Fast (sequential) Algebraic Multigrid

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]	v	The update to be computed
	d	The 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

fineOperator	The operator on the fine level.
criterion	The criterion describing the coarsening strategy. E. g. SymmetricCriterion or UnsymmetricCriterion, and providing the parameters.
parms	The 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

matrices	The already set-up matrix hierarchy.
coarseSolver	The set up solver to use on the coarse grid, must match the coarse matrix in the matrix hierarchy.
parms	The 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

fineOperator	The operator on the fine level.
criterion	The criterion describing the coarsening strategy. E. g. SymmetricCriterion or UnsymmetricCriterion, and providing the parameters.
parms	The parameters for the AMG.
pinfo	The 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

cont	The random access container to store the numbers in.

post()

template<class M , class X , class PI = SequentialInformation, class A = std::allocator<X>>

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

x	The 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
Preconditioner<X,Y> prec(...);
prec.pre(x,b);   // prepare the preconditioner
prec.apply(x,b); // can be called multiple times now...
prec.post(x);    // cleanup internal state

Parameters

x	The left hand side of the equation.
b	The 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.