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Article

Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?

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Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
2
Laboratoire J.A. Dieudonné, Centre National de la Recherche Scientifique (CNRS), University Côte d’Azur, 06000 Nice, France
*
Author to whom correspondence should be addressed.
Academic Editor: Eric T. Chung
Math. Comput. Appl. 2022, 27(3), 35; https://doi.org/10.3390/mca27030035
Received: 17 February 2022 / Revised: 19 April 2022 / Accepted: 19 April 2022 / Published: 21 April 2022
(This article belongs to the Special Issue Domain Decomposition Methods)
Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications. View Full-Text
Keywords: Helmholtz equation; domain decomposition; two-level method; coarse space; additive Schwarz method; heterogeneous problem; high frequency Helmholtz equation; domain decomposition; two-level method; coarse space; additive Schwarz method; heterogeneous problem; high frequency
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MDPI and ACS Style

Bootland, N.; Dolean, V. Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems? Math. Comput. Appl. 2022, 27, 35. https://doi.org/10.3390/mca27030035

AMA Style

Bootland N, Dolean V. Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems? Mathematical and Computational Applications. 2022; 27(3):35. https://doi.org/10.3390/mca27030035

Chicago/Turabian Style

Bootland, Niall, and Victorita Dolean. 2022. "Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?" Mathematical and Computational Applications 27, no. 3: 35. https://doi.org/10.3390/mca27030035

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