报告题目：Fast multipole method in Layered media

报告人：汪波副教授，湖南师范大学

报告时间：11月17日下午16:00-18:00

地点：数理楼144教室

报告摘要：A fast multipole method (FMM) is proposed to compute 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 components. 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 interaction of wave sources at low wave number in 3-D layered media.

报告人简介：汪波，湖南师范大学数学与统计学院副教授，博士毕业于湖南师范大学，曾在新加坡国立大学、新加坡南洋理工大学做博后研究，在美国南卫理工会大学访问。其主要研究领域为快速多极算法、间断有限元方法、散射问题的积分方法等；主要研究成果包括分层媒质中快速多极算法，多体散射问题高效、高精度迭代算法，色散媒质中麦克斯韦方程组间断有限元方法；在计算数学顶级期刊SIAM J.NUMER.ANAL.，SIAM J.SCI.COMPUT.,J. COMPUT. PHYS. 等杂志发表多篇论文；主持国家自然科学基金项目3项，其主持的“偏微分方程快速算法”获得优秀青年科学基金项目立项。