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void | AddLevel (const RCP< Level > &level) |
| Add a level at the end of the hierarchy. More...
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void | AddNewLevel () |
| Add a new level at the end of the hierarchy. More...
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RCP< Level > & | GetLevel (const int levelID=0) |
| Retrieve a certain level from hierarchy. More...
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int | GetNumLevels () const |
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int | GetGlobalNumLevels () const |
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MagnitudeType | GetRate () const |
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double | GetOperatorComplexity () const |
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void | CheckLevel (Level &level, int levelID) |
| Helper function. More...
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bool | Setup (int coarseLevelID, const RCP< const FactoryManagerBase > fineLevelManager, const RCP< const FactoryManagerBase > coarseLevelManager, const RCP< const FactoryManagerBase > nextLevelManager=Teuchos::null) |
| Multi-level setup phase: build a new level of the hierarchy. More...
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void | Setup (const FactoryManagerBase &manager=FactoryManager(), int startLevel=0, int numDesiredLevels=GetDefaultMaxLevels()) |
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void | SetupRe () |
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void | Clear (int startLevel=0) |
| Clear impermanent data from previous setup. More...
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void | ExpertClear () |
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CycleType | GetCycle () const |
| Returns multigrid cycle type (supports VCYCLE and WCYCLE) More...
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void | SetCycle (CycleType Cycle) |
| Supports VCYCLE and WCYCLE types. More...
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ReturnType | Iterate (const MultiVector &B, MultiVector &X, ConvData conv=ConvData(), bool InitialGuessIsZero=false, LO startLevel=0) |
| Apply the multigrid preconditioner. More...
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void | Write (const LO &start=-1, const LO &end=-1) |
| Print matrices in the multigrid hierarchy to file. More...
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void | EnableGraphDumping (const std::string &filename, int levelID=1) |
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template<class Node2 > |
Teuchos::RCP< Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node2 > > | clone (const RCP< Node2 > &node2) const |
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void | setlib (Xpetra::UnderlyingLib inlib) |
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Xpetra::UnderlyingLib | lib () |
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template<typename Node2 > |
Teuchos::RCP< Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node2 > > | clone (const Teuchos::RCP< Node2 > &node2) const |
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virtual | ~BaseClass () |
| Destructor. More...
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VerbLevel | GetVerbLevel () const |
| Get the verbosity level. More...
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void | SetVerbLevel (const VerbLevel verbLevel) |
| Set the verbosity level of this object. More...
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int | GetProcRankVerbose () const |
| Get proc rank used for printing. Do not use this information for any other purpose. More...
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int | SetProcRankVerbose (int procRank) const |
| Set proc rank used for printing. More...
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bool | IsPrint (MsgType type, int thisProcRankOnly=-1) const |
| Find out whether we need to print out information for a specific message type. More...
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Teuchos::FancyOStream & | GetOStream (MsgType type, int thisProcRankOnly=0) const |
| Get an output stream for outputting the input message type. More...
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Teuchos::FancyOStream & | GetBlackHole () const |
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| VerboseObject () |
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virtual | ~VerboseObject () |
| Destructor. More...
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virtual | ~Describable () |
| Destructor. More...
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virtual std::string | ShortClassName () const |
| Return the class name of the object, without template parameters and without namespace. More...
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void | describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel=Teuchos::Describable::verbLevel_default) const |
| Print the object with some verbosity level to an FancyOStream object. More...
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template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
class MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >
Provides methods to build a multigrid hierarchy and apply multigrid cycles.
Allows users to manually populate operators at different levels within a multigrid method and push them into the hierarchy via SetLevel() and/or to supply factories for automatically generating prolongators, restrictors, and coarse level discretizations. Additionally, this class contains an apply method that supports V and W cycles.
Definition at line 103 of file MueLu_Hierarchy_decl.hpp.
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
typedef Teuchos::ScalarTraits<SC> MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::STS |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
Copy constructor is not implemented.
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
static bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetDefaultImplicitTranspose |
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inlinestatic |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
static Xpetra::global_size_t MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetDefaultMaxCoarseSize |
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inlinestatic |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
static int MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetDefaultMaxLevels |
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inlinestatic |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
static bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetDefaultPRrebalance |
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inlinestatic |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
Xpetra::global_size_t MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetMaxCoarseSize |
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const |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetImplicitTranspose |
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const |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::SetMaxCoarseSize |
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Xpetra::global_size_t |
maxCoarseSize | ) |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::SetPRrebalance |
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bool |
doPRrebalance | ) |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::SetImplicitTranspose |
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const bool & |
implicit | ) |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
int MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::LastLevelID |
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const |
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inlineprivate |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >
Multi-level setup phase: build a new level of the hierarchy.
This method is aimed to be used in a loop building the hierarchy level by level. See Hierarchy::Setup(manager, startLevel, numDesiredLevels) for an example of usage.
- Parameters
-
coarseLevelID | ID of the level to be built. |
fineLevelManager | defines how to build missing data of the fineLevel (example: aggregates) |
coarseLevelManager | defines how to build the level |
nextLevelManager | defines how the next coarse level will be built. This is used to post corresponding request before building the coarse level to keep useful data. |
CoarseLevel is considered to be the last level if:
- input parameter isLastLevel == true or
- Ac->getRowMap()->getGlobalNumElements() <= maxCoarseSize_ Method return true if CoarseLevel is the last level.
Pre-condition: FineLevel:
- must have kept useful data (TODO: not tested yet)
- must be Teuchos::null when Setup is called for finest level (Setup then automatically calls Request for "Smoother" and "CoarseSolver") CoarseLevel:
- already allocated (using Hierarchy::AddLevel())
- requests already posted (exception: for finest level (=fineLevelManager==null) requests are called within setup routine) NextLevel:
- do not need to be allocate but could (FIXME: will be deleted if lastlevel...).
- should be null when Setup is called for last level
Post-condition: FineLevel:
- temporary data have been used and released (this condition is not tested) CoarseLevel:
- built, requests have been used
- if it is the last level (due to input parameter isLastLevel or getGlobalNumElements() <= maxCoarseSize_), then the coarse solver factory of the factory manager have been used instead of the smoother factory. NextLevel: If input parameter isLastLevel == false:
- have been allocated
- requests already posted.
Definition at line 178 of file MueLu_Hierarchy_def.hpp.
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >
Apply the multigrid preconditioner.
In theory, more general cycle types than just V- and W-cycles are possible. However, the enumerated type CycleType would have to be extended.
- Parameters
-
B | right-hand side of linear problem |
X | initial and final (approximate) solution of linear problem |
ConvData | struct which stores convergence criteria (maximum number of multigrid iterations or stopping tolerance) |
InitialGuessIsZero | Indicates whether the initial guess is zero |
startLevel | index of starting level to build multigrid hierarchy (default = 0) |
Definition at line 518 of file MueLu_Hierarchy_def.hpp.
template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::Write |
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const LO & |
start = -1 , |
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const LO & |
end = -1 |
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) |
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Print matrices in the multigrid hierarchy to file.
- Parameters
-
[in] | start | start level |
[in] | end | end level |
Default behavior is to print system and transfer matrices from the entire hierarchy. Files are named "A_0.m", "P_1.m", "R_1.m", etc, and are in matrix market coordinate format.
Definition at line 781 of file MueLu_Hierarchy_def.hpp.
template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::IsPreconditioner |
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const bool |
flag | ) |
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Indicate whether the multigrid method is a preconditioner or a solver.
This is used in conjunction with the verbosity level to determine whether the residuals can be printed.
Definition at line 964 of file MueLu_Hierarchy_def.hpp.
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::EnableGraphDumping |
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const std::string & |
filename, |
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int |
levelID = 1 |
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) |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
void MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::setlib |
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Xpetra::UnderlyingLib |
inlib | ) |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
Xpetra::UnderlyingLib MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::lib |
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inline |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<typename Node2 >
Teuchos::RCP<Hierarchy<Scalar, LocalOrdinal, GlobalOrdinal, Node2> > MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::clone |
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const Teuchos::RCP< Node2 > & |
node2 | ) |
const |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class S2 , class LO2 , class GO2 , class N2 >
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
Xpetra::global_size_t MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::maxCoarseSize_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::implicitTranspose_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::doPRrebalance_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::isPreconditioner_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
Xpetra::UnderlyingLib MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::lib_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
bool MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::isDumpingEnabled_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
std::string MueLu::Hierarchy< Scalar, LocalOrdinal, GlobalOrdinal, Node >::dumpFile_ |
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private |
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>
template<class Scalar = Xpetra::Operator<>::scalar_type, class LocalOrdinal = typename Xpetra::Operator<Scalar>::local_ordinal_type, class GlobalOrdinal = typename Xpetra::Operator<Scalar, LocalOrdinal>::global_ordinal_type, class Node = typename Xpetra::Operator<Scalar, LocalOrdinal, GlobalOrdinal>::node_type>