Geodesic
Asynchronous weighted additive Schwarz methods
Electronic transactions on numerical analysis, Tome 5 (1997), pp. 48-61
A class of asynchronous Schwarz methods for the parallel solution of nonsingular linear systems of the form Ax = f is investigated. This class includes, in particular, an asynchronous algebraic Schwarz method as well as asynchronous multisplitting. Theorems are obtained demonstrating convergence for the cases when A - 1 is nonnegative and when A is an H-matrix. The results shown are for both the situations with or without overlap between the domains in which an underlying mesh is divided, if such a mesh exists. Numerical experiments on systems of up to over ten million variables on up to 256 processors are presented. They illustrate the convergence properties of the method, as well as the fact that when the domains are not all of the same size, the asynchronous method can be up to 50% faster than the corresponding synchronous one.
Classification : 65F10, 65Y05
Keywords: asynchronous methods, monotone matrices, H-matrices, linear system, parallel algorithms, multisplittings, additive Schwartz 
@article{ETNA_1997__5__a2,
     author = {Frommer,  Andreas and Schwandt,  Hartmut and Szyld,  Daniel B.},
     title = {Asynchronous weighted additive {Schwarz} methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {48--61},
     year = {1997},
     volume = {5},
     zbl = {0890.65027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__5__a2/}
}
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AU  - Szyld,  Daniel B.
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EP  - 61
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%0 Journal Article
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%A Schwandt,  Hartmut
%A Szyld,  Daniel B.
%T Asynchronous weighted additive Schwarz methods
%J Electronic transactions on numerical analysis
%D 1997
%P 48-61
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%G en
%F ETNA_1997__5__a2
Frommer,  Andreas; Schwandt,  Hartmut; Szyld,  Daniel B. Asynchronous weighted additive Schwarz methods. Electronic transactions on numerical analysis, Tome 5 (1997), pp. 48-61. http://geodesic.mathdoc.fr/item/ETNA_1997__5__a2/