssertThrow(false, SolverControl::NoConvergence(iter, last_criterion));
  // otherwise exit as normal
}
 
 
 
template <class VectorType>
template <typename MatrixType, typename PreconditionerType>
void
SolverRichardson<VectorType>::Tsolve(const MatrixType &        A,
                                     VectorType &              x,
                                     const VectorType &        b,
                                     const PreconditionerType &preconditioner)
{
  SolverControl::State conv           = SolverControl::iterate;
  double               last_criterion = std::numeric_limits<double>::lowest();
 
  unsigned int iter = 0;
 
  // Memory allocation.
  // 'Vr' holds the residual, 'Vd' the preconditioned residual
  typename VectorMemory<VectorType>::Pointer Vr(this->memory);
  typename VectorMemory<VectorType>::Pointer Vd(this->memory);
 
  VectorType &r = *Vr;
  r.reinit(x);
 
  VectorType &d = *Vd;
  d.reinit(x);
 
  LogStream::Prefix prefix("RichardsonT");
 
  // Main loop
  while (conv == SolverControl::iterate)
    {
      // Do not use Tresidual,
      // but do it in 2 steps
      A.Tvmult(r, x);
      r.sadd(-1., 1., b);
      preconditioner.Tvmult(d, r);
 
      last_criterion = criterion(r, d);
      conv           = this->iteration_status(iter, last_criterion, x);
      if (conv != SolverControl::iterate)
        break;
 
      x.add(additional_data.omega, d);
      print_vectors(iter, x, r, d);
 
      ++iter;
    }
 
  // in case of failure: throw exception
  if (conv != SolverControl::success)
    AssertThrow(false, SolverControl::NoConvergence(iter, last_criterion));
 
  // otherwise exit as normal
}
 
 
template <class VectorType>
void
SolverRichardson<VectorType>::print_vectors(const unsigned int,
                                            const VectorType &,
                                            const VectorType &,
                                            const VectorType &) const
{}
 
 
 
template <class VectorType>
inline typename VectorType::value_type
SolverRichardson<VectorType>::criterion(const VectorType &r,
                                        const VectorType &d) const
{
  if (!additional_data.use_preconditioned_residual)
    return r.l2_norm();
  else
    return d.l2_norm();
}
 
 
template <class VectorType>
inline void
SolverRichardson<VectorType>::set_omega(const double om)
{
  additional_data.omega = om;
}
 
#endif // DOXYGEN
 
DEAL_II_NAMESPACE_CLOSE
 
#endif