PLANE-WAVE ANALYSIS AND COMPARISON OF SPLIT-FIELD, BIAXIAL, AND UNIAXIAL PML METHODS AS ABCS FOR PSEUDOSPECTRAL ELECTROMAGNETIC-WAVE SIMULATIONS IN CURVILINEAR COORDINATES

In this paper, we discuss and compare split-field, biaxial, and uniaxi al perfectly matched layer (PML) methods for absorbing outgoing vector waves in cylindrical and spherical coordinates. We first extend Beren ger's split-field formulation into spherical and cylindrical coordinat es in such a way that it maintains all the desirable properties it exh ibits in rectangular coordinates. Then we discuss the biaxial and the uniaxial medium PML methods in Cartesian coordinates and extend them t o spherical and cylindrical coordinates. Properties of plane-wave solu tions of the PML methods are analyzed. In particular, the decay and bo undness properties of the solutions are considered in order to provide further insight into the different formulations presented herein. Mor eover we propose a set of symmetric hyperbolic equations for both the biaxial and the uniaxial PML methods in the time-domain, which is fine -tuned in numerical experiments and very suitable for time-domain prob lems. All three types of spherical and cylindrical PML methods are app lied in simulations of plane wave scattering as well as radiating dipo le problems. We use a multidomain pseudospectral (Chebyshev) numerical scheme, and the effectiveness of the PML methods is demonstrated thro ugh the accurate numerical results obtained. The order of outer-bounda ry reflection is as low as 0.1 % of the exact solution. (C) 1998 Acade mic Press