ISSN:
1572-9125
Keywords:
65F10
;
65N20
;
65N30
;
two-level
;
multilevel methods
;
optimal preconditioners
;
survey
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We survey multilevel iterative methods applied for solving large sparse systems with matrices, which depend on a level parameter, such as arise by the discretization of boundary value problems for partial differential equations when successive refinements of an initial discretization mesh is used to construct a sequence of nested difference or finite element meshes. We discuss various two-level (two-grid) preconditioning techniques, including some for nonsymmetric problems. The generalization of these techniques to the multilevel case is a nontrivial task. We emphasize several ways this can be done including classical multigrid methods and a recently proposed algebraic multilevel preconditioning method. Conditions for which the methods have an optimal order of computational complexity are presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01932745
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