[2212.03132] How does the partition of unity influence SORAS preconditioner?
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Mathematics > Numerical Analysis

arXiv:2212.03132 (math)
[Submitted on 6 Dec 2022 (v1), last revised 24 Apr 2023 (this version, v2)]

Title:How does the partition of unity influence SORAS preconditioner?

Authors:Marcella Bonazzoli (IDEFIX), Xavier Claeys (LJLL (UMR\_7598)), Frédéric Nataf (ALPINES), Pierre-Henri Tournier (ALPINES)
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Abstract:We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overlap and on the number of subdomains. In particular, the second kind of partition of unity, which is non-zero in the interior of the whole overlapping region, gives more favorable convergence properties, especially when increasing the overlap width, in comparison with the first kind of partition of unity, whose gradient is zero on the subdomain interfaces and which would be the natural choice for ORAS solver instead.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2212.03132 [math.NA]
  (or arXiv:2212.03132v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2212.03132
Journal reference: Domain Decomposition Methods in Science and Engineering XXVII, Lecture Notes in Computational Science and Engineering, 149:61-68, 2024
Related DOI: https://doi.org/10.1007/978-3-031-50769-4_6

Submission history

From: Marcella Bonazzoli [view email] [via CCSD proxy]
[v1] Tue, 6 Dec 2022 16:55:12 UTC (74 KB)
[v2] Mon, 24 Apr 2023 12:19:25 UTC (91 KB)
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