An optimal Schwarz preconditioner for a class of parallel adaptive finite elements

A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenval...

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Vydané v:Journal of computational and applied mathematics Ročník 321; s. 90 - 107
Hlavní autori: Loisel, Sébastien, Nguyen, Hieu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.09.2017
Predmet:
Bank–Holst paradigm
Domain decomposition
Parallel adaptivity
Preconditioner
Two-grid discretisations
Bank–Holst paradigm
Two-grid discretisations
Preconditioner
65N55
65N22
65F08
Domain decomposition
Parallel adaptivity
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh sizes and the number of subdomains, which proves the proposed preconditioner is optimal. Numerical results are provided to support the theoretical findings.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2017.02.018