## An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation. (arXiv:1807.04180v1 [math.NA])

In this paper, we propose and analyze an additive domain decomposition method
(DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld
radiation condition. In the proposed method, the computational domain is
partitioned into structured subdomains along all spatial directions, and each
subdomain contains an overlapping region for source transferring. At each
iteration all subdomain PML problems are solved completely in parallel, then
all horizontal, vertical and corner directional residuals on each subdomain are
passed to its corresponding neighbor subdomains as the source for the next
iteration. This DDM method is highly scalable in nature and theoretically shown
to produce the exact solution for the PML problem defined in ${\mathbb{R}}^2$
in the constant medium case. A slightly modified version of the method for
bounded truncated domains is also developed for its use in practice and an
error estimate is rigorously proved. Various numerical experiments in two and
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