

























Abstract:We analyse the classic two-level additive Schwarz domain-decomposition GMRES preconditioner for finite-element discretisations of the Helmholtz equation with large wavenumber $k$, where both the fine and coarse spaces consist of piecewise polynomials with polynomial degree increasing like $\log k$.
We exhibit choices of these fine and coarse spaces such that -- up to factors of $\log k$ -- both are pollution free (with the ratio of the coarse-space dimension to the fine-space dimension arbitrarily small), the number of degrees of freedom per subdomain is constant, and the number of GMRES iterations is proved to be bounded independently of $k$.
These are the first $k$-explicit convergence results about a two-level Schwarz preconditioner for high-frequency Helmholtz with a coarse space that is pollution free and does not consist of problem-adapted basis functions.
From: Euan Spence [view email]
[v1]
Mon, 27 Jan 2025 11:49:59 UTC (46 KB)
[v2]
Wed, 19 Mar 2025 18:48:25 UTC (45 KB)
[v3]
Fri, 26 Sep 2025 16:04:57 UTC (54 KB)
[v4]
Thu, 18 Jun 2026 10:00:51 UTC (55 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。