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Published in:
Robust Block Preconditioners for Biot’s Model Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Convergence of Asynchronous Optimized Schwarz Methods in the Plane

Authors : José C. Garay, Frédéric Magoulès, Daniel B. Szyld

Published in: Domain Decomposition Methods in Science and Engineering XXIV

Publisher: Springer International Publishing

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Abstract

A convergence proof of Asynchronous Optimized Schwarz Methods applied to a shifted Laplacian problem, with negative shift, in \(\mathbb {R}^2\) is presented. Sufficient conditions for convergence involving initial values of the approximation of the solution are discussed.

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previous chapter Restrictions on the Use of Sweeping Type Preconditioners for Helmholtz Problems
next chapter INTERNODES for Elliptic Problems
Footnotes
1
In [5] it is indicated that given \(\hat {T}\) is contracting, then T n → 0, where T maps u(n) to u(n + 1), but this implication may not always hold. This is why we need to complete the proof in a different manner. We do so by showing explicitly that (8) holds.
 
Literature
1.
V. Dolean, P. Jolivet, F. Nataf, An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation (SIAM, Philadelphia, 2015)CrossRef
2.
3.
4.
F. Magoulés, A.-K.C. Ahamed, R. Putanowicz, Optimized Schwarz method without overlap for the gravitational potential equation on cluster of graphics processing unit. Int. J. Comput. Math. 93, 955–980 (2016)MathSciNetCrossRef
5.
F. Magoulès, D.B. Szyld, C. Venet, Asynchronous optimized Schwarz methods with and without overlap. Numer. Math. 137, 199–227 (2017)MathSciNetCrossRef
Metadata
Title
Convergence of Asynchronous Optimized Schwarz Methods in the Plane
Authors
José C. Garay
Frédéric Magoulès
Daniel B. Szyld
Copyright Year
2018
Book
Domain Decomposition Methods in Science and Engineering XXIV

Print ISBN: 978-3-319-93872-1

Electronic ISBN: 978-3-319-93873-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-93873-8_31

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