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

Romain Brunet, Victorita Dolean, Martin J. Gander

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXV
EditorsRonald Haynes, Scott MacLachlan, Xiao-Chuan Cai, Laurence Halpern, Hyea Hyun Kim, Axel Klawonn, Olof B Widlund
Place of PublicationCham, Switzerland
PublisherSpringer-Verlag
Pages425-432
Number of pages8
ISBN (Electronic)978-3-030-56750-7
ISBN (Print) 978-3-030-56749-1
Publication statusPublished - 25 Oct 2020

Keywords

  • Schwarz method
  • mathematical modeling
  • elastic media

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