Fast integral equation solver for Maxwell's equations in layered media with FMM for Bessel functions  

作　　者：CHO Min Hyung CAI Wei 

机构地区：[1]Department of Mathematics, Dartmouth College,Hanover, NH 03755, USA [2]Department of Mathematics and Statistics, University of North Carolina at Charlotte,Charlotte, NC 28223-0001, USA

出　　处：《Science China Mathematics》2013年第12期2561-2570,共10页中国科学：数学（英文版）

基　　金：supported by the US Army Ofce of Research(Grant No.W911NF11-1-0364);the National Science Foundation of USA(Grant No.DMS-1005441);National Natural Science Foundation of China(Grant No.91230105)

摘　　要：The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.The paper presents a new fast integral equation solver for Maxwell’s equations in 3-D layered media.First,the spectral domain dyadic Green’s function is derived,and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green’s function in real space.The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost.Subsequently,a fast integral equation solver with O(N2zNxNy log(NxNy))in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D.Computational cost and parallel efciency of the new algorithm are presented.

关 键 词：Maxwell＇s equations Helmholtz equation layered media Green＇s function fast multipole method 

分 类 号：O175.5[理学—数学]