Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	汪波副教授，湖南师范大学
Inviter:	郑伟英研究员
Title:	Fast multipole method in Layered media
Time & Venue:	2019.6.5 10:30-11:30 N902
Abstract:	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 satis?es the transmission conditions at material interfaces, isdecomposed into a free space component and four types of reaction ?eld component from wave re?ections and transmissions through the layered media. The proposed algorithm is a combination of the classic FMM for the free space component and FMMs speci?callydesigned 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 ?eld com-ponents. The FMMs for the reaction components, which are implemented with the target particles and equivalent polarization sources associated with the reaction ?eld components, are found to be much more e?cient 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. 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.