Closed form optimized transmission conditions for complex diffusion with many subdomains

Victorita Dolean, Martin J. Gander, Alexandros Kyriakis

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
17 Downloads (Pure)

Abstract

Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are optimized for two subdomains model configurations, and then used in practice for many subdomains. We optimizetransmission conditions here for the first time directly for many subdomains for a class of complex diffusion problems. Our asymptotic analysis leads to closed form optimized transmission conditions for many subdomains, and shows that the asymptotic best choice in the mesh size only differs from the two subdomain best choice in the constants, for which we derive the dependence on the number of subdomains explicitly, including the limiting case of an infinite number of subdomains, leading to new insight into scalability. Our results include both Robin and Ventcell transmission conditions, and we also optimize for the first time a two-sided Ventcell condition. We illustrate our results with numerical experiments, both for situations covered by our analysis and situations that go beyond.
Original languageEnglish
Pages (from-to)A829-A848
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume45
Issue number2
Early online date27 Apr 2023
DOIs
Publication statusPublished - 30 Apr 2023

Keywords

  • optimized transmission conditions
  • complex diffusion
  • optimized Schwarz methods
  • many subdomains

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