Seminars on Numerical Algorithms, Analyses, and Applications：Some convergence results for RAS-Imp and RAS-PML for the non-trapping Helmholtz problems
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：Shihua Gong (The Chinese University of Hong Kong，Shenzhen)
： 2024-11-29 10:00
：Conference Room C503 at Administration Building at Haiyun Campus
Speaker：Shihua Gong (The Chinese University of Hong Kong，Shenzhen)
Time：2024-11-29, 10:00
Location：Conference Room C503 at Administration Building at Haiyun Campus
Abstract:
We consider two variants of restricted overlapping Schwarz methods for the non-trapping Helmholtz problems, which allow the optic-rays leaving a bounded domain in a uniform time. The first method, known as RAS-Imp, incorporates impedance boundary condition to formulate the local problems. The second method, RAS-PML, employs local perfectly matched layers (PML). These methods combine the local solutions additively with a partition of unity. We have shown that RAS-Imp has power contractivity for strip domain decompositions. More recently, we shown that RAS-PML has super-algebraic convergence with respective to wavenumber after a specified number of iterations. This is the first theoretical result for the non-trapping Helmholtz problems with variable wave speed. In this talk we review these results and illustrate how the error of the Schwarz methods propagates as optic-rays. We also investigate situations not covered by the theory. In particular, the theory needs the overlap of the domains or the PML widths to be independent of k. We present numerical experiments where this distances decrease with k.
