On the Solution of a Class of Large-Body Scattering Problems Via the Extrapolation of Fdtd Solutions

Abstract

The objective of this paper is to apply an extrapolation technique in conjunction with the FDTD method to solve scattering problems involving a class of large three-dimensional metallic objects in a numerically efficient manner. The extrapolation technique is based on the observation that, for sufficiently high frequencies, the field variation near the surface of the scatterer exhibits a certain simple frequency dependence and that the knowledge of this behavior can be used to evaluate the induced current at frequencies where the body size is too large to be tractable via direct methods. The solution process begins with an application of the FDTD to obtain the field distribution on a surface enclosing the scatterer over a wide band of frequencies. The computed results in the upper end of the spectrum, where the body size is at least moderately large, are retained and these field solutions are processed by using the generalized pencil of function (GPOF) method to extract the constituent traveling wave components, that usually number only 2 or 3. Finally, the functional frequency dependences of the traveling wave components are extracted and used to derive the extrapolated solutions at higher frequencies. It is demonstrated that the above extrapolation procedure can be applied to a class of three- dimensional scatterers, even at the grazing incidence and in the shadow region, where the asymptotic methods are known to suffer from accuracy problems. An important observation regarding the extrapolation technique is that, in contrast to the direct methods, e.g., the FDTD - and MoM, the extrapolation technique is not constrained, in principle, by any CPU time and memory limitations at high frequencies.