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// $Id: trilinos_precondition.h 21411 2010-06-30 11:53:57Z bangerth $
// Version: $Name$
//
// Copyright (C) 2008, 2010 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__trilinos_precondition_h
#define __deal2__trilinos_precondition_h
#include <base/config.h>
#ifdef DEAL_II_USE_TRILINOS
# include <base/subscriptor.h>
# include <base/std_cxx1x/shared_ptr.h>
# include <lac/trilinos_vector_base.h>
# ifdef DEAL_II_COMPILER_SUPPORTS_MPI
# include <Epetra_MpiComm.h>
# else
# include <Epetra_SerialComm.h>
# endif
# include <Epetra_Map.h>
# include <Teuchos_ParameterList.hpp>
# include <Epetra_Operator.h>
# include <Epetra_Vector.h>
// forward declarations
class Ifpack_Preconditioner;
class Ifpack_Chebyshev;
namespace ML_Epetra
{
class MultiLevelPreconditioner;
}
DEAL_II_NAMESPACE_OPEN
// forward declarations
template <typename number> class SparseMatrix;
template <typename number> class Vector;
class SparsityPattern;
/*! @addtogroup TrilinosWrappers
*@{
*/
namespace TrilinosWrappers
{
// forward declarations
class SparseMatrix;
class BlockSparseMatrix;
class SolverBase;
/**
* The base class for all preconditioners based on Trilinos sparse
* matrices.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionBase : public Subscriptor
{
public:
/**
* Standardized data struct to
* pipe additional flags to the
* preconditioner.
*/
struct AdditionalData
{};
/**
* Constructor. Does not do
* anything. The
* <tt>initialize</tt> function
* of the derived classes will
* have to create the
* preconditioner from a given
* sparse matrix.
*/
PreconditionBase ();
/**
* Copy constructor.
*/
PreconditionBase (const PreconditionBase &);
/**
* Destructor.
*/
~PreconditionBase ();
/**
* Destroys the preconditioner, leaving
* an object like just after having
* called the constructor.
*/
void clear ();
/**
* Apply the preconditioner.
*/
void vmult (VectorBase &dst,
const VectorBase &src) const;
/**
* Apply the preconditioner on
* deal.II data structures
* instead of the ones provided
* in the Trilinos wrapper
* class.
*/
void vmult (dealii::Vector<double> &dst,
const dealii::Vector<double> &src) const;
/**
* Exception.
*/
DeclException1 (ExcNonMatchingMaps,
std::string,
<< "The sparse matrix the preconditioner is based on "
<< "uses a map that is not compatible to the one in vector "
<< arg1
<< ". Check preconditioner and matrix setup.");
friend class SolverBase;
friend class PreconditionStokes;
protected:
/**
* This is a pointer to the
* preconditioner object that
* is used when applying the
* preconditioner.
*/
std_cxx1x::shared_ptr<Epetra_Operator> preconditioner;
/**
* Internal communication
* pattern in case the matrix
* needs to be copied from
* deal.II format.
*/
#ifdef DEAL_II_COMPILER_SUPPORTS_MPI
Epetra_MpiComm communicator;
#else
Epetra_SerialComm communicator;
#endif
/**
* Internal Trilinos map in
* case the matrix needs to be
* copied from deal.II format.
*/
std_cxx1x::shared_ptr<Epetra_Map> vector_distributor;
};
/**
* A wrapper class for a (pointwise) Jacobi preconditioner for
* Trilinos matrices. This preconditioner works both in serial and in
* parallel, depending on the matrix it is based on.
*
* The AdditionalData data structure allows to set preconditioner
* options. For the Jacobi preconditioner, these options are the
* damping parameter <tt>omega</tt> and a <tt>min_diagonal</tt>
* argument that can be used to make the preconditioner work even if
* the matrix contains some zero elements on the diagonal. The default
* settings are 1 for the damping parameter and zero for the diagonal
* augmentation.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionJacobi : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional flags to the
* preconditioner. The
* parameter <tt>omega</tt>
* specifies the relaxation
* parameter in the Jacobi
* preconditioner. The
* parameter
* <tt>min_diagonal</tt> can be
* used to make the application
* of the preconditioner also
* possible when some diagonal
* elements are zero. In a
* default application this
* would mean that we divide by
* zero, so by setting the
* parameter
* <tt>min_diagonal</tt> to a
* small nonzero value the SOR
* will work on a matrix that
* is not too far away from the
* one we want to
* treat.
*/
struct AdditionalData
{
/**
* Constructor. By default, set
* the damping parameter to
* one, and do not modify the
* diagonal.
*/
AdditionalData (const double omega = 1,
const double min_diagonal = 0);
/**
* This specifies the
* relaxation parameter in the
* Jacobi preconditioner.
*/
double omega;
/**
* This specifies the minimum
* value the diagonal elements
* should have. This might be
* necessary when the Jacobi
* preconditioner is used on
* matrices with zero diagonal
* elements. In that case, a
* straight-forward application
* would not be possible since
* we would divide by zero.
*/
double min_diagonal;
};
/**
* Take the sparse matrix the
* preconditioner object should
* be built of, and additional
* flags (damping parameter,
* etc.) if there are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for a (pointwise) SSOR preconditioner for Trilinos
* matrices. This preconditioner works both in serial and in parallel,
* depending on the matrix it is based on.
*
* The AdditionalData data structure allows to set preconditioner
* options. For the SSOR preconditioner, these options are the
* damping/relaxation parameter <tt>omega</tt>, a
* <tt>min_diagonal</tt> argument that can be used to make the
* preconditioner work even if the matrix contains some zero elements
* on the diagonal, and a parameter <tt>overlap</tt> that determines
* if and how much overlap there should be between the matrix
* partitions on the various MPI processes. The default settings are 1
* for the relaxation parameter, 0 for the diagonal augmentation and 0
* for the overlap.
*
* Note that a parallel applicatoin of the SSOR preconditioner is
* actually a block-Jacobi preconditioner with block size equal to the
* local matrix size. Spoken more technically, this parallel operation
* is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an SSOR <em>approximate solve</em> as inner
* solver, based on the outer parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Wolfgang Bangerth, 2008
*/
class PreconditionSSOR : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional flags to the
* preconditioner. The
* parameter <tt>omega</tt>
* specifies the relaxation
* parameter in the SSOR
* preconditioner. The
* parameter
* <tt>min_diagonal</tt> can be
* used to make the application
* of the preconditioner also
* possible when some diagonal
* elements are zero. In a
* default application this
* would mean that we divide by
* zero, so by setting the
* parameter
* <tt>min_diagonal</tt> to a
* small nonzero value the SOR
* will work on a matrix that
* is not too far away from the
* one we want to
* treat. Finally,
* <tt>overlap</tt> governs the
* overlap of the partitions
* when the preconditioner runs
* in parallel, forming a
* so-called additive Schwarz
* preconditioner.
*/
struct AdditionalData
{
/**
* Constructor. By default, set
* the damping parameter to
* one, we do not modify the
* diagonal, and there is no
* overlap (i.e. in parallel,
* we run a BlockJacobi
* preconditioner, where each
* block is inverted
* approximately by an SSOR.
*/
AdditionalData (const double omega = 1,
const double min_diagonal = 0,
const unsigned int overlap = 0);
/**
* This specifies the (over-)
* relaxation parameter in the
* SSOR preconditioner.
*/
double omega;
/**
* This specifies the minimum
* value the diagonal elements
* should have. This might be
* necessary when the SSOR
* preconditioner is used on
* matrices with zero diagonal
* elements. In that case, a
* straight-forward application
* would not be possible since
* we divide by the diagonal
* element.
*/
double min_diagonal;
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Take the sparse matrix the
* preconditioner object should
* be built of, and additional
* flags (damping parameter,
* overlap in parallel
* computations, etc.) if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for a (pointwise) SOR preconditioner for Trilinos
* matrices. This preconditioner works both in serial and in parallel,
* depending on the matrix it is based on.
*
* The AdditionalData data structure allows to set preconditioner
* options. For the SOR preconditioner, these options are the
* damping/relaxation parameter <tt>omega</tt>, a
* <tt>min_diagonal</tt> argument that can be used to make the
* preconditioner work even if the matrix contains some zero elements
* on the diagonal, and a parameter <tt>overlap</tt> that determines
* if and how much overlap there should be between the matrix
* partitions on the various MPI processes. The default settings are 1
* for the relaxation parameter, 0 for the diagonal augmentation and 0
* for the overlap.
*
* Note that a parallel applicatoin of the SOR preconditioner is
* actually a block-Jacobi preconditioner with block size equal to the
* local matrix size. Spoken more technically, this parallel operation
* is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an SOR <em>approximate solve</em> as inner
* solver, based on the outer parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionSOR : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional flags to the
* preconditioner. The
* parameter <tt>omega</tt>
* specifies the relaxation
* parameter in the SOR
* preconditioner. The
* parameter
* <tt>min_diagonal</tt> can be
* used to make the application
* of the preconditioner also
* possible when some diagonal
* elements are zero. In a
* default application this
* would mean that we divide by
* zero, so by setting the
* parameter
* <tt>min_diagonal</tt> to a
* small nonzero value the SOR
* will work on a matrix that
* is not too far away from the
* one we want to
* treat. Finally,
* <tt>overlap</tt> governs the
* overlap of the partitions
* when the preconditioner runs
* in parallel, forming a
* so-called additive Schwarz
* preconditioner.
*/
struct AdditionalData
{
/**
* Constructor. By default, set
* the damping parameter to
* one, we do not modify the
* diagonal, and there is no
* overlap (i.e. in parallel,
* we run a BlockJacobi
* preconditioner, where each
* block is inverted
* approximately by an SOR.
*/
AdditionalData (const double omega = 1,
const double min_diagonal = 0,
const unsigned int overlap = 0);
/**
* This specifies the (over-)
* relaxation parameter in the
* SOR preconditioner.
*/
double omega;
/**
* This specifies the minimum
* value the diagonal elements
* should have. This might be
* necessary when the SOR
* preconditioner is used on
* matrices with zero diagonal
* elements. In that case, a
* straight-forward application
* would not be possible since
* we divide by the diagonal
* element.
*/
double min_diagonal;
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Take the sparse matrix the
* preconditioner object should
* be built of, and additional
* flags (damping parameter,
* overlap in parallel
* computations etc.) if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for an incomplete Cholesky factorization (IC)
* preconditioner for @em symmetric Trilinos matrices. This
* preconditioner works both in serial and in parallel, depending on
* the matrix it is based on. In general, an incomplete factorization
* does not take all fill-in elements that would appear in a full
* factorization (that is the basis for a direct solve). Trilinos
* allows to set the amount of fill-in elements, governed by the
* additional data argument <tt>ic_fill</tt>, so one can gradually
* choose between a factorization on the sparse matrix structure only
* (<tt>ic_fill=0</tt>) to a full factorization (<tt>ic_fill</tt> in
* the range of 10 to 50, depending on the spatial dimension of the
* PDE problem and the degree of the finite element basis functions;
* generally, more required fill-in elements require this parameter to
* be set to a higher integer value).
*
* The AdditionalData data structure allows to set preconditioner
* options. Besides the fill-in argument, these options are some
* options for perturbations (see the documentation of the
* AdditionalData structure for details), and a parameter
* <tt>overlap</tt> that determines if and how much overlap there
* should be between the matrix partitions on the various MPI
* processes. The default settings are 0 for the additional fill-in, 0
* for the absolute augmentation tolerance, 1 for the relative
* augmentation tolerance, 0 for the overlap.
*
* Note that a parallel applicatoin of the IC preconditioner is
* actually a block-Jacobi preconditioner with block size equal to the
* local matrix size. Spoken more technically, this parallel operation
* is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an IC <em>approximate solve</em> as inner
* solver, based on the (outer) parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionIC : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional parameters
* to the preconditioner. The
* Trilinos IC decomposition
* allows for some fill-in, so
* it actually is a threshold
* incomplete Cholesky
* factorization. The amount of
* fill-in, and hence, the
* amount of memory used by
* this preconditioner, is
* controlled by the parameter
* <tt>ic_fill</tt>, which
* specifies this as a
* double. When forming the
* preconditioner, for certain
* problems bad conditioning
* (or just bad luck) can cause
* the preconditioner to be
* very poorly
* conditioned. Hence it can
* help to add diagonal
* perturbations to the
* original matrix and form the
* preconditioner for this
* slightly better
* matrix. <tt>ic_atol</tt> is
* an absolute perturbation
* that is added to the
* diagonal before forming the
* prec, and <tt>ic_rtol</tt>
* is a scaling factor $rtol
* \geq 1$. The last parameter
* specifies the overlap of the
* partitions when the
* preconditioner runs in
* parallel.
*/
struct AdditionalData
{
/**
* Constructor. By default, set
* the drop tolerance to 0, the
* level of extra fill-ins is
* set to be zero (just use the
* matrix structure, do not
* generate any additional
* fill-in), the tolerance
* level are 0 and 1,
* respectively, and the
* overlap in case of a
* parallel execution is
* zero. This overlap in a
* block-application of the IC
* in the parallel case makes
* the preconditioner a
* so-called additive Schwarz
* preconditioner.
*/
AdditionalData (const unsigned int ic_fill = 0,
const double ic_atol = 0.,
const double ic_rtol = 1.,
const unsigned int overlap = 0);
/**
* This specifies the amount of
* additional fill-in elements
* besides the sparse matrix
* structure. When
* <tt>ic_fill</tt> is large,
* this means that many
* fill-ins will be added, so
* that the IC preconditioner
* comes closer to a direct
* sparse Cholesky
* decomposition. Note,
* however, that this will
* drastically increase the
* memory requirement,
* especially when the
* preconditioner is used in
* 3D.
*/
unsigned int ic_fill;
/**
* This specifies the amount of
* an absolute perturbation
* that will be added to the
* diagonal of the matrix,
* which sometimes can help to
* get better preconditioners.
*/
double ic_atol;
/**
* This specifies the factor by
* which the diagonal of the
* matrix will be scaled, which
* sometimes can help to get
* better preconditioners.
*/
double ic_rtol;
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Initialize function. Takes
* the matrix the
* preconditioner should be
* computed of, and additional
* flags if there are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for an incomplete LU factorization (ILU)
* preconditioner for Trilinos matrices. This preconditioner works
* both in serial and in parallel, depending on the matrix it is based
* on. In general, an incomplete factorization does not take all
* fill-in elements that would appear in a full factorization (that is
* the basis for a direct solve). Trilinos allows to set the amount of
* fill-in elements, governed by the additional data argument
* <tt>ilu_fill</tt>, so one can gradually choose between a
* factorization on the sparse matrix structure only
* (<tt>ilu_fill=0</tt>) to a full factorization (<tt>ilu_fill</tt> in
* the range of 10 to 50, depending on the spatial dimension of the
* PDE problem and the degree of the finite element basis functions;
* generally, more required fill-in elements require this parameter to
* be set to a higher integer value).
*
* The AdditionalData data structure allows to set preconditioner
* options. Besides the fill-in argument, these options are some
* options for perturbations (see the documentation of the
* AdditionalData structure for details), and a parameter
* <tt>overlap</tt> that determines if and how much overlap there
* should be between the matrix partitions on the various MPI
* processes. The default settings are 0 for the additional fill-in, 0
* for the absolute augmentation tolerance, 1 for the relative
* augmentation tolerance, 0 for the overlap.
*
* Note that a parallel applicatoin of the ILU preconditioner is
* actually a block-Jacobi preconditioner with block size equal to the
* local matrix size. Spoken more technically, this parallel operation
* is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an ILU <em>approximate solve</em> as inner
* solver, based on the (outer) parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionILU : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional parameters
* to the preconditioner. The
* Trilinos ILU decomposition
* allows for some fill-in, so
* it actually is a threshold
* incomplete LU
* factorization. The amount of
* fill-in, and hence, the
* amount of memory used by
* this preconditioner, is
* controlled by the parameter
* <tt>ilu_fill</tt>, which
* specifies this as a
* double. When forming the
* preconditioner, for certain
* problems bad conditioning
* (or just bad luck) can cause
* the preconditioner to be
* very poorly
* conditioned. Hence it can
* help to add diagonal
* perturbations to the
* original matrix and form the
* preconditioner for this
* slightly better
* matrix. <tt>ilu_atol</tt> is
* an absolute perturbation
* that is added to the
* diagonal before forming the
* prec, and <tt>ilu_rtol</tt>
* is a scaling factor $rtol
* \geq 1$. The last parameter
* specifies the overlap of the
* partitions when the
* preconditioner runs in
* parallel.
*/
struct AdditionalData
{
/**
* Constructor. By default, the
* level of extra fill-ins is
* set to be zero (just use the
* matrix structure, do not
* generate any additional
* fill-in), the tolerance
* level are 0 and 1,
* respectively, and the
* overlap in case of a
* parallel execution is
* zero. This overlap in a
* block-application of the ILU
* in the parallel case makes
* the preconditioner a
* so-called additive Schwarz
* preconditioner.
*/
AdditionalData (const unsigned int ilu_fill = 0,
const double ilu_atol = 0.,
const double ilu_rtol = 1.,
const unsigned int overlap = 0);
/**
* This specifies the amount of
* additional fill-in elements
* besides the sparse matrix
* structure. When
* <tt>ilu_fill</tt> is large,
* this means that many
* fill-ins will be added, so
* that the ILU preconditioner
* comes closer to a (direct)
* sparse LU
* decomposition. Note,
* however, that this will
* drastically increase the
* memory requirement,
* especially when the
* preconditioner is used in
* 3D.
*/
unsigned int ilu_fill;
/**
* This specifies the amount of
* an absolute perturbation
* that will be added to the
* diagonal of the matrix,
* which sometimes can help to
* get better preconditioners.
*/
double ilu_atol;
/**
* This specifies the factor by
* which the diagonal of the
* matrix will be scaled, which
* sometimes can help to get
* better preconditioners.
*/
double ilu_rtol;
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Initialize function. Takes
* the matrix which is used to
* form the preconditioner, and
* additional flags if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for a thresholded incomplete LU factorization (ILU-T)
* preconditioner for Trilinos matrices. This preconditioner works both in
* serial and in parallel, depending on the matrix it is based on. In
* general, an incomplete factorization does not take all fill-in elements
* that would appear in a full factorization (that is the basis for a direct
* solve). For the ILU-T precondtioner, the parameter <tt>ilut_drop</tt>
* lets the user specify which elements should be dropped (i.e., should not
* be part of the incomplete decomposition). Trilinos calculates first the
* complete factorization for one row, and then skips those elements that
* are lower than the threshold. This is the main difference to the
* non-thresholded ILU preconditioner, where the parameter
* <tt>ilut_fill</tt> governs the incomplete factorization structure. This
* parameter is available here as well, but provides only some extra
* information here.
*
* The AdditionalData data structure allows to set preconditioner
* options. Besides the fill-in arguments, these options are some options
* for perturbations (see the documentation of the AdditionalData structure
* for details), and a parameter <tt>overlap</tt> that determines if and how
* much overlap there should be between the matrix partitions on the various
* MPI processes. The default settings are 0 for the additional fill-in, 0
* for the absolute augmentation tolerance, 1 for the relative augmentation
* tolerance, 0 for the overlap.
*
* Note that a parallel applicatoin of the ILU-T preconditioner is
* actually a block-Jacobi preconditioner with block size equal to the
* local matrix size. Spoken more technically, this parallel operation
* is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an ILU <em>approximate solve</em> as inner
* solver, based on the (outer) parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2009
*/
class PreconditionILUT : public PreconditionBase
{
public:
/**
* Standardized data struct to pipe
* additional parameters to the
* preconditioner. The Trilinos ILU-T
* decomposition allows for some
* fill-in, so it actually is a
* threshold incomplete LU
* factorization. The amount of
* fill-in, and hence, the amount of
* memory used by this
* preconditioner, is controlled by
* the parameters <tt>ilut_drop</tt>
* and <tt>ilut_fill</tt>, which
* specifies a threshold about which
* values should form the incomplete
* factorization and the level of
* additional fill-in. When forming
* the preconditioner, for certain
* problems bad conditioning (or just
* bad luck) can cause the
* preconditioner to be very poorly
* conditioned. Hence it can help to
* add diagonal perturbations to the
* original matrix and form the
* preconditioner for this slightly
* better matrix. <tt>ilut_atol</tt>
* is an absolute perturbation that
* is added to the diagonal before
* forming the prec, and
* <tt>ilu_rtol</tt> is a scaling
* factor $rtol \geq 1$. The last
* parameter specifies the overlap of
* the partitions when the
* preconditioner runs in parallel.
*/
struct AdditionalData
{
/**
* Constructor. By default, no
* element will be dropped, the level
* of extra fill-ins is set to be
* zero (just use the matrix
* structure, do not generate any
* additional fill-in except the one
* that results from non-dropping
* large elements), the tolerance
* level are 0 and 1, respectively,
* and the overlap in case of a
* parallel execution is zero. This
* overlap in a block-application of
* the ILU in the parallel case makes
* the preconditioner a so-called
* additive Schwarz preconditioner.
*/
AdditionalData (const double ilut_drop = 0.,
const unsigned int ilut_fill = 0,
const double ilut_atol = 0.,
const double ilut_rtol = 1.,
const unsigned int overlap = 0);
/**
* This specifies the relative size
* of elements which should be
* dropped when forming an incomplete
* LU decomposition with threshold.
*/
double ilut_drop;
/**
* This specifies the amount of
* additional fill-in elements
* besides the sparse matrix
* structure. When
* <tt>ilu_fill</tt> is large,
* this means that many
* fill-ins will be added, so
* that the ILU preconditioner
* comes closer to a (direct)
* sparse LU
* decomposition. Note,
* however, that this will
* drastically increase the
* memory requirement,
* especially when the
* preconditioner is used in
* 3D.
*/
unsigned int ilut_fill;
/**
* This specifies the amount of
* an absolute perturbation
* that will be added to the
* diagonal of the matrix,
* which sometimes can help to
* get better preconditioners.
*/
double ilut_atol;
/**
* This specifies the factor by
* which the diagonal of the
* matrix will be scaled, which
* sometimes can help to get
* better preconditioners.
*/
double ilut_rtol;
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Initialize function. Takes
* the matrix which is used to
* form the preconditioner, and
* additional flags if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for a sparse direct LU decomposition on parallel
* blocks for Trilinos matrices. When run in serial, this corresponds
* to a direct solve on the matrix.
*
* The AdditionalData data structure allows to set preconditioner
* options.
*
* Note that a parallel applicatoin of the block direct solve
* preconditioner is actually a block-Jacobi preconditioner with block
* size equal to the local matrix size. Spoken more technically, this
* parallel operation is an <a
* href="http://en.wikipedia.org/wiki/Additive_Schwarz_method">additive
* Schwarz method</a> with an <em>exact solve</em> as inner solver,
* based on the (outer) parallel partitioning.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionBlockwiseDirect : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional parameters
* to the preconditioner.
*/
struct AdditionalData
{
/**
* Constructor.
*/
AdditionalData (const unsigned int overlap = 0);
/**
* This determines how large
* the overlap of the local
* matrix portions on each
* processor in a parallel
* application should be.
*/
unsigned int overlap;
};
/**
* Initialize function. Takes
* the matrix which is used to
* form the preconditioner, and
* additional flags if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* A wrapper class for a Chebyshev preconditioner for Trilinos matrices.
*
* The AdditionalData data structure allows to set preconditioner
* options.
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionChebyshev : public PreconditionBase
{
public:
/**
* Standardized data struct to
* pipe additional parameters
* to the preconditioner.
*/
struct AdditionalData
{
/**
* Constructor.
*/
AdditionalData (const unsigned int degree = 1,
const double max_eigenvalue = 10.,
const double eigenvalue_ratio = 30.,
const double min_eigenvalue = 1.,
const double min_diagonal = 1e-12,
const bool nonzero_starting = false);
/**
* This determines the degree of the
* Chebyshev polynomial. The degree
* of the polynomial gives the number
* of matrix-vector products to be
* performed for one application of
* the vmult() operation.
*/
unsigned int degree;
/**
* This sets the maximum eigenvalue
* of the matrix, which needs to be
* set properly for appropriate
* performance of the Chebyshev
* preconditioner.
*/
double max_eigenvalue;
/**
* This sets the ratio between the
* maximum and the minimum
* eigenvalue.
*/
double eigenvalue_ratio;
/**
* This sets the minimum eigenvalue,
* which is an optional parameter
* only used internally for checking
* whether we use an identity matrix.
*/
double min_eigenvalue;
/**
* This sets a threshold below which
* the diagonal element will not be
* inverted in the Chebyshev
* algorithm.
*/
double min_diagonal;
/**
* When this flag is set to
* <tt>true</tt>, it enables the
* method <tt>vmult(dst, src)</tt> to
* use non-zero data in the vector
* <tt>dst</tt>, appending to it the
* Chebyshev corrections. This can be
* useful in some situations
* (e.g. when used for high-frequency
* error smoothing), but not the way
* the solver classes expect a
* preconditioner to work (where one
* ignores the content in
* <tt>dst</tt> for the
* preconditioner application). The
* user should really know what she
* is doing when touching this flag.
*/
bool nonzero_starting;
};
/**
* Initialize function. Takes
* the matrix which is used to
* form the preconditioner, and
* additional flags if there
* are any.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
};
/**
* This class implements an algebraic multigrid (AMG) preconditioner based
* on the Trilinos ML implementation, which is a black-box preconditioner
* that works well for many PDE-based linear problems. What this class does
* is twofold. When the initialize() function is invoked, a ML
* preconditioner object is created based on the matrix that we want the
* preconditioner to be based on. A call of the respective
* <code>vmult</code> function does call the respective operation in the
* Trilinos package, where it is called <code>ApplyInverse</code>. Use of
* this class is explained in the step-31 tutorial program.
*
* Since the Trilinos objects we want to use are heavily dependent on Epetra
* objects, we recommend using this class in conjunction with Trilinos
* (Epetra) sparse matrices and vectors. There is support for use with
* matrices of the deal.II::SparseMatrix class and corresponding vectors,
* too, but this requires generating a copy of the matrix, which is slower
* and takes (much) more memory. When doing such a copy operation, we can
* still profit from the fact that some of the entries in the preconditioner
* matrix are zero and hence can be neglected.
*
* The implementation is able to distinguish between matrices from elliptic
* problems and convection dominated problems. We use the standard options
* provided by Trilinos ML for elliptic problems, except that we use a
* Chebyshev smoother instead of a symmetric Gauss-Seidel smoother. For
* most elliptic problems, Chebyshev provides a better damping of high
* frequencies (in the algebraic sense) than Gauss-Seidel (SSOR), and is
* faster (Chebyshev requires only some matrix-vector products, whereas SSOR
* requires substitutions which are more expensive). Moreover, Chebyshev is
* perfectly parallel in the sense that it does not degenerate when used on
* many processors. SSOR, on the other hand, gets more Jacobi-like on many
* processors.
*
* For proper functionality of this class we recommend using Trilinos v9.0
* and higher. Older versions may have problems with generating the
* coarse-matrix structure when using matrices with many nonzero entries per
* row (i.e., matrices stemming from higher order finite element
* discretizations).
*
* @ingroup TrilinosWrappers
* @ingroup Preconditioners
* @author Martin Kronbichler, 2008
*/
class PreconditionAMG : public PreconditionBase
{
public:
struct AdditionalData
{
/**
* Constructor. By default, we
* pretend to work on elliptic
* problems with linear finite
* elements on a scalar equation.
*/
AdditionalData (const bool elliptic = true,
const bool higher_order_elements = false,
const unsigned int n_cycles = 1,
const bool w_cyle = false,
const double aggregation_threshold = 1e-4,
const std::vector<std::vector<bool> > &constant_modes = std::vector<std::vector<bool> > (1),
const unsigned int smoother_sweeps = 2,
const unsigned int smoother_overlap = 0,
const bool output_details = false);
/**
* Determines whether the AMG
* preconditioner should be optimized
* for elliptic problems (ML option
* smoothed aggregation SA, using a
* Chebyshev smoother) or for
* non-elliptic problems (ML option
* non-symmetric smoothed aggregation
* NSSA, smoother is SSOR with
* underrelaxation).
*/
bool elliptic;
/**
* Determines whether the matrix that
* the preconditioner is built upon
* is generated from linear or
* higher-order elements.
*/
bool higher_order_elements;
/**
* Defines how many multigrid cycles
* should be performed by the
* preconditioner.
*/
unsigned int n_cycles;
/**
* Defines whether a w-cycle should be
* used instead of the standard setting
* of a v-cycle.
*/
bool w_cycle;
/**
* This threshold tells the AMG setup
* how the coarsening should be
* performed. In the AMG used by ML,
* all points that strongly couple
* with the tentative coarse-level
* point form one aggregate. The term
* <em>strong coupling</em> is
* controlled by the variable
* <tt>aggregation_threshold</tt>,
* meaning that all elements that are
* not smaller than
* <tt>aggregation_threshold</tt>
* times the diagonal element do
* couple strongly.
*/
double aggregation_threshold;
/**
* Specifies the constant modes (near
* null space) of the matrix. This
* parameter tells AMG whether we
* work on a scalar equation (where
* the near null space only consists
* of ones) or on a vector-valued
* equation.
*/
std::vector<std::vector<bool> > constant_modes;
/**
* Determines how many sweeps of the
* smoother should be performed. When
* the flag <tt>elliptic</tt> is set
* to <tt>true</tt>, i.e., for
* elliptic or almost elliptic
* problems, the polynomial degree of
* the Chebyshev smoother is set to
* <tt>smoother_sweeps</tt>. The term
* sweeps refers to the number of
* matrix-vector products performed
* in the Chebyshev case. In the
* non-elliptic case,
* <tt>smoother_sweeps</tt> sets the
* number of SSOR relaxation sweeps
* for post-smoothing to be
* performed.
*/
unsigned int smoother_sweeps;
/**
* Determines the overlap in the
* SSOR/Chebyshev error smoother when
* run in parallel.
*/
unsigned int smoother_overlap;
/**
* If this flag is set to
* <tt>true</tt>, then internal
* information from the ML
* preconditioner is printed to
* screen. This can be useful when
* debugging the preconditioner.
*/
bool output_details;
};
/**
* Let Trilinos compute a multilevel
* hierarchy for the solution of a
* linear system with the given
* matrix. The function uses the
* matrix format specified in
* TrilinosWrappers::SparseMatrix.
*/
void initialize (const SparseMatrix &matrix,
const AdditionalData &additional_data = AdditionalData());
/**
* Let Trilinos compute a multilevel
* hierarchy for the solution of a
* linear system with the given
* matrix. The function uses the
* matrix format specified in
* TrilinosWrappers::SparseMatrix.
*
* This function is similar to the one
* above, but allows the user to set
* all the options of the Trilinos ML
* preconditioner. In order to find out
* about all the options for ML, we
* refer to the <a
* href=http://trilinos.sandia.gov/packages/ml/mlguide5.pdf>ML
* user's guide</a>. In particular,
* users need to follow the ML
* instructions in case a vector-valued
* problem ought to be solved.
*/
void initialize (const SparseMatrix &matrix,
const Teuchos::ParameterList &ml_parameters);
/**
* Let Trilinos compute a multilevel
* hierarchy for the solution of a
* linear system with the given
* matrix. This function takes a
* deal.ii matrix and copies the
* content into a Trilinos matrix, so
* the function can be considered
* rather inefficient.
*/
template <typename number>
void initialize (const ::dealii::SparseMatrix<number> &deal_ii_sparse_matrix,
const AdditionalData &additional_data = AdditionalData(),
const double drop_tolerance = 1e-13,
const ::dealii::SparsityPattern *use_this_sparsity = 0);
/**
* This function can be used for a
* faster recalculation of the
* preconditioner construction when
* the matrix entries underlying the
* preconditioner have changed, but
* the matrix sparsity pattern has
* remained the same. What this
* function does is taking the
* already generated coarsening
* structure, computing the AMG
* prolongation and restriction
* according to a smoothed
* aggregation strategy and then
* building the whole multilevel
* hiearchy. This function can be
* considerably faster than the
* initialize function, since the
* coarsening pattern is usually the
* most difficult thing to do when
* setting up the AMG ML
* preconditioner.
*/
void reinit ();
/**
* Destroys the preconditioner, leaving
* an object like just after having
* called the constructor.
*/
void clear ();
/**
* Prints an estimate of the memory
* consumption of this class.
*/
unsigned int memory_consumption () const;
private:
/**
* A copy of the deal.II matrix into
* Trilinos format.
*/
std_cxx1x::shared_ptr<SparseMatrix> trilinos_matrix;
};
// -------------------------- inline and template functions ----------------------
#ifndef DOXYGEN
inline
void
PreconditionBase::vmult (VectorBase &dst,
const VectorBase &src) const
{
Assert (dst.vector_partitioner().SameAs(preconditioner->OperatorRangeMap()),
ExcNonMatchingMaps("dst"));
Assert (src.vector_partitioner().SameAs(preconditioner->OperatorDomainMap()),
ExcNonMatchingMaps("src"));
const int ierr = preconditioner->ApplyInverse (src.trilinos_vector(),
dst.trilinos_vector());
AssertThrow (ierr == 0, ExcTrilinosError(ierr));
}
// For the implementation of
// the <code>vmult</code>
// function with deal.II data
// structures we note that
// invoking a call of the
// Trilinos preconditioner
// requires us to use Epetra
// vectors as well. We do this
// by providing a view, i.e.,
// feed Trilinos with a
// pointer to the data, so we
// avoid copying the content
// of the vectors during the
// iteration (this function is
// only useful when used in
// serial anyway). In the
// declaration of the right
// hand side, we need to cast
// the source vector (that is
// <code>const</code> in all
// deal.II calls) to
// non-constant value, as this
// is the way Trilinos wants
// to have them.
inline
void PreconditionBase::vmult (dealii::Vector<double> &dst,
const dealii::Vector<double> &src) const
{
Epetra_Vector LHS (View, preconditioner->OperatorDomainMap(),
dst.begin());
Epetra_Vector RHS (View, preconditioner->OperatorRangeMap(),
const_cast<double*>(src.begin()));
const int ierr = preconditioner->ApplyInverse (RHS, LHS);
AssertThrow (ierr == 0, ExcTrilinosError(ierr));
}
#endif
}
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif // DEAL_II_USE_TRILINOS
/*---------------------------- trilinos_precondition.h ---------------------------*/
#endif
/*---------------------------- trilinos_precondition.h ---------------------------*/
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