Preconditioners
[Linear algebra classesMatrix classes]

Collaboration diagram for Preconditioners:

Classes

class  BlockTrianglePrecondition< number >
class  PreconditionLU< number >
class  PreconditionIdentity
class  PreconditionRichardson
class  PreconditionUseMatrix< MATRIX, VECTOR >
class  PreconditionRelaxation< MATRIX >
class  PreconditionJacobi< MATRIX >
class  PreconditionSOR< MATRIX >
class  PreconditionSSOR< MATRIX >
class  PreconditionPSOR< MATRIX >
class  PreconditionLACSolver< SOLVER, MATRIX, PRECONDITION >
class  PreconditionedMatrix< MATRIX, PRECOND, VECTOR >
class  PreconditionBlock< MATRIX, inverse_type >
class  PreconditionBlockJacobi< MATRIX, inverse_type >
class  PreconditionBlockSOR< MATRIX, inverse_type >
class  PreconditionBlockSSOR< MATRIX, inverse_type >
class  PreconditionSelector< Matrix, Vector >
class  SparseLUDecomposition< number >
class  SparseDirectMA27
class  SparseDirectMA47
class  SparseDirectUMFPACK
class  SparseILU< number >
class  SparseMIC< number >
class  SparseVanka< number >
class  SparseBlockVanka< number >
class  TrilinosWrappers::PreconditionBase
class  TrilinosWrappers::PreconditionJacobi
class  TrilinosWrappers::PreconditionSSOR
class  TrilinosWrappers::PreconditionSOR
class  TrilinosWrappers::PreconditionIC
class  TrilinosWrappers::PreconditionILU
class  TrilinosWrappers::PreconditionILUT
class  TrilinosWrappers::PreconditionBlockwiseDirect
class  TrilinosWrappers::PreconditionChebyshev
class  TrilinosWrappers::PreconditionAMG
class  TrilinosWrappers::PreconditionBlockBase
class  TrilinosWrappers::PreconditionStokes

Detailed Description

Preconditioners are used to accelerate the iterative solution of linear systems. Typical preconditioners are Jacobi, Gauss-Seidel, or SSOR, but the library also supports more complex ones such as Vanka or incomplete LU decompositions (ILU). In addition, sparse direct solvers can be used as preconditioners when available.

In principle, and in the mathematical literature, preconditioners are treated as matrices in the sense that one can do a matrix-vector multiplication with them. On the other hand, one doesn't usually have an element-by-element representation of these matrices, only their action on a vector. The preconditioner classes therefore often have a vmult() function that symbolizes the ability to perform matrix-vector multiplications, just like the real matrix classes.


deal.II documentation generated on Sat Aug 15 16:51:38 2009 by doxygen 1.5.9