/usr/include/deal.II/lac/iterative_inverse.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 1999 - 2015 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 at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__iterative_inverse_h
#define dealii__iterative_inverse_h
#include <deal.II/base/config.h>
#include <deal.II/base/smartpointer.h>
#include <deal.II/lac/solver_selector.h>
#include <deal.II/lac/vector_memory.h>
#include <deal.II/lac/pointer_matrix.h>
DEAL_II_NAMESPACE_OPEN
/**
* Implementation of the inverse of a matrix, using an iterative method.
*
* The function vmult() of this class starts an iterative solver in order to
* approximate the action of the inverse matrix.
*
* Krylov space methods like SolverCG or SolverBicgstab become inefficient if
* solution down to machine accuracy is needed. This is due to the fact, that
* round-off errors spoil the orthogonality of the vector sequences.
* Therefore, a nested iteration of two methods is proposed: The outer method
* is SolverRichardson, since it is robust with respect to round-of errors.
* The inner loop is an appropriate Krylov space method, since it is fast.
*
* @code
* // Declare related objects
* SparseMatrix<double> A;
* Vector<double> x;
* Vector<double> b;
* GrowingVectorMemory<Vector<double> > mem;
*
* ReductionControl inner_control (10, 1.e-30, 1.e-2);
* PreconditionSSOR <SparseMatrix<double> > inner_precondition;
* inner_precondition.initialize (A, 1.2);
*
* IterativeInverse<Vector<double> > precondition;
* precondition.initialize (A, inner_precondition);
* precondition.solver.select("cg");
* precondition.solver.set_control(inner_control);
*
* SolverControl outer_control(100, 1.e-16);
* SolverRichardson<Vector<double> > outer_iteration;
*
* outer_iteration.solve (A, x, b, precondition);
* @endcode
*
* Each time we call the inner loop, reduction of the residual by a factor
* <tt>1.e-2</tt> is attempted. Since the right hand side vector of the inner
* iteration is the residual of the outer loop, the relative errors are far
* from machine accuracy, even if the errors of the outer loop are in the
* range of machine accuracy.
*
* @deprecated If deal.II was configured with C++11 support, use the
* LinearOperator class instead, see the module on
* @ref LAOperators "linear operators"
* for further details.
*
* @ingroup Matrix2
* @author Guido Kanschat
* @date 2010
*/
template <typename VectorType>
class IterativeInverse : public Subscriptor
{
public:
/**
* Initialization function. Provide a matrix and preconditioner for the
* solve in vmult().
*/
template <typename MatrixType, typename PreconditionerType>
void initialize (const MatrixType &, const PreconditionerType &);
/**
* Delete the pointers to matrix and preconditioner.
*/
void clear();
/**
* Solve for right hand side <tt>src</tt>.
*/
void vmult (VectorType &dst, const VectorType &src) const;
/**
* Solve for right hand side <tt>src</tt>, but allow for the fact that the
* vectors given to this function have different type from the vectors used
* by the inner solver.
*/
template <class OtherVectorType>
void vmult (OtherVectorType &dst, const OtherVectorType &src) const;
/**
* The solver, which allows selection of the actual solver as well as
* adjustment of parameters.
*/
SolverSelector<VectorType> solver;
private:
/**
* The matrix in use.
*/
std_cxx11::shared_ptr<PointerMatrixBase<VectorType> > matrix;
/**
* The preconditioner to use.
*/
std_cxx11::shared_ptr<PointerMatrixBase<VectorType> > preconditioner;
};
template <typename VectorType>
template <typename MatrixType, typename PreconditionerType>
inline
void
IterativeInverse<VectorType>::initialize(const MatrixType &m, const PreconditionerType &p)
{
// dummy variable
VectorType *v = 0;
matrix = std_cxx11::shared_ptr<PointerMatrixBase<VectorType> > (new_pointer_matrix_base(m, *v));
preconditioner = std_cxx11::shared_ptr<PointerMatrixBase<VectorType> > (new_pointer_matrix_base(p, *v));
}
template <typename VectorType>
inline
void
IterativeInverse<VectorType>::clear()
{
matrix = 0;
preconditioner = 0;
}
template <typename VectorType>
inline void
IterativeInverse<VectorType>::vmult (VectorType &dst, const VectorType &src) const
{
Assert(matrix.get() != 0, ExcNotInitialized());
Assert(preconditioner.get() != 0, ExcNotInitialized());
dst = 0.;
solver.solve(*matrix, dst, src, *preconditioner);
}
template <typename VectorType>
template <class OtherVectorType>
inline void
IterativeInverse<VectorType>::vmult (OtherVectorType &dst, const OtherVectorType &src) const
{
Assert(matrix.get() != 0, ExcNotInitialized());
Assert(preconditioner.get() != 0, ExcNotInitialized());
GrowingVectorMemory<VectorType> mem;
typename VectorMemory<VectorType>::Pointer sol(mem);
typename VectorMemory<VectorType>::Pointer rhs(mem);
sol->reinit(dst);
*rhs = src;
solver.solve(*matrix, *sol, *rhs, *preconditioner);
dst = *sol;
}
DEAL_II_NAMESPACE_CLOSE
#endif
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