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Parallel implementation of an optimal two-level additive Schwarz preconditioner for the 3-D finite element solution of elliptic partial differential equations. (English) Zbl 1018.65127

Summary: This paper presents a description of the extension and parallel implementation of a new two level additive Schwarz (AS) preconditioner for the solution of 3-D elliptic partial differential equations (PDEs). This preconditioner, introduced by R. E. Bank, P. K. Jimack, S. A. Nadeem and S. V. Nepomuyaschikh [SIAM J. Sci. Comput. 23, 1817-1841 (2002; Zbl 1013.65139)], is based upon the use of a novel form of overlap between the subdomains which makes use of a hierarchy of meshes: with just a single layer of overlapping elements at each level of the hierarchy.
The generalization considered here is based upon the restricted AS approach reported by X.-C. Cai and M. Sarkis [SIAM J. Sci. Comput. 21, 792-797 (1999; Zbl 0944.65031)] and the parallel implementation is an extension of work in two dimensions by R. E. Bank and P. K. Jimack [Concurrency Comput. Pract. Exp. 13, 327-350 (2001; Zbl 1008.65503)].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations

Software:

ITSOL; SPARSKIT
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Full Text: DOI Link

References:

[1] Bank, SIAM Journal on Scientific Computing 23 pp 1818– (2002)
[2] Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press: Cambridge, 1996. · Zbl 0857.65126
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[14] Bank, Concurrency and Computation: Practice and Experience 13 pp 327– (2001)
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