• Corpus ID: 239998561

Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems

@article{Gong2021ConvergenceOR,
  title={Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems},
  author={Shihua Gong and Ivan G. Graham and Euan A. Spence},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.14495}
}
The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method, which has been successfully used as an iterative solver and as a preconditioner for discretized Helmholtz boundary-value problems. In this paper, we give, for the first time, a convergence analysis for ORAS as an iterative solver – and also as a preconditioner – for nodal… 
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The theory developed here shows that if the absorption is large enough, and if the subdomain and coarse mesh diameters and overlap are chosen appropriately, then the classical two-level overlapping Additive Schwarz preconditioner performs optimally -- in the sense that GMRES converges in a wavenumber-independent number of iterations -- for the problem with absorption.
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