In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global domain. Such problems arise, for instance, in solvation models in computational chemistry. Existing results on the scalability of the one-level PSM are limited to situations where each subdomain has access to the external boundary, and at most only two subdomains have a common overlap. We develop a systematic framework that allows us to bound the norm of the Schwarz iteration operator for domain decomposition problems in which subdomains may be completely embedded in the interior of the global domain and an arbitrary number of subdomains may have a common overlap.
DOI: 10.5802/smai-jcm.61
Keywords: Domain decomposition methods; Schwarz methods; chain of atoms; Laplace equation; ddCOSMO; Scalability analysis.
Gabriele Ciaramella 1; Muhammad Hassan 2; Benjamin Stamm 2
CC-BY-NC-ND 4.0
@article{SMAI-JCM_2020__6__33_0,
author = {Gabriele Ciaramella and Muhammad Hassan and Benjamin Stamm},
title = {On the {Scalability} of the {Schwarz} {Method}},
journal = {The SMAI Journal of computational mathematics},
pages = {33--68},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {6},
year = {2020},
doi = {10.5802/smai-jcm.61},
zbl = {07207993},
mrnumber = {4100531},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.61/}
}
TY - JOUR AU - Gabriele Ciaramella AU - Muhammad Hassan AU - Benjamin Stamm TI - On the Scalability of the Schwarz Method JO - The SMAI Journal of computational mathematics PY - 2020 SP - 33 EP - 68 VL - 6 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.61/ DO - 10.5802/smai-jcm.61 LA - en ID - SMAI-JCM_2020__6__33_0 ER -
%0 Journal Article %A Gabriele Ciaramella %A Muhammad Hassan %A Benjamin Stamm %T On the Scalability of the Schwarz Method %J The SMAI Journal of computational mathematics %D 2020 %P 33-68 %V 6 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.61/ %R 10.5802/smai-jcm.61 %G en %F SMAI-JCM_2020__6__33_0
Gabriele Ciaramella; Muhammad Hassan; Benjamin Stamm. On the Scalability of the Schwarz Method. The SMAI Journal of computational mathematics, Volume 6 (2020), pp. 33-68. doi : 10.5802/smai-jcm.61. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.61/
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