威尼人斯娱乐全部网址

学术报告-龚世华

发布人:
责任人:
点击数:
更新时间:
2020-12-07 08:52:57

学术报告


题      目: Convergence of overlapping domain decomposition methods for the Helmholtz equation

报  告  人:龚世华   助理研究员  (邀请人:钟柳强 )

                                   University of Bath



时      间:2020-12-07 16:00--17:00


地      点:学院502


报告人简介:

        龚世华,巴斯大学威尼人斯娱乐全部网址助理研究员。2013在中山大学获得信息与计算科学学士学位,2018年在北京大学获得计算数学博士学位,2018.08-2019.03年在宾夕法尼亚州立大学从事博士后研究工作,2019.03至今在巴斯大学担任助理研究员。研究方向主要包含科学计算、混合有限元法、区域分解法、多层网格法和非线性预处理Newton法等。曾获得BICMR北大数学研究生奖和国家奖学金。

摘      要:

       The impedance boundary condition has been widely used in designing domain decomposition methods for the Helmholtz equation. The first algorithm with a rigorous convergence theory (Bennamou and Despr`es, 1997) was based on a nonoverlapping domain decomposition with general subdomains and swapped impedance data of neighbouring subdomains at each iteration. The convergence proof (but without a rate of convergence) was carried out using a “pseudo-energy” norm constructed from the sum of the $L^2$ norms of the impedance data on subdomain boundaries. This is a norm on the space of local solutions to the homogeneous Helmholtz equation and the convergence proof used the fact that the norms of the inward and outward impedance data are equal for solutions of the homogenous Helmholtz equation on each subdomain. In this talk, we will present some corresponding results for overlapping domain decomposition methods. We will show how convergence of the parallel Schwarz method (as an iterative method) .