Seminars on Numerical Algorithms, Analyses, and Applications：Some convergence results for RAS-Imp and RAS-PML for the non-trapping Helmholtz problems

：龚世华（香港中文大学（深圳））
：2024-11-29 10:00
：海韵园行政楼C503

报告人：龚世华（香港中文大学（深圳））

时  间：2024年11月29日10:00

地  点：海韵园行政楼C503

内容摘要:

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.

个人简介：

Shihua Gong obtained his PhD degree in computational mathematics from Peking University in 2018. Before joining the Chinese University of Hong Kong (Shenzhen), he worked as a postdoctoral scholar at Pennsylvania State University and then as a research associate at the University of Bath. His research interests include scientific computing and numerical analysis, mainly focusing on finite element and preconditioning techniques for frequency-domain wave equations and coupled equations in multiphysics problems. He has published academic papers in leading international journals, such as Numerische Mathematik, Mathematics of Computation, SIAM Journal on Scientific Computing.

 

联系人：陈黄鑫