Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media  

作　　者：Wenzhong Zhang Bo Wang Wei Cai 

机构地区：[1]Suzhou Institute for Advanced Research,University of Science and Technology of China,Suzhou,Jiangsu 215127,China [2]LCSM(MOE),School of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China [3]Department of Mathematics,Southern Methodist University,Dallas,TX 75275,USA

出　　处：《Annals of Applied Mathematics》2023年第2期99-148,共50页应用数学年刊（英文版）

基　　金：supported by the US National Science Foundation (Grant No.DMS-1950471);the US Army Research Office (Grant No.W911NF-17-1-0368);partially supported by NSFC (grant Nos.12201603 and 12022104)。

摘　　要：In this paper,we establish the exponential convergence theory for the multipole and local expansions,shifting and translation operators for the Green's function of 3-dimensional Laplace equation in layered media.An immediate application of the theory is to ensure the exponential convergence of the FMM which has been shown by the numerical results reported in[27].As the Green's function in layered media consists of free space and reaction field components and the theory for the free space components is well known,this paper will focus on the analysis for the reaction components.We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex wave number plane.Then,by using the Cagniard-de Hoop transform and contour deformations,estimates for the remainder terms of the truncated expansions are given,and,as a result,the exponential convergence for the expansions and translation operators is proven.

关 键 词：Fast multipole method layered media multipole expansions local expansions 3-D Laplace equation Cagniard–de Hoop transform equivalent polarization sources 

分 类 号：O17[理学—数学]