/usr/include/deal.II/lac/solver

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//
// Copyright (C) 1999 - 2015 by the deal.II authors
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#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/lac/solver.h>
#include <deal.II/lac/solver_control.h>
#include <deal.II/base/subscriptor.h>

DEAL_II_NAMESPACE_OPEN

/*!@addtogroup Solvers */
/*@{*/

/**
 * Implementation of the preconditioned Richardson iteration method. The
 * stopping criterion is the norm of the residual.
 *
 * For the requirements on matrices and vectors in order to work with this
 * class, see the documentation of the Solver base class.
 *
 * Like all other solver classes, this class has a local structure called @p
 * AdditionalData which is used to pass additional parameters to the solver,
 * like damping parameters or the number of temporary vectors. We use this
 * additional structure instead of passing these values directly to the
 * constructor because this makes the use of the @p SolverSelector and other
 * classes much easier and guarantees that these will continue to work even if
 * number or type of the additional parameters for a certain solver changes.
 *
 * For the Richardson method, the additional data is the damping parameter,
 * which is the only content of the @p AdditionalData structure. By default,
 * the constructor of the structure sets it to one.
 *
 *
 * <h3>Observing the progress of linear solver iterations</h3>
 *
 * The solve() function of this class uses the mechanism described in the
 * Solver base class to determine convergence. This mechanism can also be used
 * to observe the progress of the iteration.
 *
 *
 * @author Ralf Hartmann
 */
template <class VectorType = Vector<double> >
class SolverRichardson : public Solver<VectorType>
{
public:
  /**
   * Standardized data struct to pipe additional data to the solver.
   */
  struct AdditionalData
  {
    /**
     * Constructor. By default, set the damping parameter to one.
     */
    explicit
    AdditionalData (const double omega                       = 1,
                    const bool   use_preconditioned_residual = false);

    /**
     * Relaxation parameter.
     */
    double omega;

    /**
     * Parameter for stopping criterion.
     */
    bool use_preconditioned_residual;

  };

  /**
   * Constructor.
   */
  SolverRichardson (SolverControl            &cn,
                    VectorMemory<VectorType> &mem,
                    const AdditionalData     &data=AdditionalData());

  /**
   * Constructor. Use an object of type GrowingVectorMemory as a default to
   * allocate memory.
   */
  SolverRichardson (SolverControl        &cn,
                    const AdditionalData &data=AdditionalData());

  /**
   * Virtual destructor.
   */
  virtual ~SolverRichardson ();

  /**
   * Solve the linear system $Ax=b$ for x.
   */
  template<typename MatrixType, typename PreconditionerType>
  void
  solve (const MatrixType         &A,
         VectorType               &x,
         const VectorType         &b,
         const PreconditionerType &precondition);

  /**
   * Solve $A^Tx=b$ for $x$.
   */
  template<typename MatrixType, typename PreconditionerType>
  void
  Tsolve (const MatrixType         &A,
          VectorType               &x,
          const VectorType         &b,
          const PreconditionerType &precondition);

  /**
   * Set the damping-coefficient. Default is 1., i.e. no damping.
   */
  void set_omega (const double om=1.);

  /**
   * Interface for derived class. This function gets the current iteration
   * vector, the residual and the update vector in each step. It can be used
   * for a graphical output of the convergence history.
   */
  virtual void print_vectors (const unsigned int step,
                              const VectorType &x,
                              const VectorType &r,
                              const VectorType &d) const;

protected:
  /**
   * Implementation of the computation of the norm of the residual.
   */
  virtual typename VectorType::value_type criterion();

  /**
   * Residual. Temporary vector allocated through the VectorMemory object at
   * the start of the actual solution process and deallocated at the end.
   */
  VectorType *Vr;
  /**
   * Preconditioned residual. Temporary vector allocated through the
   * VectorMemory object at the start of the actual solution process and
   * deallocated at the end.
   */
  VectorType *Vd;

  /**
   * Control parameters.
   */
  AdditionalData additional_data;

  /**
   * Within the iteration loop, the norm of the residual is stored in this
   * variable. The function @p criterion uses this variable to compute the
   * convergence value, which in this class is the norm of the residual vector
   * and thus the square root of the @p res2 value.
   */
  typename VectorType::value_type res;
};

/*@}*/
/*----------------- 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)
  :
  Solver<VectorType> (cn,mem),
  additional_data(data)
{}



template <class VectorType>
SolverRichardson<VectorType>::SolverRichardson(SolverControl        &cn,
                                               const AdditionalData &data)
  :
  Solver<VectorType> (cn),
  additional_data(data)
{}



template <class VectorType>
SolverRichardson<VectorType>::~SolverRichardson()
{}


template <class VectorType>
template <typename MatrixType, typename PreconditionerType>
void
SolverRichardson<VectorType>::solve (const MatrixType         &A,
                                     VectorType               &x,
                                     const VectorType         &b,
                                     const PreconditionerType &precondition)
{
  SolverControl::State conv=SolverControl::iterate;

  double last_criterion = -std::numeric_limits<double>::max();

  unsigned int iter = 0;

  // Memory allocation
  Vr  = this->memory.alloc();
  VectorType &r  = *Vr;
  r.reinit(x);
  Vd  = this->memory.alloc();
  VectorType &d  = *Vd;
  d.reinit(x);

  deallog.push("Richardson");

  try
    {
      // 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);
          precondition.vmult(d,r);

          // The required norm of the
          // (preconditioned)
          // residual is computed in
          // criterion() and stored
          // in res.
          last_criterion = criterion();
          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;
        }
    }
  catch (...)
    {
      this->memory.free(Vr);
      this->memory.free(Vd);
      deallog.pop();
      throw;
    }
  // Deallocate Memory
  this->memory.free(Vr);
  this->memory.free(Vd);
  deallog.pop();

  // 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 &precondition)
{
  SolverControl::State conv=SolverControl::iterate;
  double last_criterion = -std::numeric_limits<double>::max();

  unsigned int iter = 0;

  // Memory allocation
  Vr  = this->memory.alloc();
  VectorType &r  = *Vr;
  r.reinit(x);
  Vd  =this-> memory.alloc();
  VectorType &d  = *Vd;
  d.reinit(x);

  deallog.push("RichardsonT");

  try
    {
      // 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);
          precondition.Tvmult(d,r);

          last_criterion = criterion();
          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;
        }
    }
  catch (...)
    {
      this->memory.free(Vr);
      this->memory.free(Vd);
      deallog.pop();
      throw;
    }

  // Deallocate Memory
  this->memory.free(Vr);
  this->memory.free(Vd);
  deallog.pop();
  // 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()
{
  if (!additional_data.use_preconditioned_residual)
    res = Vr->l2_norm();
  else
    res = Vd->l2_norm();
  return res;
}


template <class VectorType>
inline void
SolverRichardson<VectorType>::set_omega (const double om)
{
  additional_data.omega=om;
}

#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif
libdeal.ii-dev 8.4.2-2+b1 / usr / include / deal.II / lac / solver_richardson.h
