| Abstract: |
| We present a novel massively parallel variant of the Restricted Additive Schwarz method with Perfectly Matched Layers (RAS-PML) as a fixed point iteration for solving the Helmholtz equation in $d$-dimensional space and at high-frequency $k$. We are able to solve $\mathcal{O}(k^d)$-scale linear systems coming from $\mathcal{O}(k^{-1})$-diameter mesh discretizations of the Helmholtz problems in $\mathcal{O}(k)$ runtime with $\mathcal{O}(k^d)$ processors. The method is motivated by the theory in {\tt arXiv:2404.02156}, where the authors proved that a related Schwarz method using fixed subdomain and PML configuration has a contraction rate which decays super-algebraically fast with respective to $k\to \infty$. The proposed algorithm can be implemented easily using standard routines in the parallel domain decomposition packages. |
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