报告人：汪波教授

报告题目：Fast multipole method in layered media

报告摘要：

(1) A fast multipole method (FMM) is presented for the computation of long-range interactions of sources embedded in 3-D layered media. The layered media Green's functions, which satisfies the transmission conditions at material interfaces, is decomposed into free space components and four types of reaction field components from reflections and transmissions through the layered media. The proposed algorithm is a combination of the classic FMM for the free space components and FMMs specifically designed for the four types reaction components, made possible by new multipole expansions (MEs) and local expansions (LEs) as well as the multipole-to-local translation (M2L) operators for the reaction field components.

(2) The FMMs for the reaction components, which are implemented with the target particles and equivalent polarization sources associated with the reaction field components, are found to be much more efficient than that for the free space component due to the fact that the equivalent polarization sources and the target particles are always separated by a material interface. As a result, the FMM algorithm developed for layered media has a similar computational cost as that for the free space. Numerical results validate the fast convergence of the MEs and the $O(N)$ complexity of the FMM for $N$ particle problem in 3-D layered media.

报告时间：2022年6月18日9:00-12:00

报告形式：腾讯会议；会议号：736-529-650

报告人简介：汪波，湖南师范大学数学与统计学院教授，国家高层次青年人才计划入选者。2011年在湖南师范大学获计算数学博士学位。2011年至2013年在新加坡国立大学从事博士后研究工作。主要研究方向包括超材料中电磁场计算的DG方法、波散射问题高精度方法、界面问题HDG方法、多层媒质中的快速多极法等。在《SIAM J. Sci. Comp.》、《SIAM J. Numer. Anal.》、《Comput. Methods Appl. Mech. Engrg.》、《SIAM J. Appl. Math.》等国内外著名刊物发表论文20多篇，主持国家基金4项。