Dune Core Modules (unstable)

An Algebraic Multigrid based on Agglomeration that saves memory bandwidth. More...

Classes

class  Dune::Amg::FastAMG< M, X, PI, A >
 A fast (sequential) algebraic multigrid based on agglomeration that saves memory bandwidth. More...
 

Typedefs

typedef M Dune::Amg::FastAMG< M, X, PI, A >::Operator
 The matrix operator type.
 
typedef PI Dune::Amg::FastAMG< M, X, PI, A >::ParallelInformation
 The type of the parallel information. Either OwnerOverlapCommunication or another type describing the parallel data distribution and providing communication methods.
 
typedef MatrixHierarchy< M, ParallelInformation, A > Dune::Amg::FastAMG< M, X, PI, A >::OperatorHierarchy
 The operator hierarchy type.
 
typedef OperatorHierarchy::ParallelInformationHierarchy Dune::Amg::FastAMG< M, X, PI, A >::ParallelInformationHierarchy
 The parallal data distribution hierarchy type.
 
typedef X Dune::Amg::FastAMG< M, X, PI, A >::Domain
 The domain type.
 
typedef X Dune::Amg::FastAMG< M, X, PI, A >::Range
 The range type.
 
typedef InverseOperator< X, X > Dune::Amg::FastAMG< M, X, PI, A >::CoarseSolver
 the type of the coarse solver.
 

Functions

 Dune::Amg::FastAMG< M, X, PI, A >::FastAMG (OperatorHierarchy &matrices, CoarseSolver &coarseSolver, const Parameters &parms, bool symmetric=true)
 Construct a new amg with a specific coarse solver. More...
 
template<class C >
 Dune::Amg::FastAMG< M, X, PI, A >::FastAMG (std::shared_ptr< const Operator > fineOperator, const C &criterion, const Parameters &parms=Parameters(), bool symmetric=true, const ParallelInformation &pinfo=ParallelInformation())
 Construct an AMG with an inexact coarse solver based on the smoother. More...
 
template<class C >
 Dune::Amg::FastAMG< M, X, PI, A >::FastAMG (const Operator &fineOperator, const C &criterion, const Parameters &parms=Parameters(), bool symmetric=true, const ParallelInformation &pinfo=ParallelInformation())
 Construct an AMG with an inexact coarse solver based on the smoother. More...
 
 Dune::Amg::FastAMG< M, X, PI, A >::FastAMG (const FastAMG &amg)
 Copy constructor.
 
void Dune::Amg::FastAMG< M, X, PI, A >::pre (Domain &x, Range &b)
 Prepare the preconditioner. More...
 
void Dune::Amg::FastAMG< M, X, PI, A >::apply (Domain &v, const Range &d)
 Apply one step of the preconditioner to the system A(v)=d. More...
 
virtual SolverCategory::Category Dune::Amg::FastAMG< M, X, PI, A >::category () const
 Category of the preconditioner (see SolverCategory::Category)
 
void Dune::Amg::FastAMG< M, X, PI, A >::post (Domain &x)
 Clean up. More...
 
template<class A1 >
void Dune::Amg::FastAMG< M, X, PI, A >::getCoarsestAggregateNumbers (std::vector< std::size_t, A1 > &cont)
 Get the aggregate number of each unknown on the coarsest level. More...
 
void Dune::Amg::FastAMG< M, X, PI, A >::recalculateHierarchy ()
 Recalculate the matrix hierarchy. More...
 
bool Dune::Amg::FastAMG< M, X, PI, A >::usesDirectCoarseLevelSolver () const
 Check whether the coarse solver used is a direct solver. More...
 

Variables

OperatorHierarchy::ParallelMatrixHierarchy::ConstIterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::matrix
 The iterator over the matrices.
 
ParallelInformationHierarchy::Iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::pinfo
 The iterator over the parallel information.
 
OperatorHierarchy::RedistributeInfoList::const_iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::redist
 The iterator over the redistribution information.
 
OperatorHierarchy::AggregatesMapList::const_iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::aggregates
 The iterator over the aggregates maps.
 
Hierarchy< Domain, A >::Iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::lhs
 The iterator over the left hand side.
 
Hierarchy< Domain, A >::Iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::residual
 The iterator over the residuals.
 
Hierarchy< Range, A >::Iterator Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::rhs
 The iterator over the right hand sided.
 
std::size_t Dune::Amg::FastAMG< M, X, PI, A >::LevelContext::level
 The level index.
 

Detailed Description

An Algebraic Multigrid based on Agglomeration that saves memory bandwidth.

Function Documentation

◆ apply()

template<class M , class X , class PI , class A >
void Dune::Amg::FastAMG< M, X, PI, A >::apply ( Domain v,
const Range d 
)

Apply one step of the preconditioner to the system A(v)=d.

On entry v=0 and d=b-A(x) (although this might not be computed in that way. On exit v contains the update, i.e one step computes \( v = M^{-1} d \) where \( M \) is the approximate inverse of the operator \( A \) characterizing the preconditioner.

Parameters
[out]vThe update to be computed
dThe current defect.

◆ FastAMG() [1/3]

template<class M , class X , class PI = SequentialInformation, class A = std::allocator<X>>
template<class C >
Dune::Amg::FastAMG< M, X, PI, A >::FastAMG ( const Operator fineOperator,
const C &  criterion,
const Parameters parms = Parameters(),
bool  symmetric = true,
const ParallelInformation pinfo = ParallelInformation() 
)
inline

Construct an AMG with an inexact coarse solver based on the smoother.

As coarse solver a preconditioned CG method with the smoother as preconditioner will be used. The matrix hierarchy is built automatically.

Parameters
fineOperatorThe operator on the fine level.
criterionThe criterion describing the coarsening strategy. E. g. SymmetricCriterion or UnsymmetricCriterion, and providing the parameters.
parmsThe parameters for the AMG.

NOTE: This constructor uses the default constructed ParallelInformation.

◆ FastAMG() [2/3]

template<class M , class X , class PI , class A >
Dune::Amg::FastAMG< M, X, PI, A >::FastAMG ( OperatorHierarchy matrices,
CoarseSolver coarseSolver,
const Parameters parms,
bool  symmetric = true 
)

Construct a new amg with a specific coarse solver.

Parameters
matricesThe already set-up matrix hierarchy.
coarseSolverThe set up solver to use on the coarse grid, must match the coarse matrix in the matrix hierarchy.
parmsThe parameters for the AMG.

◆ FastAMG() [3/3]

template<class M , class X , class PI , class A >
template<class C >
Dune::Amg::FastAMG< M, X, PI, A >::FastAMG ( std::shared_ptr< const Operator fineOperator,
const C &  criterion,
const Parameters parms = Parameters(),
bool  symmetric = true,
const ParallelInformation pinfo = ParallelInformation() 
)

Construct an AMG with an inexact coarse solver based on the smoother.

As coarse solver a preconditioned CG method with the smoother as preconditioner will be used. The matrix hierarchy is built automatically.

Parameters
fineOperatorThe operator on the fine level.
criterionThe criterion describing the coarsening strategy. E. g. SymmetricCriterion or UnsymmetricCriterion, and providing the parameters.
parmsThe parameters for the AMG.
pinfoThe information about the parallel distribution of the data.

◆ getCoarsestAggregateNumbers()

template<class M , class X , class PI , class A >
template<class A1 >
void Dune::Amg::FastAMG< M, X, PI, A >::getCoarsestAggregateNumbers ( std::vector< std::size_t, A1 > &  cont)

Get the aggregate number of each unknown on the coarsest level.

Parameters
contThe random access container to store the numbers in.

◆ post()

template<class M , class X , class PI , class A >
void Dune::Amg::FastAMG< M, X, PI, A >::post ( Domain x)
virtual

Clean up.

This method is called after the last apply call for the linear system to be solved. Memory may be deallocated safely here. x is the solution of the linear equation.

Parameters
xThe right hand side of the equation.

Implements Dune::Preconditioner< X, X >.

◆ pre()

template<class M , class X , class PI , class A >
void Dune::Amg::FastAMG< M, X, PI, A >::pre ( Domain x,
Range b 
)

Prepare the preconditioner.

A solver solves a linear operator equation A(x)=b by applying one or several steps of the preconditioner. The method pre() is called before the first apply operation. b and x are right hand side and solution vector of the linear system respectively. It may. e.g., scale the system, allocate memory or compute a (I)LU decomposition. Note: The ILU decomposition could also be computed in the constructor or with a separate method of the derived method if several linear systems with the same matrix are to be solved.

Note
if a preconditioner is copied (e.g. for a second thread) again the pre() method has to be called to ensure proper memory management.
X x(0.0);
Y b = ...; // rhs
prec.pre(x,b); // prepare the preconditioner
prec.apply(x,b); // can be called multiple times now...
prec.post(x); // cleanup internal state
Base class for matrix free definition of preconditioners.
Definition: preconditioner.hh:33
Parameters
xThe left hand side of the equation.
bThe right hand side of the equation.

◆ recalculateHierarchy()

template<class M , class X , class PI = SequentialInformation, class A = std::allocator<X>>
void Dune::Amg::FastAMG< M, X, PI, A >::recalculateHierarchy ( )
inline

Recalculate the matrix hierarchy.

It is assumed that the coarsening for the changed fine level matrix would yield the same aggregates. In this case it suffices to recalculate all the Galerkin products for the matrices of the coarser levels.

◆ usesDirectCoarseLevelSolver()

template<class M , class X , class PI , class A >
bool Dune::Amg::FastAMG< M, X, PI, A >::usesDirectCoarseLevelSolver

Check whether the coarse solver used is a direct solver.

Returns
True if the coarse level solver is a direct solver.
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