Parallel Algebraic Multigrid

A Parallel Algebraic Multigrid based on Agglomeration. More...

Files
file	aggregates.hh
	Provides classes for the Coloring process of AMG.
file	amg.hh
	The AMG preconditioner.
file	construction.hh
	Helper classes for the construction of classes without empty constructor.
file	dependency.hh
	Provides classes for initializing the link attributes of a matrix graph.
file	galerkin.hh
	Provides a class for building the galerkin product based on a aggregation scheme.
file	globalaggregates.hh
	Provdes class for identifying aggregates globally.
file	graph.hh
	Provides classes for building the matrix graph.
file	hierarchy.hh
	Provides a classes representing the hierarchies in AMG.
file	indicescoarsener.hh
	Provides a class for building the index set and remote indices on the coarse level.
file	kamg.hh
	Provides an algebraic multigrid using a Krylov cycle.
file	matrixhierarchy.hh
	Provides a classes representing the hierarchies in AMG.
file	parameters.hh
	Parameter classes for customizing AMG.
file	properties.hh
	Provides classes for handling internal properties in a graph.
file	smoother.hh
	Classes for the generic construction and application of the smoothers.
file	transfer.hh
	Prolongation and restriction for amg.
file	twolevelmethod.hh
	Algebraic twolevel methods.

Namespaces
namespace	Dune
	Dune namespace.

Classes
class	Dune::Amg::AggregationCriterion< T >
	Base class of all aggregation criterions. More...
class	Dune::Amg::SymmetricMatrixDependency< M, N >
	Dependency policy for symmetric matrices. More...
class	Dune::Amg::Dependency< M, N >
	Dependency policy for symmetric matrices. More...
class	Dune::Amg::SymmetricDependency< M, N >
	Dependency policy for symmetric matrices. More...
class	Dune::Amg::Diagonal< N >
	Norm that uses only the [N][N] entry of the block to determine couplings. More...
class	Dune::Amg::FirstDiagonal
	Norm that uses only the [0][0] entry of the block to determine couplings. More...
struct	Dune::Amg::RowSum
	Functor using the row sum (infinity) norm to determine strong couplings. More...
class	Dune::Amg::SymmetricCriterion< M, Norm >
	Criterion taking advantage of symmetric matrices. More...
class	Dune::Amg::UnSymmetricCriterion< M, Norm >
	Criterion suitable for unsymmetric matrices. More...
class	Dune::Amg::Aggregator< G >
	Class for building the aggregates. More...
class	Dune::Amg::AggregatesMap< V >
	Class providing information about the mapping of the vertices onto aggregates. More...
class	Dune::Amg::AggregatesMap< V >::DummyEdgeVisitor
	A Dummy visitor that does nothing for each visited edge. More...
class	Dune::Amg::Aggregate< G, S >
	A class for temporarily storing the vertices of an aggregate in. More...
class	Dune::Amg::KAMG< M, X, S, PI, K, A >
	an algebraic multigrid method using a Krylov-cycle. More...
class	Dune::Amg::KAmgTwoGrid< AMG >
	Two grid operator for AMG with Krylov cycle. More...
class	Dune::Amg::AMG< M, X, S, PI, A >
	Parallel algebraic multigrid based on agglomeration. More...
struct	Dune::Amg::ConstructionTraits< T >
	Traits class for generically constructing non default constructable types. More...
class	Dune::Amg::EdgeProperties
	Class representing the properties of an edge in the matrix graph. More...
class	Dune::Amg::VertexProperties
	Class representing a node in the matrix graph. More...
class	Dune::Amg::SparsityBuilder< M >
	Functor for building the sparsity pattern of the matrix using examineConnectivity. More...
class	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >
	Visitor for identifying connected aggregates during a breadthFirstSearch. More...
class	Dune::Amg::MatrixGraph< M >
	The (undirected) graph of a matrix. More...
class	Dune::Amg::SubGraph< G, T >
	A subgraph of a graph. More...
class	Dune::Amg::VertexPropertiesGraph< G, VP, VM >
	Attaches properties to the vertices of a graph. More...
class	Dune::Amg::PropertiesGraph< G, VP, EP, VM, EM >
	Attaches properties to the edges and vertices of a graph. More...
class	Dune::Amg::GraphVertexPropertiesSelector< G >
	Wrapper to access the internal edge properties of a graph via operator[]() More...
class	Dune::Amg::GraphEdgePropertiesSelector< G >
	Wrapper to access the internal vertex properties of a graph via operator[]() More...
class	Dune::Amg::Hierarchy< T, A >
	A hierarchy of containers (e.g. matrices or vectors) More...
class	Dune::Amg::IndicesCoarsener< OwnerOverlapCopyCommunication< G, L >, E >
	Coarsen Indices in the parallel case. More...
class	Dune::Amg::IndicesCoarsener< SequentialInformation, E >
	Coarsen Indices in the sequential case. More...
class	Dune::Amg::MatrixHierarchy< M, PI, A >
	The hierarchies build by the coarsening process. More...
class	Dune::Amg::CoarsenCriterion< T >
	The criterion describing the stop criteria for the coarsening process. More...
class	Dune::Amg::DependencyParameters
	Parameters needed to check whether a node depends on another. More...
class	Dune::Amg::AggregationParameters
	Parameters needed for the aggregation process. More...
class	Dune::Amg::CoarseningParameters
	Parameters for the complete coarsening process. More...
class	Dune::Amg::Parameters
	All parameters for AMG. More...
struct	Dune::Amg::VertexVisitedTag
	Tag idnetifying the visited property of a vertex. More...
class	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >
	A property map that extracts one property out of a bundle using operator[]() More...
struct	Dune::Amg::DefaultSmootherArgs< T >
	The default class for the smoother arguments. More...
struct	Dune::Amg::SmootherTraits< T >
	Traits class for getting the attribute class of a smoother. More...
class	Dune::Amg::DefaultConstructionArgs< T >
	Construction Arguments for the default smoothers. More...
struct	Dune::Amg::ConstructionTraits< SeqSSOR< M, X, Y, l > >
	Policy for the construction of the SeqSSOR smoother. More...
struct	Dune::Amg::ConstructionTraits< SeqSOR< M, X, Y, l > >
	Policy for the construction of the SeqSOR smoother. More...
struct	Dune::Amg::ConstructionTraits< SeqJac< M, X, Y, l > >
	Policy for the construction of the SeqJac smoother. More...
struct	Dune::Amg::ConstructionTraits< Richardson< X, Y > >
	Policy for the construction of the Richardson smoother. More...
struct	Dune::Amg::ConstructionTraits< SeqILU< M, X, Y > >
	Policy for the construction of the SeqILU smoother. More...
struct	Dune::Amg::ConstructionTraits< ParSSOR< M, X, Y, C > >
	Policy for the construction of the ParSSOR smoother. More...
struct	Dune::Amg::SmootherApplier< T >
	Helper class for applying the smoothers. More...

Typedefs
typedef T	Dune::Amg::AggregationCriterion< T >::DependencyPolicy
	The policy for calculating the dependency graph.
typedef M	Dune::Amg::SymmetricMatrixDependency< M, N >::Matrix
	The matrix type we build the dependency of.
typedef N	Dune::Amg::SymmetricMatrixDependency< M, N >::Norm
	The norm to use for examining the matrix entries.
typedef Matrix::row_type	Dune::Amg::SymmetricMatrixDependency< M, N >::Row
	Constant Row iterator of the matrix.
typedef Matrix::ConstColIterator	Dune::Amg::SymmetricMatrixDependency< M, N >::ColIter
	Constant column iterator of the matrix.
typedef Matrix::field_type	Dune::Amg::SymmetricMatrixDependency< M, N >::field_type
	The current max value.
typedef M	Dune::Amg::Dependency< M, N >::Matrix
	The matrix type we build the dependency of.
typedef N	Dune::Amg::Dependency< M, N >::Norm
	The norm to use for examining the matrix entries.
typedef Matrix::row_type	Dune::Amg::Dependency< M, N >::Row
	Constant Row iterator of the matrix.
typedef Matrix::ConstColIterator	Dune::Amg::Dependency< M, N >::ColIter
	Constant column iterator of the matrix.
typedef Matrix::field_type	Dune::Amg::Dependency< M, N >::field_type
	The current max value.
typedef M	Dune::Amg::SymmetricDependency< M, N >::Matrix
	The matrix type we build the dependency of.
typedef N	Dune::Amg::SymmetricDependency< M, N >::Norm
	The norm to use for examining the matrix entries.
typedef Matrix::row_type	Dune::Amg::SymmetricDependency< M, N >::Row
	Constant Row iterator of the matrix.
typedef Matrix::ConstColIterator	Dune::Amg::SymmetricDependency< M, N >::ColIter
	Constant column iterator of the matrix.
typedef Matrix::field_type	Dune::Amg::SymmetricDependency< M, N >::field_type
	The current max value.
typedef V	Dune::Amg::AggregatesMap< V >::VertexDescriptor
	The vertex descriptor type.
typedef V	Dune::Amg::AggregatesMap< V >::AggregateDescriptor
	The aggregate descriptor type.
typedef PoolAllocator< VertexDescriptor, 100 >	Dune::Amg::AggregatesMap< V >::Allocator
	The allocator we use for our lists and the set.
typedef SLList< VertexDescriptor, Allocator >	Dune::Amg::AggregatesMap< V >::VertexList
	The type of a single linked list of vertex descriptors.
typedef MatrixGraph::VertexDescriptor	Dune::Amg::Aggregate< G, S >::Vertex
	The vertex descriptor type.
typedef PoolAllocator< Vertex, 100 >	Dune::Amg::Aggregate< G, S >::Allocator
	The allocator we use for our lists and the set.
typedef S	Dune::Amg::Aggregate< G, S >::VertexSet
	The type of a single linked list of vertex descriptors.
typedef VertexSet::const_iterator	Dune::Amg::Aggregate< G, S >::const_iterator
	Const iterator over a vertex list.
typedef std::size_t *	Dune::Amg::Aggregate< G, S >::SphereMap
	Type of the mapping of aggregate members onto distance spheres.
typedef G	Dune::Amg::Aggregator< G >::MatrixGraph
	The matrix graph type used.
typedef MatrixGraph::VertexDescriptor	Dune::Amg::Aggregator< G >::Vertex
	The vertex identifier.
typedef MatrixGraph::VertexDescriptor	Dune::Amg::Aggregator< G >::AggregateDescriptor
	The type of the aggregate descriptor.
typedef V	Dune::Amg::Aggregator< G >::AggregateVisitor< V >::Visitor
	The type of the adapted visitor.
typedef M	Dune::Amg::AMG< M, X, S, PI, A >::Operator
	The matrix operator type.
typedef PI	Dune::Amg::AMG< M, X, S, 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::AMG< M, X, S, PI, A >::OperatorHierarchy
	The operator hierarchy type.
typedef OperatorHierarchy::ParallelInformationHierarchy	Dune::Amg::AMG< M, X, S, PI, A >::ParallelInformationHierarchy
	The parallal data distribution hierarchy type.
typedef X	Dune::Amg::AMG< M, X, S, PI, A >::Domain
	The domain type.
typedef X	Dune::Amg::AMG< M, X, S, PI, A >::Range
	The range type.
typedef InverseOperator< X, X >	Dune::Amg::AMG< M, X, S, PI, A >::CoarseSolver
	the type of the coarse solver.
typedef S	Dune::Amg::AMG< M, X, S, PI, A >::Smoother
	The type of the smoother. More...
typedef SmootherTraits< Smoother >::Arguments	Dune::Amg::AMG< M, X, S, PI, A >::SmootherArgs
	The argument type for the construction of the smoother.
typedef const void *	Dune::Amg::ConstructionTraits< T >::Arguments
	A type holding all the arguments needed to call the constructor.
typedef G	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::Graph
	The type of the graph with internal properties.
typedef std::bitset< VertexProperties::SIZE >	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::BitSet
	The type of the bitset.
typedef BitSet::reference	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::Reference
	The reference type.
typedef bool	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::ValueType
	The value type.
typedef G::VertexDescriptor	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::Vertex
	The vertex descriptor.
typedef T	Dune::Amg::OverlapVertex< T >::Aggregate
	The aggregate descriptor.
typedef T	Dune::Amg::OverlapVertex< T >::Vertex
	The vertex descriptor.
typedef G	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::Graph
	The type of the graph.
typedef Graph::ConstEdgeIterator	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::ConstEdgeIterator
	The constant edge iterator.
typedef S	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::Set
	The type of the connected set.
typedef V	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::VisitedMap
	The type of the map for marking vertices as visited.
typedef Graph::VertexDescriptor	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::Vertex
	The vertex descriptor of the graph.
typedef E	Dune::Amg::ParallelIndicesCoarsener< T, E >::ExcludedAttributes
	The set of excluded attributes.
typedef T	Dune::Amg::ParallelIndicesCoarsener< T, E >::ParallelInformation
	The type of the parallel information.
typedef ParallelIndexSet::GlobalIndex	Dune::Amg::ParallelIndicesCoarsener< T, E >::GlobalIndex
	The type of the global index.
typedef ParallelIndexSet::LocalIndex	Dune::Amg::ParallelIndicesCoarsener< T, E >::LocalIndex
	The type of the local index.
typedef LocalIndex::Attribute	Dune::Amg::ParallelIndicesCoarsener< T, E >::Attribute
	The type of the attribute.
typedef Dune::RemoteIndices< ParallelIndexSet >	Dune::Amg::ParallelIndicesCoarsener< T, E >::RemoteIndices
	The type of the remote indices.
typedef C	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::Container
	The container that holds the properties.
typedef R	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::Reference
	The reference type of the container.
typedef K	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::Key
	The key of the property map.
typedef LvaluePropertyMapTag	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::Category
	The category of the property map.
typedef FieldTraits< T >::real_type	Dune::Amg::DefaultSmootherArgs< T >::RelaxationFactor
	The type of the relaxation factor.

Enumerations
enum
	Flags of the link.
enum	{ Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::index = i }
enum	{ Dune::Amg::MAX_PROCESSES = 72000 }
enum	Dune::Amg::AccumulationMode { Dune::Amg::noAccu = 0 , Dune::Amg::atOnceAccu =1 , Dune::Amg::successiveAccu =2 }
	Identifiers for the different accumulation modes. More...
enum	{ Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::index = i }

Functions
	Dune::Amg::AggregationCriterion< T >::AggregationCriterion ()
	Constructor. More...
void	Dune::Amg::AggregationCriterion< T >::setDefaultValuesIsotropic (std::size_t dim, std::size_t diameter=2)
	Sets reasonable default values for an isotropic problem. More...
void	Dune::Amg::AggregationCriterion< T >::setDefaultValuesAnisotropic (std::size_t dim, std::size_t diameter=2)
	Sets reasonable default values for an aisotropic problem. More...
template<class M >
FieldTraits< typenameM::field_type >::real_type	Dune::Amg::Diagonal< N >::operator() (const M &m, typename std::enable_if_t<!Dune::IsNumber< M >::value > *sfinae=nullptr) const
	compute the norm of a matrix. More...
template<class M >
auto	Dune::Amg::Diagonal< N >::operator() (const M &m, typename std::enable_if_t< Dune::IsNumber< M >::value > *sfinae=nullptr) const
	Compute the norm of a scalar. More...
template<class M >
FieldTraits< typenameM::field_type >::real_type	Dune::Amg::RowSum::operator() (const M &m) const
	compute the norm of a matrix. More...
template<class M >
FieldTraits< typenameM::field_type >::real_type	Dune::Amg::FrobeniusNorm::operator() (const M &m) const
	compute the norm of a matrix. More...
template<class M >
FieldTraits< typenameM::field_type >::real_type	Dune::Amg::AlwaysOneNorm::operator() (const M &m) const
	compute the norm of a matrix. More...
	Dune::Amg::AggregatesMap< V >::AggregatesMap ()
	Constructs without allocating memory.
	Dune::Amg::AggregatesMap< V >::AggregatesMap (std::size_t noVertices)
	Constructs with allocating memory. More...
	Dune::Amg::AggregatesMap< V >::~AggregatesMap ()
	Destructor.
template<class M , class G , class C >
std::tuple< int, int, int, int >	Dune::Amg::AggregatesMap< V >::buildAggregates (const M &matrix, G &graph, const C &criterion, bool finestLevel)
	Build the aggregates. More...
template<bool reset, class G , class F , class VM >
std::size_t	Dune::Amg::AggregatesMap< V >::breadthFirstSearch (const VertexDescriptor &start, const AggregateDescriptor &aggregate, const G &graph, F &aggregateVisitor, VM &visitedMap) const
	Breadth first search within an aggregate. More...
template<bool remove, bool reset, class G , class L , class F1 , class F2 , class VM >
std::size_t	Dune::Amg::AggregatesMap< V >::breadthFirstSearch (const VertexDescriptor &start, const AggregateDescriptor &aggregate, const G &graph, L &visited, F1 &aggregateVisitor, F2 &nonAggregateVisitor, VM &visitedMap) const
	Breadth first search within an aggregate. More...
void	Dune::Amg::AggregatesMap< V >::allocate (std::size_t noVertices)
	Allocate memory for holding the information. More...
std::size_t	Dune::Amg::AggregatesMap< V >::noVertices () const
	Get the number of vertices.
void	Dune::Amg::AggregatesMap< V >::free ()
	Free the allocated memory.
AggregateDescriptor &	Dune::Amg::AggregatesMap< V >::operator[] (const VertexDescriptor &v)
	Get the aggregate a vertex belongs to. More...
const AggregateDescriptor &	Dune::Amg::AggregatesMap< V >::operator[] (const VertexDescriptor &v) const
	Get the aggregate a vertex belongs to. More...
template<class G , class C >
void	Dune::Amg::buildDependency (G &graph, const typename C::Matrix &matrix, C criterion, bool finestLevel)
	Build the dependency of the matrix graph.
	Dune::Amg::Aggregate< G, S >::Aggregate (MatrixGraph &graph, AggregatesMap< Vertex > &aggregates, VertexSet &connectivity, std::vector< Vertex > &front_)
	Constructor. More...
void	Dune::Amg::Aggregate< G, S >::reconstruct (const Vertex &vertex)
	Reconstruct the aggregat from an seed node. More...
void	Dune::Amg::Aggregate< G, S >::seed (const Vertex &vertex)
	Initialize the aggregate with one vertex.
void	Dune::Amg::Aggregate< G, S >::add (const Vertex &vertex)
	Add a vertex to the aggregate.
void	Dune::Amg::Aggregate< G, S >::clear ()
	Clear the aggregate.
VertexSet::size_type	Dune::Amg::Aggregate< G, S >::size ()
	Get the size of the aggregate.
VertexSet::size_type	Dune::Amg::Aggregate< G, S >::connectSize ()
	Get the number of connections to other aggregates.
int	Dune::Amg::Aggregate< G, S >::id ()
	Get the id identifying the aggregate.
const_iterator	Dune::Amg::Aggregate< G, S >::begin () const
	get an iterator over the vertices of the aggregate.
const_iterator	Dune::Amg::Aggregate< G, S >::end () const
	get an iterator over the vertices of the aggregate.
	Dune::Amg::Aggregator< G >::Aggregator ()
	Constructor.
	Dune::Amg::Aggregator< G >::~Aggregator ()
	Destructor.
template<class M , class C >
std::tuple< int, int, int, int >	Dune::Amg::Aggregator< G >::build (const M &m, G &graph, AggregatesMap< Vertex > &aggregates, const C &c, bool finestLevel)
	Build the aggregates. More...
	Dune::Amg::Aggregator< G >::AggregateVisitor< V >::AggregateVisitor (const AggregatesMap< Vertex > &aggregates, const AggregateDescriptor &aggregate, Visitor &visitor)
	Constructor. More...
void	Dune::Amg::Aggregator< G >::AggregateVisitor< V >::operator() (const typename MatrixGraph::ConstEdgeIterator &edge)
	Examine an edge. More...
	Dune::Amg::Aggregator< G >::Counter::Counter ()
	Constructor.
int	Dune::Amg::Aggregator< G >::Counter::value ()
	Access the current count.
void	Dune::Amg::Aggregator< G >::Counter::increment ()
	Increment counter.
void	Dune::Amg::Aggregator< G >::Counter::decrement ()
	Decrement counter.
	Dune::Amg::Aggregator< G >::FrontNeighbourCounter::FrontNeighbourCounter (const MatrixGraph &front)
	Constructor. More...
	Dune::Amg::Aggregator< G >::ConnectivityCounter::ConnectivityCounter (const VertexSet &connected, const AggregatesMap< Vertex > &aggregates)
	Constructor. More...
	Dune::Amg::Aggregator< G >::DependencyCounter::DependencyCounter ()
	Constructor.
	Dune::Amg::Aggregator< G >::FrontMarker::FrontMarker (std::vector< Vertex > &front, MatrixGraph &graph)
	Constructor. More...
	Dune::Amg::AMG< M, X, S, PI, A >::AMG (OperatorHierarchy &matrices, CoarseSolver &coarseSolver, const SmootherArgs &smootherArgs, const Parameters &parms)
	Construct a new amg with a specific coarse solver. More...
template<class C >
	Dune::Amg::AMG< M, X, S, PI, A >::AMG (const Operator &fineOperator, const C &criterion, const SmootherArgs &smootherArgs=SmootherArgs(), const ParallelInformation &pinfo=ParallelInformation())
	Construct an AMG with an inexact coarse solver based on the smoother. More...
	Dune::Amg::AMG< M, X, S, PI, A >::AMG (std::shared_ptr< const Operator > fineOperator, const ParameterTree &configuration, const ParallelInformation &pinfo=ParallelInformation())
	Constructor an AMG via ParameterTree. More...
	Dune::Amg::AMG< M, X, S, PI, A >::AMG (const AMG &amg)
	Copy constructor.
void	Dune::Amg::AMG< M, X, S, PI, A >::pre (Domain &x, Range &b)
	Prepare the preconditioner. More...
void	Dune::Amg::AMG< M, X, S, 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::AMG< M, X, S, PI, A >::category () const
	Category of the preconditioner (see SolverCategory::Category)
void	Dune::Amg::AMG< M, X, S, PI, A >::post (Domain &x)
	Clean up. More...
template<class A1 >
void	Dune::Amg::AMG< M, X, S, 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::AMG< M, X, S, PI, A >::recalculateHierarchy ()
	Recalculate the matrix hierarchy. More...
bool	Dune::Amg::AMG< M, X, S, PI, A >::usesDirectCoarseLevelSolver () const
	Check whether the coarse solver used is a direct solver. More...
static std::shared_ptr< T >	Dune::Amg::ConstructionTraits< T >::construct (Arguments &args)
	Construct an object with the specified arguments. More...
	Dune::Amg::EdgeProperties::EdgeProperties ()
	Constructor.
std::bitset< SIZE >::reference	Dune::Amg::EdgeProperties::operator[] (std::size_t v)
	Access the bits directly.
bool	Dune::Amg::EdgeProperties::operator[] (std::size_t v) const
	Access the bits directly.
bool	Dune::Amg::EdgeProperties::depends () const
	Checks whether the vertex the edge points to depends on the vertex the edge starts. More...
void	Dune::Amg::EdgeProperties::setDepends ()
	Marks the edge as one of which the end point depends on the starting point.
void	Dune::Amg::EdgeProperties::resetDepends ()
	Resets the depends flag.
bool	Dune::Amg::EdgeProperties::influences () const
	Checks whether the start vertex is influenced by the end vertex. More...
void	Dune::Amg::EdgeProperties::setInfluences ()
	Marks the edge as one of which the start vertex by the end vertex.
void	Dune::Amg::EdgeProperties::resetInfluences ()
	Resets the influence flag.
bool	Dune::Amg::EdgeProperties::isOneWay () const
	Checks whether the edge is one way. I.e. either the influence or the depends flag but is set.
bool	Dune::Amg::EdgeProperties::isTwoWay () const
	Checks whether the edge is two way. I.e. both the influence flag and the depends flag are that.
bool	Dune::Amg::EdgeProperties::isStrong () const
	Checks whether the edge is strong. I.e. the influence or depends flag is set.
void	Dune::Amg::EdgeProperties::reset ()
	Reset all flags.
void	Dune::Amg::EdgeProperties::printFlags () const
	Prints the attributes of the edge for debugging.
	Dune::Amg::VertexProperties::VertexProperties ()
	Constructor.
std::bitset< SIZE >::reference	Dune::Amg::VertexProperties::operator[] (std::size_t v)
	Access the bits directly.
bool	Dune::Amg::VertexProperties::operator[] (std::size_t v) const
	Access the bits directly.
void	Dune::Amg::VertexProperties::setIsolated ()
	Marks that node as being isolated. More...
bool	Dune::Amg::VertexProperties::isolated () const
	Checks whether the node is isolated.
void	Dune::Amg::VertexProperties::resetIsolated ()
	Resets the isolated flag.
void	Dune::Amg::VertexProperties::setVisited ()
	Mark the node as already visited.
bool	Dune::Amg::VertexProperties::visited () const
	Checks whether the node is marked as visited.
void	Dune::Amg::VertexProperties::resetVisited ()
	Resets the visited flag.
void	Dune::Amg::VertexProperties::setFront ()
	Marks the node as belonging to the current clusters front.
bool	Dune::Amg::VertexProperties::front () const
	Checks whether the node is marked as a front node.
void	Dune::Amg::VertexProperties::resetFront ()
	Resets the front node flag.
void	Dune::Amg::VertexProperties::setExcludedBorder ()
	Marks the vertex as excluded from the aggregation.
bool	Dune::Amg::VertexProperties::excludedBorder () const
	Tests whether the vertex is excluded from the aggregation. More...
void	Dune::Amg::VertexProperties::resetExcludedBorder ()
	Marks the vertex as included in the aggregation.
void	Dune::Amg::VertexProperties::reset ()
	Reset all flags.
	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::PropertyGraphVertexPropertyMap (G &g)
	Constructor. More...
	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::PropertyGraphVertexPropertyMap ()
	Default constructor.
Reference	Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::operator[] (const Vertex &vertex) const
	Get the properties associated to a vertex. More...
	Dune::Amg::SparsityBuilder< M >::SparsityBuilder (M &matrix)
	Constructor. More...
template<class M , class V , class I , class O >
void	Dune::Amg::BaseGalerkinProduct::calculate (const M &fine, const AggregatesMap< V > &aggregates, M &coarse, const I &pinfo, const O &copy)
	Calculate the galerkin product. More...
template<class G , class V , class Set >
G::MutableMatrix *	Dune::Amg::GalerkinProduct< T >::build (G &fineGraph, V &visitedMap, const ParallelInformation &pinfo, AggregatesMap< typename G::VertexDescriptor > &aggregates, const typename G::Matrix::size_type &size, const Set &copy)
	Calculates the coarse matrix via a Galerkin product. More...
template<class G , class V , class Set >
G::MutableMatrix *	Dune::Amg::GalerkinProduct< SequentialInformation >::build (G &fineGraph, V &visitedMap, const SequentialInformation &pinfo, const AggregatesMap< typename G::VertexDescriptor > &aggregates, const typename G::Matrix::size_type &size, const Set &copy)
	Calculates the coarse matrix via a Galerkin product. More...
template<class R , class G , class V >
static void	Dune::Amg::BaseConnectivityConstructor::constructNonOverlapConnectivity (R &row, G &graph, V &visitedMap, const AggregatesMap< typename G::VertexDescriptor > &aggregates, const typename G::VertexDescriptor &seed)
	Construct the connectivity of an aggregate in the overlap.
	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::ConnectedBuilder (const AggregatesMap< Vertex > &aggregates, Graph &graph, VisitedMap &visitedMap, Set &connected)
	Constructor. More...
void	Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::operator() (const ConstEdgeIterator &edge)
	Process an edge pointing to another aggregate. More...
template<class G , class V >
int	Dune::Amg::visitNeighbours (const G &graph, const typename G::VertexDescriptor &vertex, V &visitor)
	Visit all neighbour vertices of a vertex in a graph. More...
template<typename Graph , typename VM >
static Graph::VertexDescriptor	Dune::Amg::ParallelIndicesCoarsener< T, E >::coarsen (ParallelInformation &fineInfo, Graph &fineGraph, VM &visitedMap, AggregatesMap< typename Graph::VertexDescriptor > &aggregates, ParallelInformation &coarseInfo, typename Graph::VertexDescriptor noAggregates, bool useFixedOrder=false)
	Build the coarse index set after the aggregatio. More...
	Dune::Amg::DependencyParameters::DependencyParameters ()
	Constructor.
void	Dune::Amg::DependencyParameters::setBeta (double b)
	Set threshold for marking nodes as isolated. The default value is 1.0E-5.
double	Dune::Amg::DependencyParameters::beta () const
	Get the threshold for marking nodes as isolated. The default value is 1.0E-5. More...
void	Dune::Amg::DependencyParameters::setAlpha (double a)
	Set the scaling value for marking connections as strong. Default value is 1/3.
double	Dune::Amg::DependencyParameters::alpha () const
	Get the scaling value for marking connections as strong. Default value is 1/3.
	Dune::Amg::AggregationParameters::AggregationParameters ()
	Constructor. More...
void	Dune::Amg::AggregationParameters::setDefaultValuesIsotropic (std::size_t dim, std::size_t diameter=2)
	Sets reasonable default values for an isotropic problem. More...
void	Dune::Amg::AggregationParameters::setDefaultValuesAnisotropic (std::size_t dim, std::size_t diameter=2)
	Sets reasonable default values for an anisotropic problem. More...
std::size_t	Dune::Amg::AggregationParameters::maxDistance () const
	Get the maximal distance allowed between two nodes in a aggregate. More...
void	Dune::Amg::AggregationParameters::setMaxDistance (std::size_t distance)
	Set the maximal distance allowed between two nodes in a aggregate. More...
bool	Dune::Amg::AggregationParameters::skipIsolated () const
	Whether isolated aggregates will not be represented on the coarse level. More...
void	Dune::Amg::AggregationParameters::setSkipIsolated (bool skip)
	Set whether isolated aggregates will not be represented on the coarse level. More...
std::size_t	Dune::Amg::AggregationParameters::minAggregateSize () const
	Get the minimum number of nodes a aggregate has to consist of. More...
void	Dune::Amg::AggregationParameters::setMinAggregateSize (std::size_t size)
	Set the minimum number of nodes a aggregate has to consist of. More...
std::size_t	Dune::Amg::AggregationParameters::maxAggregateSize () const
	Get the maximum number of nodes a aggregate is allowed to have. More...
void	Dune::Amg::AggregationParameters::setMaxAggregateSize (std::size_t size)
	Set the maximum number of nodes a aggregate is allowed to have. More...
std::size_t	Dune::Amg::AggregationParameters::maxConnectivity () const
	Get the maximum number of connections a aggregate is allowed to have. More...
void	Dune::Amg::AggregationParameters::setMaxConnectivity (std::size_t connectivity)
	Set the maximum number of connections a aggregate is allowed to have. More...
void	Dune::Amg::CoarseningParameters::setMaxLevel (int l)
	Set the maximum number of levels allowed in the hierarchy.
int	Dune::Amg::CoarseningParameters::maxLevel () const
	Get the maximum number of levels allowed in the hierarchy.
void	Dune::Amg::CoarseningParameters::setCoarsenTarget (int nodes)
	Set the maximum number of unknowns allowed on the coarsest level.
int	Dune::Amg::CoarseningParameters::coarsenTarget () const
	Get the maximum number of unknowns allowed on the coarsest level.
void	Dune::Amg::CoarseningParameters::setMinCoarsenRate (double rate)
	Set the minimum coarsening rate to be achieved in each coarsening. More...
double	Dune::Amg::CoarseningParameters::minCoarsenRate () const
	Get the minimum coarsening rate to be achieved.
AccumulationMode	Dune::Amg::CoarseningParameters::accumulate () const
	Whether the data should be accumulated on fewer processes on coarser levels.
void	Dune::Amg::CoarseningParameters::setAccumulate (AccumulationMode accu)
	Set whether the data should be accumulated on fewer processes on coarser levels.
bool	Dune::Amg::CoarseningParameters::useFixedOrder () const
	Check if the indices for the coarser levels should be created in a fixed order.
void	Dune::Amg::CoarseningParameters::setProlongationDampingFactor (double d)
	Set the damping factor for the prolongation. More...
double	Dune::Amg::CoarseningParameters::getProlongationDampingFactor () const
	Get the damping factor for the prolongation. More...
	Dune::Amg::CoarseningParameters::CoarseningParameters (int maxLevel=100, int coarsenTarget=1000, double minCoarsenRate=1.2, double prolongDamp=1.6, AccumulationMode accumulate=successiveAccu, bool useFixedOrder=false)
	Constructor. More...
void	Dune::Amg::Parameters::setDebugLevel (int level)
	Set the debugging level. More...
int	Dune::Amg::Parameters::debugLevel () const
	Get the debugging Level. More...
void	Dune::Amg::Parameters::setNoPreSmoothSteps (std::size_t steps)
	Set the number of presmoothing steps to apply. More...
std::size_t	Dune::Amg::Parameters::getNoPreSmoothSteps () const
	Get the number of presmoothing steps to apply. More...
void	Dune::Amg::Parameters::setNoPostSmoothSteps (std::size_t steps)
	Set the number of postsmoothing steps to apply. More...
std::size_t	Dune::Amg::Parameters::getNoPostSmoothSteps () const
	Get the number of postsmoothing steps to apply. More...
void	Dune::Amg::Parameters::setGamma (std::size_t gamma)
	Set the value of gamma; 1 for V-cycle, 2 for W-cycle.
std::size_t	Dune::Amg::Parameters::getGamma () const
	Get the value of gamma; 1 for V-cycle, 2 for W-cycle.
void	Dune::Amg::Parameters::setAdditive (bool additive)
	Set whether to use additive multigrid. More...
bool	Dune::Amg::Parameters::getAdditive () const
	Get whether to use additive multigrid. More...
	Dune::Amg::Parameters::Parameters (int maxLevel=100, int coarsenTarget=1000, double minCoarsenRate=1.2, double prolongDamp=1.6, AccumulationMode accumulate=successiveAccu, bool useFixedOrder=false)
	Constructor. More...
Reference	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::operator[] (const Key &key) const
	Get the property for a key. More...
	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::RandomAccessBundledPropertyMap (Container &container)
	Constructor. More...
	Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::RandomAccessBundledPropertyMap ()
	The default constructor.
	Dune::Amg::DefaultSmootherArgs< T >::DefaultSmootherArgs ()
	Default constructor.
static void	Dune::Amg::SmootherApplier< T >::preSmooth (Smoother &smoother, Domain &v, const Range &d)
	apply pre smoothing in forward direction More...
static void	Dune::Amg::SmootherApplier< T >::postSmooth (Smoother &smoother, Domain &v, const Range &d)
	apply post smoothing in forward direction More...
template<typename LevelContext >
void	Dune::Amg::presmooth (LevelContext &levelContext, size_t steps)
	Apply pre smoothing on the current level. More...
template<typename LevelContext >
void	Dune::Amg::postsmooth (LevelContext &levelContext, size_t steps)
	Apply post smoothing on the current level. More...
	Dune::Amg::Hierarchy< T, A >::Hierarchy (const std::shared_ptr< MemberType > &first)
	Construct a new hierarchy. More...
	Dune::Amg::Hierarchy< T, A >::Hierarchy (const Hierarchy &other)
	Copy constructor (deep copy!). More...
std::size_t	Dune::Amg::Hierarchy< T, A >::levels () const
	Get the number of levels in the hierarchy. More...
void	Dune::Amg::Hierarchy< T, A >::addCoarser (Arguments &args)
	Add an element on a coarser level. More...
void	Dune::Amg::Hierarchy< T, A >::addFiner (Arguments &args)
	Add an element on a finer level. More...
Iterator	Dune::Amg::Hierarchy< T, A >::finest ()
	Get an iterator positioned at the finest level. More...
Iterator	Dune::Amg::Hierarchy< T, A >::coarsest ()
	Get an iterator positioned at the coarsest level. More...
ConstIterator	Dune::Amg::Hierarchy< T, A >::finest () const
	Get an iterator positioned at the finest level. More...
ConstIterator	Dune::Amg::Hierarchy< T, A >::coarsest () const
	Get an iterator positioned at the coarsest level. More...
	Dune::Amg::KAMG< M, X, S, PI, K, A >::KAMG (OperatorHierarchy &matrices, CoarseSolver &coarseSolver, const SmootherArgs &smootherArgs, const Parameters &parms, std::size_t maxLevelKrylovSteps=3, double minDefectReduction=1e-1)
	Construct a new amg with a specific coarse solver. More...
template<class C >
	Dune::Amg::KAMG< M, X, S, PI, K, A >::KAMG (const Operator &fineOperator, const C &criterion, const SmootherArgs &smootherArgs=SmootherArgs(), std::size_t maxLevelKrylovSteps=3, double minDefectReduction=1e-1, const ParallelInformation &pinfo=ParallelInformation())
	Construct an AMG with an inexact coarse solver based on the smoother. More...
void	Dune::Amg::KAMG< M, X, S, PI, K, A >::pre (Domain &x, Range &b)
	Prepare the preconditioner. More...
void	Dune::Amg::KAMG< M, X, S, PI, K, A >::post (Domain &x)
	Clean up. More...
void	Dune::Amg::KAMG< M, X, S, PI, K, A >::apply (Domain &v, const Range &d)
	Apply one step of the preconditioner to the system A(v)=d. More...
	Dune::Amg::MatrixHierarchy< M, PI, A >::MatrixHierarchy (std::shared_ptr< MatrixOperator > fineMatrix, std::shared_ptr< ParallelInformation > pinfo=std::make_shared< ParallelInformation >())
	Constructor. More...
template<typename O , typename T >
void	Dune::Amg::MatrixHierarchy< M, PI, A >::build (const T &criterion)
	Build the matrix hierarchy using aggregation. More...
const ParallelMatrixHierarchy &	Dune::Amg::MatrixHierarchy< M, PI, A >::matrices () const
	Get the matrix hierarchy. More...
const ParallelInformationHierarchy &	Dune::Amg::MatrixHierarchy< M, PI, A >::parallelInformation () const
	Get the hierarchy of the parallel data distribution information. More...
void	Dune::Amg::MatrixHierarchy< M, PI, A >::getCoarsestAggregatesOnFinest (std::vector< std::size_t > &data) const
	Get the mapping of fine level unknowns to coarse level aggregates. More...
const AggregatesMapList &	Dune::Amg::MatrixHierarchy< M, PI, A >::aggregatesMaps () const
	Get the hierarchy of the mappings of the nodes onto aggregates. More...
const RedistributeInfoList &	Dune::Amg::MatrixHierarchy< M, PI, A >::redistributeInformation () const
	Get the hierarchy of the information about redistributions,. More...
template<class V , class BA , class TA >
void	Dune::Amg::MatrixHierarchy< M, PI, A >::coarsenVector (Hierarchy< BlockVector< V, BA >, TA > &hierarchy) const
	Coarsen the vector hierarchy according to the matrix hierarchy. More...
template<class S , class TA >
void	Dune::Amg::MatrixHierarchy< M, PI, A >::coarsenSmoother (Hierarchy< S, TA > &smoothers, const typename SmootherTraits< S >::Arguments &args) const
	Coarsen the smoother hierarchy according to the matrix hierarchy. More...
template<class F >
void	Dune::Amg::MatrixHierarchy< M, PI, A >::recalculateGalerkin (const F &copyFlags)
	Recalculate the galerkin products. More...
std::size_t	Dune::Amg::MatrixHierarchy< M, PI, A >::levels () const
	Get the number of levels in the hierarchy. More...
std::size_t	Dune::Amg::MatrixHierarchy< M, PI, A >::maxlevels () const
	Get the max number of levels in the hierarchy of processors. More...
bool	Dune::Amg::MatrixHierarchy< M, PI, A >::isBuilt () const
	Whether the hierarchy was built. More...

Variables
const Matrix *	Dune::Amg::SymmetricMatrixDependency< M, N >::matrix_
	The matrix we work on.
Norm	Dune::Amg::SymmetricMatrixDependency< M, N >::norm_
	The functor for calculating the norm.
int	Dune::Amg::SymmetricMatrixDependency< M, N >::row_
	index of the currently evaluated row.
real_type	Dune::Amg::SymmetricMatrixDependency< M, N >::diagonal_
	The norm of the current diagonal.
const Matrix *	Dune::Amg::Dependency< M, N >::matrix_
	The matrix we work on.
Norm	Dune::Amg::Dependency< M, N >::norm_
	The functor for calculating the norm.
int	Dune::Amg::Dependency< M, N >::row_
	index of the currently evaluated row.
real_type	Dune::Amg::Dependency< M, N >::diagonal_
	The norm of the current diagonal.
const Matrix *	Dune::Amg::SymmetricDependency< M, N >::matrix_
	The matrix we work on.
Norm	Dune::Amg::SymmetricDependency< M, N >::norm_
	The functor for calculating the norm.
int	Dune::Amg::SymmetricDependency< M, N >::row_
	index of the currently evaluated row.
real_type	Dune::Amg::SymmetricDependency< M, N >::diagonal_
	The norm of the current diagonal.
static const V	Dune::Amg::AggregatesMap< V >::UNAGGREGATED
	Identifier of not yet aggregated vertices.
static const V	Dune::Amg::AggregatesMap< V >::ISOLATED
	Identifier of isolated vertices.
Hierarchy< Smoother, A >::Iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::smoother
	The iterator over the smoothers.
OperatorHierarchy::ParallelMatrixHierarchy::ConstIterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::matrix
	The iterator over the matrices.
ParallelInformationHierarchy::Iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::pinfo
	The iterator over the parallel information.
OperatorHierarchy::RedistributeInfoList::const_iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::redist
	The iterator over the redistribution information.
OperatorHierarchy::AggregatesMapList::const_iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::aggregates
	The iterator over the aggregates maps.
Hierarchy< Domain, A >::Iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::lhs
	The iterator over the left hand side.
Hierarchy< Domain, A >::Iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::update
	The iterator over the updates.
Hierarchy< Range, A >::Iterator	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::rhs
	The iterator over the right hand sided.
std::size_t	Dune::Amg::AMG< M, X, S, PI, A >::LevelContext::level
	The level index.
Aggregate *	Dune::Amg::OverlapVertex< T >::aggregate
	The aggregate the vertex belongs to.
Vertex	Dune::Amg::OverlapVertex< T >::vertex
	The vertex descriptor.
int	Dune::Amg::DefaultSmootherArgs< T >::iterations
	The number of iterations to perform.
RelaxationFactor	Dune::Amg::DefaultSmootherArgs< T >::relaxationFactor
	The relaxation factor to use.

Detailed Description

A Parallel Algebraic Multigrid based on Agglomeration.

Typedef Documentation

Smoother

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

typedef S Dune::Amg::AMG< M, X, S, PI, A >::Smoother

The type of the smoother.

One of the preconditioners implementing the Preconditioner interface. Note that the smoother has to fit the ParallelInformation.

Enumeration Type Documentation

anonymous enum

template<typename G , std::size_t i>

anonymous enum

Enumerator
index	the index to access in the bitset.

anonymous enum

anonymous enum

Enumerator
MAX_PROCESSES	Hard limit for the number of processes allowed. This is needed to prevent overflows when calculating the coarsening rate. Currently set 72,000 which is enough for JUGENE.

anonymous enum

template<typename C , typename K , std::size_t i, typename T = typename C::ValueType, typename R = typename C::Reference>

anonymous enum

Enumerator
index	The index of the property in the bundle.

AccumulationMode

enum Dune::Amg::AccumulationMode

Identifiers for the different accumulation modes.

Enumerator
noAccu	No data accumulution. The coarse level data will be distributed to all processes.
atOnceAccu	Accumulate data to one process at once. Once no further coarsening is possible all data will be accumulated to one process
successiveAccu	Successively accumulate to fewer processes.

Function Documentation

addCoarser()

template<class T , class A >

void Dune::Amg::Hierarchy< T, A >::addCoarser

(

Arguments &

args

)

Add an element on a coarser level.

Parameters

args	The arguments needed for the construction.

References Dune::Amg::ConstructionTraits< T >::construct().

Referenced by Dune::Amg::MatrixHierarchy< M, PI, A >::coarsenSmoother().

addFiner()

template<class T , class A >

void Dune::Amg::Hierarchy< T, A >::addFiner

(

Arguments &

args

)

Add an element on a finer level.

Parameters

args	The arguments needed for the construction.

References Dune::Amg::ConstructionTraits< T >::construct().

Aggregate()

template<class G , class S >

Dune::Amg::Aggregate< G, S >::Aggregate	(	MatrixGraph &	graph,
		AggregatesMap< Vertex > &	aggregates,
		VertexSet &	connectivity,
		std::vector< Vertex > &	front_
	)

Constructor.

Parameters

graph	The matrix graph we work on.
aggregates	The mapping of vertices onto aggregates.
connectivity	The set of vertices connected to the aggregate. distance spheres.
front_	The vertices of the current aggregate front.

AggregatesMap()

template<class V >

Dune::Amg::AggregatesMap< V >::AggregatesMap

(

std::size_t

noVertices

)

Constructs with allocating memory.

Parameters

noVertices

The number of vertices we will hold information for.

aggregatesMaps()

template<class M , class IS , class A >

const MatrixHierarchy< M, IS, A >::AggregatesMapList & Dune::Amg::MatrixHierarchy< M, IS, A >::aggregatesMaps

Get the hierarchy of the mappings of the nodes onto aggregates.

Returns

The hierarchy of the mappings of the nodes onto aggregates.

AggregateVisitor()

template<class G >

template<class V >

Dune::Amg::Aggregator< G >::AggregateVisitor< V >::AggregateVisitor	(	const AggregatesMap< Vertex > &	aggregates,
		const AggregateDescriptor &	aggregate,
		Visitor &	visitor
	)

Constructor.

Parameters

aggregates	The aggregate numbers of the vertices.
aggregate	The id of the aggregate to visit.
visitor	The visitor.

AggregationCriterion()

template<class T >

Dune::Amg::AggregationCriterion< T >::AggregationCriterion ( )

inline

Constructor.

The parameters will be initialized with default values suitable for 2D isotropic problems.

If that does not fit your needs either use setDefaultValuesIsotropic setDefaultValuesAnisotropic or setup the values by hand

AggregationParameters()

Dune::Amg::AggregationParameters::AggregationParameters ( )

inline

Constructor.

The parameters will be initialized with default values suitable for 2D isotropic problems.

If that does not fit your needs either use setDefaultValuesIsotropic setDefaultValuesAnisotropic or setup the values by hand

allocate()

template<class V >

void Dune::Amg::AggregatesMap< V >::allocate

(

std::size_t

noVertices

)

Allocate memory for holding the information.

Parameters

noVertices

The total number of vertices to be mapped.

AMG() [1/3]

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

template<class C >

Dune::Amg::AMG< M, X, S, PI, A >::AMG	(	const Operator &	fineOperator,
		const C &	criterion,
		const SmootherArgs &	smootherArgs = SmootherArgs(),
		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.
smootherArgs	The arguments for constructing the smoothers.
pinfo	The information about the parallel distribution of the data.

AMG() [2/3]

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

Dune::Amg::AMG< M, X, S, PI, A >::AMG	(	OperatorHierarchy &	matrices,
		CoarseSolver &	coarseSolver,
		const SmootherArgs &	smootherArgs,
		const Parameters &	parms
	)

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.
smootherArgs	The arguments needed for thesmoother to use for pre and post smoothing.
parms	The parameters for the AMG.

AMG() [3/3]

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

Dune::Amg::AMG< M, X, S, PI, A >::AMG	(	std::shared_ptr< const Operator >	fineOperator,
		const ParameterTree &	configuration,
		const ParallelInformation &	pinfo = ParallelInformation()
	)

Constructor an AMG via ParameterTree.

Parameters

fineOperator	The operator on the fine level.
configuration	ParameterTree containing AMG parameters.
pinfo	Optionally, specify ParallelInformation

ParameterTree Key	Meaning
smootherIterations	The number of iterations to perform.
smootherRelaxation	The relaxation factor
maxLevel	Maximum number of levels allowed in the hierarchy.
coarsenTarget	Maximum number of unknowns on the coarsest level.
minCoarseningRate	Coarsening will stop if the rate is below this threshold.
accumulationMode	If and how data is agglomerated on coarser level to

| fewer processors. ("atOnce": do agglomeration once and | to one process; "successive": Multiple agglomerations to | fewer processes until all data is on one process; | "none": Do no agglomeration at all and solve coarse level | iteratively). prolongationDampingFactor | Damping factor for the prolongation. alpha | Scaling value for marking connections as strong. beta | Threshold for marking nodes as isolated. additive | Whether to use additive multigrid. gamma | 1 for V-cycle, 2 for W-cycle. preSteps | Number of presmoothing steps. postSteps | Number of postsmoothing steps. verbosity | Output verbosity. default=2. criterionSymmetric | If true use SymmetricCriterion (default), else UnSymmetricCriterion strengthMeasure | What conversion to use to convert a matrix block | to a scalar when determining strength of connection: | diagonal (use a diagonal of row diagonalRowIndex, class Diagonal, default); | rowSum (rowSum norm), frobenius (Frobenius norm); | one (use always one and neglect the actual entries). diagonalRowIndex | The index to use for the diagonal strength (default 0) | if this is i and strengthMeasure is "diagonal", then | block[i][i] will be used when determining strength of | connection. defaultAggregationSizeMode | Whether to set default values depending on isotropy of | problem uses parameters "defaultAggregationDimension" and | "maxAggregateDistance" (isotropic: For and isotropic problem; | anisotropic: for an anisotropic problem). defaultAggregationDimension | Dimension of the problem (used for setting default aggregate size). maxAggregateDistance | Maximum distance in an aggregte (in term of minimum edges needed to travel. | one vertex to another within the aggregate). minAggregateSize | Minimum number of vertices an aggregate should consist of. maxAggregateSize | Maximum number of vertices an aggregate should consist of.

See ISTL_Factory for the ParameterTree layout and examples.

apply() [1/2]

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

void Dune::Amg::AMG< M, X, S, 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.

apply() [2/2]

template<class M , class X , class S , class P , class K , class A >

void Dune::Amg::KAMG< M, X, S, P, K, 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.

beta()

double Dune::Amg::DependencyParameters::beta ( ) const

inline

Get the threshold for marking nodes as isolated. The default value is 1.0E-5.

Returns

beta

breadthFirstSearch() [1/2]

template<class V >

template<bool reset, class G , class F , class VM >

std::size_t Dune::Amg::AggregatesMap< V >::breadthFirstSearch	(	const VertexDescriptor &	start,
		const AggregateDescriptor &	aggregate,
		const G &	graph,
		F &	aggregateVisitor,
		VM &	visitedMap
	)		const

Breadth first search within an aggregate.

Template Parameters

reset	If true the visited flags of the vertices will be reset after the search
G	The type of the graph we perform the search on
F	The type of the visitor to operate on the vertices

Parameters

start	The vertex where the search should start from. This does not need to belong to the aggregate.
aggregate	The aggregate id.
graph	The matrix graph to perform the search on.
visitedMap	A map to mark the already visited vertices
aggregateVisitor	A functor that is called with each G::ConstEdgeIterator with an edge pointing to the aggregate. Use DummyVisitor if these are of no interest.

breadthFirstSearch() [2/2]

template<class V >

template<bool remove, bool reset, class G , class L , class F1 , class F2 , class VM >

std::size_t Dune::Amg::AggregatesMap< V >::breadthFirstSearch	(	const VertexDescriptor &	start,
		const AggregateDescriptor &	aggregate,
		const G &	graph,
		L &	visited,
		F1 &	aggregateVisitor,
		F2 &	nonAggregateVisitor,
		VM &	visitedMap
	)		const

Breadth first search within an aggregate.

Template Parameters

L	A container type providing push_back(Vertex), and pop_front() in case remove is true
remove	If true the entries in the visited list will be removed.
reset	If true the visited flag will be reset after the search

Parameters

start	The vertex where the search should start from. This does not need to belong to the aggregate.
aggregate	The aggregate id.
graph	The matrix graph to perform the search on.
visited	A list to store the visited vertices in.
aggregateVisitor	A functor that is called with each G::ConstEdgeIterator with an edge pointing to the aggregate. Use DummyVisitor these are of no interest.
nonAggregateVisitor	A functor that is called with each G::ConstEdgeIterator with an edge pointing to another aggregate. Use DummyVisitor these are of no interest.
visitedMap	A map to mark the already visited vertices

build() [1/4]

template<class G >

template<class M , class C >

std::tuple< int, int, int, int > Dune::Amg::Aggregator< G >::build	(	const M &	m,
		G &	graph,
		AggregatesMap< Vertex > &	aggregates,
		const C &	c,
		bool	finestLevel
	)

Build the aggregates.

Template Parameters

C	The type of the coarsening Criterion to use

Parameters

m	The matrix to build the aggregates accordingly.
graph	A (sub) graph of the matrix.
aggregates	Aggregate map we will build. All entries should be initialized to UNAGGREGATED!
c	The coarsening criterion to use.
finestLevel	Whether this the finest level. In that case rows representing Dirichlet boundaries will be detected and ignored during aggregation.

Returns

A tuple of the total number of aggregates, the number of isolated aggregates, the number of isolated aggregates, the number of aggregates consisting only of one vertex, and the number of skipped aggregates built.

build() [2/4]

template<class M , class IS , class A >

template<typename O , typename T >

void Dune::Amg::MatrixHierarchy< M, IS, A >::build

(

const T &

criterion

)

Build the matrix hierarchy using aggregation.

criterion The criterion describing the aggregation process.

References Dune::Amg::atOnceAccu, Dune::countNonZeros(), Dune::Amg::MAX_PROCESSES, Dune::size(), and Dune::Amg::successiveAccu.

build() [3/4]

template<class T >

template<class G , class V , class Set >

G::MutableMatrix * Dune::Amg::GalerkinProduct< T >::build	(	G &	fineGraph,
		V &	visitedMap,
		const ParallelInformation &	pinfo,
		AggregatesMap< typename G::VertexDescriptor > &	aggregates,
		const typename G::Matrix::size_type &	size,
		const Set &	copy
	)

Calculates the coarse matrix via a Galerkin product.

Parameters

fineGraph	The graph of the fine matrix.
visitedMap	Map for marking vertices as visited.
pinfo	Parallel information about the fine level.
aggregates	The mapping of the fine level unknowns onto aggregates.
size	The number of columns and rows of the coarse matrix.
copy	The attribute set identifying the copy nodes of the graph.

build() [4/4]

template<class G , class V , class Set >

G::MutableMatrix * Dune::Amg::GalerkinProduct< SequentialInformation >::build	(	G &	fineGraph,
		V &	visitedMap,
		const SequentialInformation &	pinfo,
		const AggregatesMap< typename G::VertexDescriptor > &	aggregates,
		const typename G::Matrix::size_type &	size,
		const Set &	copy
	)

Calculates the coarse matrix via a Galerkin product.

Parameters

fineGraph	The graph of the fine matrix.
visitedMap	Map for marking vertices as visited.
pinfo	Parallel information about the fine level.
aggregates	The mapping of the fine level unknowns onto aggregates.
size	The number of columns and rows of the coarse matrix.
copy	The attribute set identifying the copy nodes of the graph.

References Dune::dinfo, Dune::size(), and Dune::GeometryTypes::vertex.

buildAggregates()

template<class V >

template<class M , class G , class C >

std::tuple< int, int, int, int > Dune::Amg::AggregatesMap< V >::buildAggregates	(	const M &	matrix,
		G &	graph,
		const C &	criterion,
		bool	finestLevel
	)

Build the aggregates.

Parameters

matrix	The matrix describing the dependency.
graph	The graph corresponding to the matrix.
criterion	The aggregation criterion.
finestLevel	Whether this the finest level. In that case rows representing Dirichlet boundaries will be detected and ignored during aggregation.

Returns

A tuple of the total number of aggregates, the number of isolated aggregates, the number of isolated aggregates, the number of aggregates consisting only of one vertex, and the number of skipped aggregates built.

calculate()

template<class M , class V , class I , class O >

void Dune::Amg::BaseGalerkinProduct::calculate	(	const M &	fine,
		const AggregatesMap< V > &	aggregates,
		M &	coarse,
		const I &	pinfo,
		const O &	copy
	)

Calculate the galerkin product.

Parameters

fine	The fine matrix.
aggregates	The aggregate mapping.
coarse	The coarse Matrix.
pinfo	Parallel information about the fine level.
copy	The attribute set identifying the copy nodes of the graph.

coarsen()

template<typename T , typename E >

template<typename Graph , typename VM >

Graph::VertexDescriptor Dune::Amg::ParallelIndicesCoarsener< T, E >::coarsen ( ParallelInformation &  fineInfo, Graph &  fineGraph, VM &  visitedMap, AggregatesMap< typename Graph::VertexDescriptor > &  aggregates, ParallelInformation &  coarseInfo, typename Graph::VertexDescriptor  noAggregates, bool  useFixedOrder = false  )

inlinestatic

Build the coarse index set after the aggregatio.

Parameters

fineInfo	The parallel information at the fine level.
fineGraph	The graph of the fine lecel,
visitedMap	Map for marking vertices as visited.
aggregates	The mapping of unknowns onto aggregates.
coarseInfo	The information about the parallel data decomposition on the coarse level.
noAggregates
useFixedOrder	Flag indicating if creating indices for the coarser level should be done in a fixed order, i.e., the order in which the rows were sent. If set to true, this makes the runs reproducible but it might slow down performance.

Returns

The number of unknowns on the coarse level.

CoarseningParameters()

Dune::Amg::CoarseningParameters::CoarseningParameters ( int  maxLevel = 100, int  coarsenTarget = 1000, double  minCoarsenRate = 1.2, double  prolongDamp = 1.6, AccumulationMode  accumulate = successiveAccu, bool  useFixedOrder = false  )

inline

Constructor.

Parameters

maxLevel	The maximum number of levels allowed in the matrix hierarchy (default: 100).
coarsenTarget	If the number of nodes in the matrix is below this threshold the coarsening will stop (default: 1000).
minCoarsenRate	If the coarsening rate falls below this threshold the coarsening will stop (default: 1.2)
prolongDamp	The damping factor to apply to the prolongated update (default: 1.6)
accumulate	Whether to accumulate the data onto fewer processors on coarser levels.
useFixedOrder	Flag indicating if creating indices for the coarser level should be done in a fixed order, i.e., the order in which the rows were sent. If set to true, this makes the runs reproducible but it might slow down performance.

coarsenSmoother()

template<class M , class IS , class A >

template<class S , class TA >

void Dune::Amg::MatrixHierarchy< M, IS, A >::coarsenSmoother	(	Hierarchy< S, TA > &	smoothers,
		const typename SmootherTraits< S >::Arguments &	args
	)		const

Coarsen the smoother hierarchy according to the matrix hierarchy.

Parameters

smoothers	The smoother hierarchy to coarsen.
args	The arguments for the construction of the coarse level smoothers.

References Dune::Amg::Hierarchy< T, A >::addCoarser(), and Dune::Amg::Hierarchy< T, A >::levels().

coarsenVector()

template<class M , class IS , class A >

template<class V , class BA , class TA >

void Dune::Amg::MatrixHierarchy< M, IS, A >::coarsenVector

(

Hierarchy< BlockVector< V, BA >, TA > &

hierarchy

)

const

Coarsen the vector hierarchy according to the matrix hierarchy.

Parameters

hierarchy

The vector hierarchy to coarsen.

References Dune::dvverb.

coarsest() [1/2]

template<class T , class A >

Hierarchy< T, A >::Iterator Dune::Amg::Hierarchy< T, A >::coarsest

Get an iterator positioned at the coarsest level.

Returns

An iterator positioned at the coarsest level.

Referenced by Dune::Amg::AMG< M, X, S, PI, A >::post().

coarsest() [2/2]

template<class T , class A >

Hierarchy< T, A >::ConstIterator Dune::Amg::Hierarchy< T, A >::coarsest

Get an iterator positioned at the coarsest level.

Returns

An iterator positioned at the coarsest level.

ConnectedBuilder()

template<class G , class S , class V >

Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::ConnectedBuilder	(	const AggregatesMap< Vertex > &	aggregates,
		Graph &	graph,
		VisitedMap &	visitedMap,
		Set &	connected
	)

Constructor.

Parameters

aggregates	The mapping of the vertices onto the aggregates.
graph	The graph to work on.
visitedMap	The map for marking vertices as visited
connected	The set to added the connected aggregates to.

ConnectivityCounter()

template<class G >

Dune::Amg::Aggregator< G >::ConnectivityCounter::ConnectivityCounter	(	const VertexSet &	connected,
		const AggregatesMap< Vertex > &	aggregates
	)

Constructor.

Parameters

connected	The set of connected aggregates.
aggregates	Mapping of the vertices onto the aggregates.
aggregates	The mapping of aggregates to vertices.

construct()

template<typename T >

static std::shared_ptr< T > Dune::Amg::ConstructionTraits< T >::construct ( Arguments &  args )

inlinestatic

Construct an object with the specified arguments.

In the default implementation the copy constructor is called.

Parameters

args	The arguments for the construction.

Referenced by Dune::Amg::Hierarchy< T, A >::addCoarser(), and Dune::Amg::Hierarchy< T, A >::addFiner().

debugLevel()

int Dune::Amg::Parameters::debugLevel ( ) const

inline

Get the debugging Level.

Returns

0 if no debugging output will be generated.

depends()

bool Dune::Amg::EdgeProperties::depends ( ) const

inline

Checks whether the vertex the edge points to depends on the vertex the edge starts.

Returns

True if it depends on the starting point.

excludedBorder()

bool Dune::Amg::VertexProperties::excludedBorder ( ) const

inline

Tests whether the vertex is excluded from the aggregation.

Returns

True if the vertex is excluded from the aggregation process.

finest() [1/2]

template<class T , class A >

Hierarchy< T, A >::Iterator Dune::Amg::Hierarchy< T, A >::finest

Get an iterator positioned at the finest level.

Returns

An iterator positioned at the finest level.

finest() [2/2]

template<class T , class A >

Hierarchy< T, A >::ConstIterator Dune::Amg::Hierarchy< T, A >::finest

Get an iterator positioned at the finest level.

Returns

An iterator positioned at the finest level.

FrontMarker()

template<class G >

Dune::Amg::Aggregator< G >::FrontMarker::FrontMarker	(	std::vector< Vertex > &	front,
		MatrixGraph &	graph
	)

Constructor.

Parameters

front	The list to store the front vertices in.
graph	The matrix graph we work on.

FrontNeighbourCounter()

template<class G >

Dune::Amg::Aggregator< G >::FrontNeighbourCounter::FrontNeighbourCounter

(

const MatrixGraph &

front

)

Constructor.

Parameters

front

The vertices of the front.

getAdditive()

bool Dune::Amg::Parameters::getAdditive ( ) const

inline

Get whether to use additive multigrid.

Returns

True if multigrid should be additive.

getCoarsestAggregateNumbers()

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

template<class A1 >

void Dune::Amg::AMG< M, X, S, 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.

getCoarsestAggregatesOnFinest()

template<class M , class IS , class A >

void Dune::Amg::MatrixHierarchy< M, IS, A >::getCoarsestAggregatesOnFinest

(

std::vector< std::size_t > &

data

)

const

Get the mapping of fine level unknowns to coarse level aggregates.

For each fine level unknown i the corresponding data[i] is the aggregate it belongs to on the coarsest level.

Parameters

[out]

data

The mapping of fine level unknowns to coarse level aggregates.

References Dune::Amg::AggregatesMap< V >::ISOLATED, and Dune::size().

getNoPostSmoothSteps()

std::size_t Dune::Amg::Parameters::getNoPostSmoothSteps ( ) const

inline

Get the number of postsmoothing steps to apply.

Returns

The number of steps:

getNoPreSmoothSteps()

std::size_t Dune::Amg::Parameters::getNoPreSmoothSteps ( ) const

inline

Get the number of presmoothing steps to apply.

Returns

The number of steps:

getProlongationDampingFactor()

double Dune::Amg::CoarseningParameters::getProlongationDampingFactor ( ) const

inline

Get the damping factor for the prolongation.

Returns

d The damping factor.

Hierarchy() [1/2]

template<class T , class A >

Dune::Amg::Hierarchy< T, A >::Hierarchy

(

const Hierarchy< T, A > &

other

)

Copy constructor (deep copy!).

deep copy of a given hierarchy

Hierarchy() [2/2]

template<class T , class A >

Dune::Amg::Hierarchy< T, A >::Hierarchy

(

const std::shared_ptr< MemberType > &

first

)

Construct a new hierarchy.

Parameters

first

std::shared_ptr to the first element in the hierarchy.

influences()

bool Dune::Amg::EdgeProperties::influences ( ) const

inline

Checks whether the start vertex is influenced by the end vertex.

Returns

True if it is influenced.

isBuilt()

template<class M , class IS , class A >

bool Dune::Amg::MatrixHierarchy< M, IS, A >::isBuilt

Whether the hierarchy was built.

Returns

true if the MatrixHierarchy::build method was called.

KAMG() [1/2]

template<class M , class X , class S , class P , class K , class A >

template<class C >

Dune::Amg::KAMG< M, X, S, P, K, A >::KAMG	(	const Operator &	fineOperator,
		const C &	criterion,
		const SmootherArgs &	smootherArgs = SmootherArgs(),
		std::size_t	maxLevelKrylovSteps = 3,
		double	minDefectReduction = 1e-1,
		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.
smootherArgs	The arguments for constructing the smoothers.
maxLevelKrylovSteps	maximum of krylov iterations on a particular level (default=3)
minDefectReduction	minimal defect reduction during the krylov iterations on a particular level (default=1e-1)
pinfo	The information about the parallel distribution of the data.

KAMG() [2/2]

template<class M , class X , class S , class P , class K , class A >

Dune::Amg::KAMG< M, X, S, P, K, A >::KAMG	(	OperatorHierarchy &	matrices,
		CoarseSolver &	coarseSolver,
		const SmootherArgs &	smootherArgs,
		const Parameters &	parms,
		std::size_t	maxLevelKrylovSteps = 3,
		double	minDefectReduction = 1e-1
	)

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.
smootherArgs	The arguments needed for thesmoother to use for pre and post smoothing.
parms	The parameters for the AMG.
maxLevelKrylovSteps	maximum of krylov iterations on a particular level (default=3)
minDefectReduction	minimal defect reduction during the krylov iterations on a particular level (default=1e-1)

levels() [1/2]

template<class T , class A >

std::size_t Dune::Amg::Hierarchy< T, A >::levels

Get the number of levels in the hierarchy.

Returns

The number of levels.

Referenced by Dune::Amg::MatrixHierarchy< M, PI, A >::coarsenSmoother().

levels() [2/2]

template<class M , class IS , class A >

std::size_t Dune::Amg::MatrixHierarchy< M, IS, A >::levels

Get the number of levels in the hierarchy.

Returns

The number of levels.

matrices()

template<class M , class IS , class A >

const MatrixHierarchy< M, IS, A >::ParallelMatrixHierarchy & Dune::Amg::MatrixHierarchy< M, IS, A >::matrices

Get the matrix hierarchy.

Returns

The matrix hierarchy.

MatrixHierarchy()

template<class M , class IS , class A >

Dune::Amg::MatrixHierarchy< M, IS, A >::MatrixHierarchy	(	std::shared_ptr< MatrixOperator >	fineMatrix,
		std::shared_ptr< ParallelInformation >	pinfo = std::make_shared<ParallelInformation>()
	)

Constructor.

Parameters

fineMatrix	The matrix to coarsen.
pinfo	The information about the parallel data decomposition at the first level.

References Dune::SolverCategory::category(), and DUNE_THROW.

maxAggregateSize()

std::size_t Dune::Amg::AggregationParameters::maxAggregateSize ( ) const

inline

Get the maximum number of nodes a aggregate is allowed to have.

Returns

The maximum number of nodes.

maxConnectivity()

std::size_t Dune::Amg::AggregationParameters::maxConnectivity ( ) const

inline

Get the maximum number of connections a aggregate is allowed to have.

This limit exists to achieve sparsity of the coarse matrix. the default value is 15.

Returns

The maximum number of connections a aggregate is allowed to have.

maxDistance()

std::size_t Dune::Amg::AggregationParameters::maxDistance ( ) const

inline

Get the maximal distance allowed between two nodes in a aggregate.

The distance between two nodes in a aggregate is the minimal number of edges it takes to travel from one node to the other without leaving the aggregate.

Returns

The maximum distance allowed.

maxlevels()

template<class M , class IS , class A >

std::size_t Dune::Amg::MatrixHierarchy< M, IS, A >::maxlevels

Get the max number of levels in the hierarchy of processors.

Returns

The maximum number of levels.

minAggregateSize()

std::size_t Dune::Amg::AggregationParameters::minAggregateSize ( ) const

inline

Get the minimum number of nodes a aggregate has to consist of.

Returns

The minimum number of nodes.

operator()() [1/7]

template<class G , class S , class V >

void Dune::Amg::BaseConnectivityConstructor::ConnectedBuilder< G, S, V >::operator()

(

const ConstEdgeIterator &

edge

)

Process an edge pointing to another aggregate.

Parameters

edge	The iterator positioned at the edge.

References Dune::GeometryTypes::vertex.

operator()() [2/7]

template<class M >

FieldTraits< typenameM::field_type >::real_type Dune::Amg::RowSum::operator() ( const M &  m ) const

inline

compute the norm of a matrix.

Parameters

m	The matrix row to compute the norm of.

operator()() [3/7]

template<class M >

FieldTraits< typenameM::field_type >::real_type Dune::Amg::FrobeniusNorm::operator() ( const M &  m ) const

inline

compute the norm of a matrix.

Parameters

m	The matrix row to compute the norm of.

operator()() [4/7]

template<class M >

FieldTraits< typenameM::field_type >::real_type Dune::Amg::AlwaysOneNorm::operator() ( const M &  m ) const

inline

compute the norm of a matrix.

Parameters

m	The matrix row to compute the norm of.

operator()() [5/7]

template<int N>

template<class M >

auto Dune::Amg::Diagonal< N >::operator() ( const M &  m, typename std::enable_if_t< Dune::IsNumber< M >::value > *  sfinae = nullptr  ) const

inline

Compute the norm of a scalar.

Parameters

m	The scalar to compute the norm of

operator()() [6/7]

template<int N>

template<class M >

FieldTraits< typenameM::field_type >::real_type Dune::Amg::Diagonal< N >::operator() ( const M &  m, typename std::enable_if_t<!Dune::IsNumber< M >::value > *  sfinae = nullptr  ) const

inline

compute the norm of a matrix.

Parameters

m	The matrix to compute the norm of

operator()() [7/7]

template<class G >

template<class V >

void Dune::Amg::Aggregator< G >::AggregateVisitor< V >::operator()

(

const typename MatrixGraph::ConstEdgeIterator &

edge

)

Examine an edge.

The edge will be examined by the adapted visitor if it belongs to the right aggregate.

operator[]() [1/4]

template<typename C , typename K , std::size_t i, typename T = typename C::ValueType, typename R = typename C::Reference>

Reference Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::operator[] ( const Key &  key ) const

inline

Get the property for a key.

Parameters

key

The key.

Returns

The corresponding property.

References Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::index.

operator[]() [2/4]

template<typename G , std::size_t i>

Reference Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::operator[] ( const Vertex &  vertex ) const

inline

Get the properties associated to a vertex.

Parameters

vertex

The vertex whose Properties we want.

References Dune::GeometryTypes::vertex.

operator[]() [3/4]

template<class V >

AggregateDescriptor & Dune::Amg::AggregatesMap< V >::operator[]

(

const VertexDescriptor &

v

)

Get the aggregate a vertex belongs to.

Parameters

v	The vertex we want to know the aggregate of.

Returns

The aggregate the vertex is mapped to.

operator[]() [4/4]

template<class V >

const AggregateDescriptor & Dune::Amg::AggregatesMap< V >::operator[]

(

const VertexDescriptor &

v

)

const

Get the aggregate a vertex belongs to.

Parameters

v	The vertex we want to know the aggregate of.

Returns

The aggregate the vertex is mapped to.

parallelInformation()

template<class M , class IS , class A >

const MatrixHierarchy< M, IS, A >::ParallelInformationHierarchy & Dune::Amg::MatrixHierarchy< M, IS, A >::parallelInformation

Get the hierarchy of the parallel data distribution information.

Returns

The hierarchy of the parallel data distribution information.

Parameters()

Dune::Amg::Parameters::Parameters ( int  maxLevel = 100, int  coarsenTarget = 1000, double  minCoarsenRate = 1.2, double  prolongDamp = 1.6, AccumulationMode  accumulate = successiveAccu, bool  useFixedOrder = false  )

inline

Constructor.

Parameters

maxLevel	The maximum number of levels allowed in the matrix hierarchy (default: 100).
coarsenTarget	If the number of nodes in the matrix is below this threshold the coarsening will stop (default: 1000).
minCoarsenRate	If the coarsening rate falls below this threshold the coarsening will stop (default: 1.2)
prolongDamp	The damping factor to apply to the prolongated update (default: 1.6)
accumulate	Whether to accumulate the data onto fewer processors on coarser levels.

post() [1/2]

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

void Dune::Amg::AMG< M, X, S, 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 >.

References Dune::Amg::Hierarchy< T, A >::coarsest().

post() [2/2]

template<class M , class X , class S , class P , class K , class A >

void Dune::Amg::KAMG< M, X, S, P, K, 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 >.

postsmooth()

template<typename LevelContext >

void Dune::Amg::postsmooth	(	LevelContext &	levelContext,
		size_t	steps
	)

Apply post smoothing on the current level.

Parameters

levelContext	the iterators of the current level.
steps	The number of smoothing steps to apply.

References Dune::Amg::SmootherApplier< T >::postSmooth().

Referenced by Dune::Amg::KAmgTwoGrid< AMG >::apply().

postSmooth()

template<class T >

static void Dune::Amg::SmootherApplier< T >::postSmooth ( Smoother &  smoother, Domain &  v, const Range &  d  )

inlinestatic

apply post smoothing in forward direction

Parameters

smoother	The smoother to use.
d	The current defect.
v	handle to store the update in.

Referenced by Dune::Amg::postsmooth().

pre() [1/2]

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

void Dune::Amg::AMG< M, X, S, 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.

pre() [2/2]

template<class M , class X , class S , class P , class K , class A >

void Dune::Amg::KAMG< M, X, S, P, K, 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.

presmooth()

template<typename LevelContext >

void Dune::Amg::presmooth	(	LevelContext &	levelContext,
		size_t	steps
	)

Apply pre smoothing on the current level.

Parameters

levelContext	the iterators of the current level.
steps	The number of smoothing steps to apply.

References Dune::Amg::SmootherApplier< T >::preSmooth().

Referenced by Dune::Amg::KAmgTwoGrid< AMG >::apply().

preSmooth()

template<class T >

static void Dune::Amg::SmootherApplier< T >::preSmooth ( Smoother &  smoother, Domain &  v, const Range &  d  )

inlinestatic

apply pre smoothing in forward direction

Parameters

smoother	The smoother to use.
d	The current defect.
v	handle to store the update in.

Referenced by Dune::Amg::presmooth().

PropertyGraphVertexPropertyMap()

template<typename G , std::size_t i>

Dune::Amg::PropertyGraphVertexPropertyMap< G, i >::PropertyGraphVertexPropertyMap ( G &  g )

inline

Constructor.

Parameters

g	The graph whose properties we access.

RandomAccessBundledPropertyMap()

template<typename C , typename K , std::size_t i, typename T = typename C::ValueType, typename R = typename C::Reference>

Dune::Amg::RandomAccessBundledPropertyMap< C, K, i, T, R >::RandomAccessBundledPropertyMap ( Container &  container )

inline

Constructor.

Parameters

container

The container with the property bundle.

recalculateGalerkin()

template<class M , class IS , class A >

template<class F >

void Dune::Amg::MatrixHierarchy< M, IS, A >::recalculateGalerkin

(

const F &

copyFlags

)

Recalculate the galerkin products.

If the data of the fine matrix changes but not its sparsity pattern this will recalculate all coarser levels without starting the expensive aggregation process all over again.

recalculateHierarchy()

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

void Dune::Amg::AMG< M, X, S, 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.

reconstruct()

template<class G , class S >

void Dune::Amg::Aggregate< G, S >::reconstruct

(

const Vertex &

vertex

)

Reconstruct the aggregat from an seed node.

Will determine all vertices of the same aggregate and reference those.

redistributeInformation()

template<class M , class IS , class A >

const MatrixHierarchy< M, IS, A >::RedistributeInfoList & Dune::Amg::MatrixHierarchy< M, IS, A >::redistributeInformation

Get the hierarchy of the information about redistributions,.

Returns

The hierarchy of the information about redistributions of the data to fewer processes.

setAdditive()

void Dune::Amg::Parameters::setAdditive ( bool  additive )

inline

Set whether to use additive multigrid.

Parameters

additive

True if multigrid should be additive.

setDebugLevel()

void Dune::Amg::Parameters::setDebugLevel ( int  level )

inline

Set the debugging level.

Parameters

level

If 0 no debugging output will be generated.

Warning

In parallel the level has to be consistent over all procceses.

setDefaultValuesAnisotropic() [1/2]

template<class T >

void Dune::Amg::AggregationCriterion< T >::setDefaultValuesAnisotropic ( std::size_t  dim, std::size_t  diameter = 2  )

inline

Sets reasonable default values for an aisotropic problem.

Reasonable means that we should end up with cube aggregates with sides of diameter 2 and sides in one dimension that are longer (e.g. for 3D: 2x2x3).

Parameters

dim	The dimension of the problem.
diameter	The preferred diameter for the aggregation.

References Dune::Amg::AggregationCriterion< T >::setDefaultValuesIsotropic().

setDefaultValuesAnisotropic() [2/2]

void Dune::Amg::AggregationParameters::setDefaultValuesAnisotropic ( std::size_t  dim, std::size_t  diameter = 2  )

inline

Sets reasonable default values for an anisotropic problem.

Reasonable means that we should end up with cube aggregates with sides of diameter 2 and sides in one dimension that are longer (e.g. for 3D: 2x2x3).

Parameters

dim	The dimension of the problem.
diameter	The preferred diameter for the aggregation.

References Dune::Amg::AggregationParameters::setDefaultValuesIsotropic().

setDefaultValuesIsotropic() [1/2]

template<class T >

void Dune::Amg::AggregationCriterion< T >::setDefaultValuesIsotropic ( std::size_t  dim, std::size_t  diameter = 2  )

inline

Sets reasonable default values for an isotropic problem.

Reasonable means that we should end up with cube aggregates of diameter 2.

Parameters

dim	The dimension of the problem.
diameter	The preferred diameter for the aggregation.

Referenced by Dune::Amg::AggregationCriterion< T >::setDefaultValuesAnisotropic().

setDefaultValuesIsotropic() [2/2]

void Dune::Amg::AggregationParameters::setDefaultValuesIsotropic ( std::size_t  dim, std::size_t  diameter = 2  )

inline

Sets reasonable default values for an isotropic problem.

Reasonable means that we should end up with cube aggregates of diameter 2.

Parameters

dim	The dimension of the problem.
diameter	The preferred diameter for the aggregation.

Referenced by Dune::Amg::AggregationParameters::setDefaultValuesAnisotropic().

setIsolated()

void Dune::Amg::VertexProperties::setIsolated ( )

inline

Marks that node as being isolated.

A node is isolated if it ha not got any strong connections to other nodes in the matrix graph.

setMaxAggregateSize()

void Dune::Amg::AggregationParameters::setMaxAggregateSize ( std::size_t  size )

inline

Set the maximum number of nodes a aggregate is allowed to have.

The default values is 6.

Parameters

size	The maximum number of nodes.

References Dune::size().

setMaxConnectivity()

void Dune::Amg::AggregationParameters::setMaxConnectivity ( std::size_t  connectivity )

inline

Set the maximum number of connections a aggregate is allowed to have.

This limit exists to achieve sparsity of the coarse matrix. the default value is 15.

Parameters

connectivity

The maximum number of connections a aggregate is allowed to have.

setMaxDistance()

void Dune::Amg::AggregationParameters::setMaxDistance ( std::size_t  distance )

inline

Set the maximal distance allowed between two nodes in a aggregate.

The distance between two nodes in a aggregate is the minimal number of edges it takes to travel from one node to the other without leaving the aggregate. The default value is 2.

Parameters

distance

The maximum distance allowed.

setMinAggregateSize()

void Dune::Amg::AggregationParameters::setMinAggregateSize ( std::size_t  size )

inline

Set the minimum number of nodes a aggregate has to consist of.

the default value is 4.

References Dune::size().

setMinCoarsenRate()

void Dune::Amg::CoarseningParameters::setMinCoarsenRate ( double  rate )

inline

Set the minimum coarsening rate to be achieved in each coarsening.

The default value is 1.2

setNoPostSmoothSteps()

void Dune::Amg::Parameters::setNoPostSmoothSteps ( std::size_t  steps )

inline

Set the number of postsmoothing steps to apply.

Parameters

steps

The number of steps:

setNoPreSmoothSteps()

void Dune::Amg::Parameters::setNoPreSmoothSteps ( std::size_t  steps )

inline

Set the number of presmoothing steps to apply.

Parameters

steps

The number of steps:

setProlongationDampingFactor()

void Dune::Amg::CoarseningParameters::setProlongationDampingFactor ( double  d )

inline

Set the damping factor for the prolongation.

Parameters

d	The new damping factor.

setSkipIsolated()

void Dune::Amg::AggregationParameters::setSkipIsolated ( bool  skip )

inline

Set whether isolated aggregates will not be represented on the coarse level.

Parameters

skip	True if these aggregates will be skipped.

skipIsolated()

bool Dune::Amg::AggregationParameters::skipIsolated ( ) const

inline

Whether isolated aggregates will not be represented on the coarse level.

Returns

True if these aggregates will be skipped.

SparsityBuilder()

template<class M >

Dune::Amg::SparsityBuilder< M >::SparsityBuilder

(

M &

matrix

)

Constructor.

Parameters

matrix

The matrix whose sparsity pattern we should set up.

usesDirectCoarseLevelSolver()

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

bool Dune::Amg::AMG< M, X, S, PI, A >::usesDirectCoarseLevelSolver

Check whether the coarse solver used is a direct solver.

Returns

True if the coarse level solver is a direct solver.

visitNeighbours()

template<class G , class V >

int Dune::Amg::visitNeighbours	(	const G &	graph,
		const typename G::VertexDescriptor &	vertex,
		V &	visitor
	)

Visit all neighbour vertices of a vertex in a graph.

Parameters

graph	The graph whose vertices to visit.
vertex	The vertex whose neighbours we want to visit.
visitor	The visitor evaluated for each EdgeIterator (by its method operator()(const ConstEdgeIterator& edge)

Returns

The number of neighbours of the vertex.