Reference documentation for deal.II version Git 7916fb8 2017-12-10 11:04:15 +0100
TrilinosWrappers::PreconditionAMG Class Reference

#include <deal.II/lac/trilinos_precondition.h>

Inheritance diagram for TrilinosWrappers::PreconditionAMG:
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## Public Member Functions

~PreconditionAMG ()

void initialize (const SparseMatrix &matrix, const Teuchos::ParameterList &ml_parameters)

void initialize (const Epetra_RowMatrix &matrix, const Teuchos::ParameterList &ml_parameters)

template<typename number >

void reinit ()

void clear ()

size_type memory_consumption () const

Public Member Functions inherited from TrilinosWrappers::PreconditionBase
PreconditionBase ()

PreconditionBase (const PreconditionBase &)

~PreconditionBase ()=default

void clear ()

MPI_Comm get_mpi_communicator () const

void transpose ()

virtual void vmult (MPI::Vector &dst, const MPI::Vector &src) const

virtual void Tvmult (MPI::Vector &dst, const MPI::Vector &src) const

virtual void vmult (::Vector< double > &dst, const ::Vector< double > &src) const

virtual void Tvmult (::Vector< double > &dst, const ::Vector< double > &src) const

virtual void vmult (::LinearAlgebra::distributed::Vector< double > &dst, const ::LinearAlgebra::distributed::Vector< double > &src) const

virtual void Tvmult (::LinearAlgebra::distributed::Vector< double > &dst, const ::LinearAlgebra::distributed::Vector< double > &src) const

Epetra_Operator & trilinos_operator () const

IndexSet locally_owned_domain_indices () const

IndexSet locally_owned_range_indices () const

Public Member Functions inherited from Subscriptor
Subscriptor ()

Subscriptor (const Subscriptor &)

Subscriptor (Subscriptor &&)

virtual ~Subscriptor ()

Subscriptoroperator= (const Subscriptor &)

Subscriptoroperator= (Subscriptor &&)

void subscribe (const char *identifier=nullptr) const

void unsubscribe (const char *identifier=nullptr) const

unsigned int n_subscriptions () const

void list_subscribers () const

template<class Archive >
void serialize (Archive &ar, const unsigned int version)

## Private Attributes

std::shared_ptr< SparseMatrixtrilinos_matrix

Public Types inherited from TrilinosWrappers::PreconditionBase
typedef ::types::global_dof_index size_type

Static Public Member Functions inherited from TrilinosWrappers::PreconditionBase
static::ExceptionBase & ExcNonMatchingMaps (std::string arg1)

Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)

static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)

Protected Attributes inherited from TrilinosWrappers::PreconditionBase
std::shared_ptr< Epetra_Operator > preconditioner

Epetra_MpiComm communicator

std::shared_ptr< Epetra_Map > vector_distributor

## Detailed Description

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 vmult function does call the respective operation in the Trilinos package, where it is called ApplyInverse. 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).

Definition at line 1355 of file trilinos_precondition.h.

## Constructor & Destructor Documentation

 TrilinosWrappers::PreconditionAMG::~PreconditionAMG ( )

Destructor.

Definition at line 69 of file trilinos_precondition_ml.cc.

## Member Function Documentation

 void TrilinosWrappers::PreconditionAMG::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.

Definition at line 78 of file trilinos_precondition_ml.cc.

 void TrilinosWrappers::PreconditionAMG::initialize ( const Epetra_RowMatrix & matrix, const AdditionalData & additional_data = AdditionalData() )

Let Trilinos compute a multilevel hierarchy for the solution of a linear system with the given matrix. As opposed to the other initialize function above, this function uses an abstract interface to an object of type Epetra_RowMatrix which allows a user to pass quite general objects to the ML preconditioner.

This initialization routine is useful in cases where the operator to be preconditioned is not a TrilinosWrappers::SparseMatrix object but still allows getting a copy of the entries in each of the locally owned matrix rows (method ExtractMyRowCopy) and implements a matrix-vector product (methods Multiply or Apply). An example are operators which provide faster matrix-vector multiplications than possible with matrix entries (matrix-free methods). These implementations can be beneficially combined with Chebyshev smoothers that only perform matrix-vector products. The interface class Epetra_RowMatrix is very flexible to enable this kind of implementation.

Definition at line 87 of file trilinos_precondition_ml.cc.

 void TrilinosWrappers::PreconditionAMG::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. 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 ML user's guide. In particular, users need to follow the ML instructions in case a vector-valued problem ought to be solved.

Definition at line 212 of file trilinos_precondition_ml.cc.

 void TrilinosWrappers::PreconditionAMG::initialize ( const Epetra_RowMatrix & matrix, const Teuchos::ParameterList & ml_parameters )

Let Trilinos compute a multilevel hierarchy for the solution of a linear system with the given matrix. As opposed to the other initialize function above, this function uses an abstract interface to an object of type Epetra_RowMatrix which allows a user to pass quite general objects to the ML preconditioner.

Definition at line 221 of file trilinos_precondition_ml.cc.

template<typename number >
 void TrilinosWrappers::PreconditionAMG::initialize ( const ::SparseMatrix< number > & deal_ii_sparse_matrix, const AdditionalData & additional_data = AdditionalData(), const double drop_tolerance = 1e-13, const ::SparsityPattern * use_this_sparsity = nullptr )

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.

Definition at line 234 of file trilinos_precondition_ml.cc.

 void TrilinosWrappers::PreconditionAMG::reinit ( )

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 hierarchy. 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.

Definition at line 261 of file trilinos_precondition_ml.cc.

 void TrilinosWrappers::PreconditionAMG::clear ( )

Destroys the preconditioner, leaving an object like just after having called the constructor.

Definition at line 270 of file trilinos_precondition_ml.cc.

 PreconditionAMG::size_type TrilinosWrappers::PreconditionAMG::memory_consumption ( ) const

Prints an estimate of the memory consumption of this class.

Definition at line 279 of file trilinos_precondition_ml.cc.

## Member Data Documentation

 std::shared_ptr TrilinosWrappers::PreconditionAMG::trilinos_matrix
private

A copy of the deal.II matrix into Trilinos format.

Definition at line 1608 of file trilinos_precondition.h.

The documentation for this class was generated from the following files: