Numerical Modeling and Analysis of Transient Electromagnetic Wave Propagation and Scattering

Our sponge layers are the only ones for which a proof of the reflectionless property has been given in cylindrical and spherical coordinates. More significantly, we have obtained initial results (presented at the 14th ACES conference) that indicates our sponge layer in spherical coordinates produces the same error as the exact ABC but at a fraction of the computational cost. We are continuing with analysis and numerical comparisons with exact ABC's in ABC's instead of the simpler Dirichlet boundary condition to terminate the sponge layers in the time-domain is desirable only for shallow layers and for layers of any depth but with a constant loss profile. Our efforts to determine the numerical reflection of the discrete sponge layer in cylindrical and spherical coordinates necessitated the derivation and study of the numerical dispersion relation of the discrete wave equation in these two curvilinear coordinate systems. With this work we have for the first time derived guidelines to limit the phase error when using finite difference schemes in curvilinear coordinates and have opened the avenue towards determining the numerical reflection of a given layer in such coordinate systems and optimizing it.