# Dune Core Modules (2.9.0)

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 (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.

## ◆ apply()

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

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.

Implements Dune::Preconditioner< X, X >.

## ◆ FastAMG() [1/2]

template<class M , class X , class PI , class A >
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.

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.

## ◆ FastAMG() [2/2]

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 matix 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.

## ◆ 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 )
virtual

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 mangement.
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.

Implements Dune::Preconditioner< X, X >.

## ◆ 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. |  Legal Statements / Impressum  |  generated with Hugo v0.80.0 (Sep 25, 22:29, 2023)