题目：Some Convergence Results for RAS-Imp and RAS-PML for the Non-Trapping Helmholtz Problems

报告人：龚世华 助理教授（香港中文大学（深圳））

地点：致远楼101室

时间：2024年9月27日 18:30-19:30

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.

报告人简介：龚世华， 香港中文大学（深圳）助理教授。2013年7月本科毕业于中山大学，2018年7月在北京大学取得博士学位。2018年8月-2021年12月先后在美国宾夕法尼亚州立大学和英国巴斯大学从事博士后研究工作。研究兴趣包括大规模科学计算和数值分析，主要研究有限元方法，大规模代数系统的线性与非线性预条件子，高频波散射问题的快速求解器。

欢迎各位参加！