• Corpus ID: 235377235

Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation

@article{Gong2021ConvergenceOP,
  title={Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation},
  author={Shihua Gong and Martin J. Gander and Ivan G. Graham and David Lafontaine and Euan A. Spence},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.05218}
}
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains is achieved using a partition of unity. We provide a novel analysis of this method at the PDE level (without discretization). First, we formulate the method as a fixed point iteration, and show (in dimensions 1,2,3) that it is welldefined in a tensor product… 
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