Can classical Schwarz methods for time-harmonic elastic waves converge?

Can classical Schwarz methods for time-harmonic elastic waves converge?

We show that applying a classical Schwarz method to the time harmonic Navier equations, which are an important model for linear elasticity, leads in general to a divergent method for low to intermediate frequencies. This is even worse than for Helmholtz and time harmonic Maxwell's equations, wh...

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Bibliographic Details
Main Authors: Brunet, Romain, Dolean, Victorita, Gander, Martin J
Format: Journal Article
Language:English
Published: 31-10-2018
Subjects:
Mathematics - Numerical Analysis
Online Access:Get full text
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Summary:We show that applying a classical Schwarz method to the time harmonic Navier equations, which are an important model for linear elasticity, leads in general to a divergent method for low to intermediate frequencies. This is even worse than for Helmholtz and time harmonic Maxwell's equations, where the classical Schwarz method is also not convergent, but low frequencies only stagnate, they do not diverge. We illustrate the divergent modes by numerical examples, and also show that when using the classical Schwarz method as a preconditioner for a Krylov method, convergence difficulties remain.
DOI:10.48550/arxiv.1810.13174