Reference documentation for deal.II version Git 87130829be 2021-04-14 12:03:57 -0400
TrilinosWrappers::PreconditionAMG Class Reference

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

Inheritance diagram for TrilinosWrappers::PreconditionAMG:
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## Public Types

using size_type = ::types::global_dof_index

## Public Member Functions

~PreconditionAMG () override

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

MPI_Comm get_mpi_communicator () const

void transpose ()

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

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

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

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

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

Epetra_Operatortrilinos_operator () const

Partitioners
IndexSet locally_owned_domain_indices () const

IndexSet locally_owned_range_indices () const

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int n_subscriptions () const

template<typename StreamType >
void list_subscribers (StreamType &stream) const

void list_subscribers () const

## Static Public Member Functions

static ::ExceptionBaseExcNonMatchingMaps (std::string arg1)

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Protected Attributes

Teuchos::RCP< Epetra_Operatorpreconditioner

Epetra_MpiComm communicator

std::shared_ptr< Epetra_Map > vector_distributor

## Private Attributes

std::shared_ptr< SparseMatrixtrilinos_matrix

## 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 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 1344 of file trilinos_precondition.h.

## ◆ size_type

 inherited

Declare the type for container size.

Definition at line 86 of file trilinos_precondition.h.

## ◆ ~PreconditionAMG()

 TrilinosWrappers::PreconditionAMG::~PreconditionAMG ( )
override

Destructor.

Definition at line 213 of file trilinos_precondition_ml.cc.

## ◆ initialize() [1/5]

 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 222 of file trilinos_precondition_ml.cc.

## ◆ initialize() [2/5]

 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 231 of file trilinos_precondition_ml.cc.

## ◆ initialize() [3/5]

 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 documentation page. In particular, users need to follow the ML instructions in case a vector-valued problem ought to be solved.

Definition at line 257 of file trilinos_precondition_ml.cc.

## ◆ initialize() [4/5]

 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 266 of file trilinos_precondition_ml.cc.

## ◆ initialize() [5/5]

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 277 of file trilinos_precondition_ml.cc.

## ◆ reinit()

 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 311 of file trilinos_precondition_ml.cc.

## ◆ clear()

 void TrilinosWrappers::PreconditionAMG::clear ( )

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

Definition at line 321 of file trilinos_precondition_ml.cc.

## ◆ memory_consumption()

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

Prints an estimate of the memory consumption of this class.

Definition at line 330 of file trilinos_precondition_ml.cc.

## ◆ get_mpi_communicator()

 MPI_Comm TrilinosWrappers::PreconditionBase::get_mpi_communicator ( ) const
inherited

Return the MPI communicator object in use with this matrix.

Definition at line 67 of file trilinos_precondition.cc.

## ◆ transpose()

 void TrilinosWrappers::PreconditionBase::transpose ( )
inherited

Sets an internal flag so that all operations performed by the matrix, i.e., multiplications, are done in transposed order. However, this does not reshape the matrix to transposed form directly, so care should be taken when using this flag.

Note
Calling this function any even number of times in succession will return the object to its original state.

## ◆ vmult() [1/3]

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

Apply the preconditioner.

Reimplemented in TrilinosWrappers::PreconditionIdentity.

## ◆ vmult() [2/3]

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

Apply the preconditioner on deal.II data structures instead of the ones provided in the Trilinos wrapper class.

Reimplemented in TrilinosWrappers::PreconditionIdentity.

## ◆ vmult() [3/3]

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

Apply the preconditioner on deal.II parallel data structures instead of the ones provided in the Trilinos wrapper class.

## ◆ Tvmult() [1/3]

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

Apply the transpose preconditioner.

Reimplemented in TrilinosWrappers::PreconditionIdentity.

## ◆ Tvmult() [2/3]

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

Apply the transpose preconditioner on deal.II data structures instead of the ones provided in the Trilinos wrapper class.

Reimplemented in TrilinosWrappers::PreconditionIdentity.

## ◆ Tvmult() [3/3]

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

Apply the transpose preconditioner on deal.II parallel data structures instead of the ones provided in the Trilinos wrapper class.

## ◆ trilinos_operator()

 Epetra_Operator & TrilinosWrappers::PreconditionBase::trilinos_operator ( ) const
inherited

Calling this function from an uninitialized object will cause an exception.

Definition at line 78 of file trilinos_precondition.cc.

## ◆ locally_owned_domain_indices()

 IndexSet TrilinosWrappers::PreconditionBase::locally_owned_domain_indices ( ) const
inherited

Return the partitioning of the domain space of this matrix, i.e., the partitioning of the vectors this matrix has to be multiplied with.

Definition at line 87 of file trilinos_precondition.cc.

## ◆ locally_owned_range_indices()

 IndexSet TrilinosWrappers::PreconditionBase::locally_owned_range_indices ( ) const
inherited

Return the partitioning of the range space of this matrix, i.e., the partitioning of the vectors that are result from matrix-vector products.

Definition at line 94 of file trilinos_precondition.cc.

## ◆ subscribe()

 void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

## ◆ unsubscribe()

 void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

## ◆ n_subscriptions()

 unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 301 of file subscriptor.h.

## ◆ list_subscribers() [1/2]

template<typename StreamType >
 void Subscriptor::list_subscribers ( StreamType & stream ) const
inlineinherited

List the subscribers to the input stream.

Definition at line 318 of file subscriptor.h.

## ◆ list_subscribers() [2/2]

 void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

## ◆ serialize()

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

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 310 of file subscriptor.h.

## ◆ trilinos_matrix

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

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

Definition at line 1697 of file trilinos_precondition.h.

## ◆ preconditioner

 Teuchos::RCP TrilinosWrappers::PreconditionBase::preconditioner
protectedinherited

This is a pointer to the preconditioner object that is used when applying the preconditioner.

Definition at line 236 of file trilinos_precondition.h.

## ◆ communicator

 Epetra_MpiComm TrilinosWrappers::PreconditionBase::communicator
protectedinherited

Internal communication pattern in case the matrix needs to be copied from deal.II format.

Definition at line 243 of file trilinos_precondition.h.

## ◆ vector_distributor

 std::shared_ptr TrilinosWrappers::PreconditionBase::vector_distributor
protectedinherited

Internal Trilinos map in case the matrix needs to be copied from deal.II format.

Definition at line 252 of file trilinos_precondition.h.

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