تقرير
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
| العنوان: | Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition |
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| المؤلفون: | Lafontaine, David, Spence, Euan A. |
| المصدر: | Pure Appl. Analysis 5 (2023) 927-972 |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis |
| الوصف: | We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high-frequency) using semiclassical defect measures. The paper [GGGLS] (Gong-Gander-Graham-Lafontaine-Spence, 2022) recently showed that the behaviour of these impedance-to-impedance maps (and their compositions) dictates the convergence of the parallel overlapping Schwarz domain-decomposition method with impedance boundary conditions on the subdomain boundaries. For a model decomposition with two subdomains and sufficiently-large overlap, the results of this paper combined with those in [GGGLS] show that the parallel Schwarz method is power contractive, independent of the wavenumber. For strip-type decompositions with many subdomains, the results of this paper show that the composite impedance-to-impedance maps, in general, behave "badly" with respect to the wavenumber; nevertheless, by proving results about the composite maps applied to a restricted class of data, we give insight into the wavenumber-robustness of the parallel Schwarz method observed in the numerical experiments in [GGGLS]. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.2140/paa.2023.5.927 |
| URL الوصول: | http://arxiv.org/abs/2211.14659 |
| رقم الأكسشن: | edsarx.2211.14659 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.2140/paa.2023.5.927 |
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