Title: Two new numerical algorithms in computational electromagnetics

Wei Cai
Department of Mathematics & Statistics
University of North Carolina at Charlotte
Charlotte, NC 28223

Abstract

In this talk, we will present two new results in electro-statics and 
scattering in inhomogeneous media. First, result on constructing 
finite number of discrete images for a charge inside or outside a dielectric sphere.
It is found that in most cases only 4 discrete images are needed to
obtain a 5 digit accuracy for the potential. Based on this result,
we will extend the popular fast multipole method (FMM) to calculating 
electrostatic potential for charges inside/outside a dielectric sphere. 
Such an extension can find applications in the hybrid explicit/implicit 
solvation model for proteins. Secondly, we will present a parallel algorithm 
for scattering in block layered media based on generalized eigenfunction
expansions and domain decomposition with application in phase shift
mask modeling in lithography.Numerical Results for both algorithms will
be included.