A comparison of coarse spaces for Helmholtz problems in the high frequency regime

Niall Bootland, Victorita Dolean, Pierre Jolivet, Pierre-Henri Tournier

Research output: Contribution to journalArticlepeer-review

Abstract

Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational challenges and try to identify the best algorithm and numerical strategy for a few well-known benchmark cases arising in applications. The aim is to cover, through numerical experimentation and consideration of the best implementation strategies, the main two-level domain decomposition methods developed in recent years for the Helmholtz equation. The theory for these methods is either out of reach with standard mathematical tools or does not cover all cases of practical interest. More precisely, we will focus on the comparison of three coarse spaces that yield two-level methods: the grid coarse space, DtN coarse space, and GenEO coarse space. We will show that they display different pros and cons, and properties depending on the problem and particular numerical setting.
Original languageEnglish
Pages (from-to)239-253
Number of pages15
JournalComputers and Mathematics with Applications
Volume98
Early online date12 Aug 2021
DOIs
Publication statusPublished - 15 Sep 2021

Keywords

  • Helmholtz equations
  • domain decomposition methods
  • two-level methods
  • coarse spaces
  • high frequency

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