Title: Fast multipole method in layered media

報告人：汪波

時   間：2019年6月25日（周二）10:00-11:30

地   點👨🏼：張江校區微電子樓369會議室

Abstract:

A fast multipole method (FMM) is presented for the computation of long-range interactions of wave sources embedded in 3-D layered media. The layered media Green’s function for the Helmholtz equation, which satisfies the transmission conditions at material interfaces, is decomposed into a free space component and four types of reaction field component from wave reflections and transmissions through the layered media. The proposed algorithm is a combination of the classic FMM for the free space component and FMMs specifically designed for the four types reaction component, 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 com- ponents. 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 com- putational cost as that for the free space. 

個人簡介👂🏼：

汪波 博士🎰，副教授⛓️‍💥，於2011年在湖南師範大學獲得博士學位🧑🏽‍🎄。2011年9月至2013年8月期間在新加波國立大學Singapore-MIT Alliance從事博士後研究工作👮🏻，此後2014年9月至2016年1月期間在新加波南洋理工大學交流訪學9️⃣，合作老師王立聯教授。2018年1月至今在美國南衛理公會大學(smu)交流訪學，合作老師蔡偉教授🚫。主要研究方向包括求解超材料中麥克斯韋方程組的間斷有限元方法、散射問題的高精度數值模擬方法♦️、一致網格上求解界面問題的雜交間斷有限元方法、分層介質中快速多極算法等。先後在SIAM Appl. Math., IMA J. Numer. Anal., J. Comput. Phys., Comput. Methods Appl. Mech. Eng., J. Comput. Appl. Math.等期刊上發表論文近10多篇，主持國際自然科學基金項目三項。

聯系人🚣🏽‍♂️：曾璇、嚴昌浩