solver_bicgstab.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 1998 - 2019 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_bicgstab_h
#define dealii_solver_bicgstab_h


#include <deal.II/base/config.h>

#include <deal.II/base/logstream.h>
#include <deal.II/base/signaling_nan.h>
#include <deal.II/base/subscriptor.h>

#include <deal.II/lac/solver.h>
#include <deal.II/lac/solver_control.h>

#include <cmath>

DEAL_II_NAMESPACE_OPEN


namespace internal
{
  class SolverBicgstabData
  {
  protected:
    double alpha;
    double beta;
    double omega;
    double rho;
    double rhobar;

    unsigned int step;

    double res;

    SolverBicgstabData();
  };
} // namespace internal

template <typename VectorType = Vector<double>>
class SolverBicgstab : public SolverBase<VectorType>,
                       protected internal::SolverBicgstabData
{
public:
  struct AdditionalData
  {
    explicit AdditionalData(const bool   exact_residual = true,
                            const double breakdown      = 1.e-10)
      : exact_residual(exact_residual)
      , breakdown(breakdown)
    {}
    bool exact_residual;
    double breakdown;
  };

  SolverBicgstab(SolverControl &           cn,
                 VectorMemory<VectorType> &mem,
                 const AdditionalData &    data = AdditionalData());

  SolverBicgstab(SolverControl &       cn,
                 const AdditionalData &data = AdditionalData());

  virtual ~SolverBicgstab() override = default;

  template <typename MatrixType, typename PreconditionerType>
  void
  solve(const MatrixType &        A,
        VectorType &              x,
        const VectorType &        b,
        const PreconditionerType &preconditioner);

protected:
  VectorType *Vx;

  typename VectorMemory<VectorType>::Pointer Vr;

  typename VectorMemory<VectorType>::Pointer Vrbar;

  typename VectorMemory<VectorType>::Pointer Vp;

  typename VectorMemory<VectorType>::Pointer Vy;

  typename VectorMemory<VectorType>::Pointer Vz;

  typename VectorMemory<VectorType>::Pointer Vt;

  typename VectorMemory<VectorType>::Pointer Vv;

  const VectorType *Vb;

  template <typename MatrixType>
  double
  criterion(const MatrixType &A, const VectorType &x, const VectorType &b);

  virtual void
  print_vectors(const unsigned int step,
                const VectorType & x,
                const VectorType & r,
                const VectorType & d) const;

  AdditionalData additional_data;

private:
  template <typename MatrixType>
  SolverControl::State
  start(const MatrixType &A);

  struct IterationResult
  {
    bool                 breakdown;
    SolverControl::State state;
    unsigned int         last_step;
    double               last_residual;

    IterationResult(const bool                 breakdown,
                    const SolverControl::State state,
                    const unsigned int         last_step,
                    const double               last_residual);
  };

  template <typename MatrixType, typename PreconditionerType>
  IterationResult
  iterate(const MatrixType &A, const PreconditionerType &preconditioner);
};

/*-------------------------Inline functions -------------------------------*/

#ifndef DOXYGEN


template <typename VectorType>
SolverBicgstab<VectorType>::IterationResult::IterationResult(
  const bool                 breakdown,
  const SolverControl::State state,
  const unsigned int         last_step,
  const double               last_residual)
  : breakdown(breakdown)
  , state(state)
  , last_step(last_step)
  , last_residual(last_residual)
{}



template <typename VectorType>
SolverBicgstab<VectorType>::SolverBicgstab(SolverControl &           cn,
                                           VectorMemory<VectorType> &mem,
                                           const AdditionalData &    data)
  : SolverBase<VectorType>(cn, mem)
  , Vx(nullptr)
  , Vb(nullptr)
  , additional_data(data)
{}



template <typename VectorType>
SolverBicgstab<VectorType>::SolverBicgstab(SolverControl &       cn,
                                           const AdditionalData &data)
  : SolverBase<VectorType>(cn)
  , Vx(nullptr)
  , Vb(nullptr)
  , additional_data(data)
{}



template <typename VectorType>
template <typename MatrixType>
double
SolverBicgstab<VectorType>::criterion(const MatrixType &A,
                                      const VectorType &x,
                                      const VectorType &b)
{
  A.vmult(*Vt, x);
  Vt->add(-1., b);
  res = Vt->l2_norm();

  return res;
}



template <typename VectorType>
template <typename MatrixType>
SolverControl::State
SolverBicgstab<VectorType>::start(const MatrixType &A)
{
  A.vmult(*Vr, *Vx);
  Vr->sadd(-1., 1., *Vb);
  res = Vr->l2_norm();

  return this->iteration_status(step, res, *Vx);
}



template <typename VectorType>
void
SolverBicgstab<VectorType>::print_vectors(const unsigned int,
                                          const VectorType &,
                                          const VectorType &,
                                          const VectorType &) const
{}



template <typename VectorType>
template <typename MatrixType, typename PreconditionerType>
typename SolverBicgstab<VectorType>::IterationResult
SolverBicgstab<VectorType>::iterate(const MatrixType &        A,
                                    const PreconditionerType &preconditioner)
{
  // TODO:[GK] Implement "use the length of the computed orthogonal residual" in
  // the BiCGStab method.
  SolverControl::State state = SolverControl::iterate;
  alpha = omega = rho = 1.;

  VectorType &r    = *Vr;
  VectorType &rbar = *Vrbar;
  VectorType &p    = *Vp;
  VectorType &y    = *Vy;
  VectorType &z    = *Vz;
  VectorType &t    = *Vt;
  VectorType &v    = *Vv;

  rbar         = r;
  bool startup = true;

  do
    {
      ++step;

      rhobar = r * rbar;
      beta   = rhobar * alpha / (rho * omega);
      rho    = rhobar;
      if (startup == true)
        {
          p       = r;
          startup = false;
        }
      else
        {
          p.sadd(beta, 1., r);
          p.add(-beta * omega, v);
        }

      preconditioner.vmult(y, p);
      A.vmult(v, y);
      rhobar = rbar * v;

      alpha = rho / rhobar;

      // TODO:[?] Find better breakdown criterion

      if (std::fabs(alpha) > 1.e10)
        return IterationResult(true, state, step, res);

      res = std::sqrt(r.add_and_dot(-alpha, v, r));

      // check for early success, see the lac/bicgstab_early testcase as to
      // why this is necessary
      //
      // note: the vector *Vx we pass to the iteration_status signal here is
      // only the current approximation, not the one we will return with, which
      // will be x=*Vx + alpha*y
      if (this->iteration_status(step, res, *Vx) == SolverControl::success)
        {
          Vx->add(alpha, y);
          print_vectors(step, *Vx, r, y);
          return IterationResult(false, SolverControl::success, step, res);
        }

      preconditioner.vmult(z, r);
      A.vmult(t, z);
      rhobar = t * r;
      omega  = rhobar / (t * t);
      Vx->add(alpha, y, omega, z);

      if (additional_data.exact_residual)
        {
          r.add(-omega, t);
          res = criterion(A, *Vx, *Vb);
        }
      else
        res = std::sqrt(r.add_and_dot(-omega, t, r));

      state = this->iteration_status(step, res, *Vx);
      print_vectors(step, *Vx, r, y);
    }
  while (state == SolverControl::iterate);
  return IterationResult(false, state, step, res);
}


template <typename VectorType>
template <typename MatrixType, typename PreconditionerType>
void
SolverBicgstab<VectorType>::solve(const MatrixType &        A,
                                  VectorType &              x,
                                  const VectorType &        b,
                                  const PreconditionerType &preconditioner)
{
  LogStream::Prefix prefix("Bicgstab");
  Vr    = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vrbar = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vp    = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vy    = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vz    = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vt    = typename VectorMemory<VectorType>::Pointer(this->memory);
  Vv    = typename VectorMemory<VectorType>::Pointer(this->memory);

  Vr->reinit(x, true);
  Vrbar->reinit(x, true);
  Vp->reinit(x, true);
  Vy->reinit(x, true);
  Vz->reinit(x, true);
  Vt->reinit(x, true);
  Vv->reinit(x, true);

  Vx = &x;
  Vb = &b;

  step = 0;

  IterationResult state(false, SolverControl::failure, 0, 0);

  // iterate while the inner iteration returns a breakdown
  do
    {
      if (step != 0)
        deallog << "Restart step " << step << std::endl;
      if (start(A) == SolverControl::success)
        {
          state.state = SolverControl::success;
          break;
        }
      state = iterate(A, preconditioner);
      ++step;
    }
  while (state.breakdown == true);

  // in case of failure: throw exception
  AssertThrow(state.state == SolverControl::success,
              SolverControl::NoConvergence(state.last_step,
                                           state.last_residual));
  // otherwise exit as normal
}

#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif