# 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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