Open Access

ARTICLE

Development of New Algorithms for High Frequency Electromagnetic Scattering

by

1 Monopole Research, Thousand Oaks, CA 91360, USA

Computer Modeling in Engineering & Sciences 2004, 5(4), 295-318. https://doi.org/10.3970/cmes.2004.005.295

Abstract

We describe elements of our current work on the development of new methods for high frequency electromagnetic scattering, based on the wavefront (WF) representation of propagating fields and on the asymptotic but rigorous solution of integral equations for surface currents. In the wavefront evolution technique, surfaces of constant phase are constructed and treated not merely as collections of independent rays, but as well defined geometrical objects endowed with the full connectivity information. Hence, a precise determination of shadow and reflection boundaries, a construction of (multiply) diffracted wavefronts, a dynamic adjustment of the number of rays, an approximately constant ray-ray distance, and an accurate evaluation of fields on the wavefronts by means of interpolation between the neighboring rays are possible. As such, the wavefront evolution approach constitutes a significant improvement over conventional ray tracing methods. An essential element of the asymptotic, high frequency integral-equation (HFIE) method is the solution Ansatz, i.e., the representation of the current as a sum of known rapidly oscillating functions multiplied by unknown smooth functions varying slowly over the distance of a wavelength. While the form of the Ansatz is relatively straightforward for simple geometries, it becomes quite complicated for complex objects. We propose a general numerical procedure for the Ansatz construction which is based on determination of the rapidly oscillating components of the Ansatz from surface fields generated by a sequence of wavefronts corresponding to physically relevant multiple reflection and diffraction processes. Since both the Ansatz construction and the asymptotic integral equation approach will require the same discretization, determined not by the wavelength but by the geometrical complexity of the scatterer and the desired accuracy of the asymptotic expansion, the number of unknowns in the approach will be frequency independent. We also present results of our analysis of the ability and accuracy of the WF and HFIE approaches in capturing such important physical phenomena as multiple scattering, diffraction, surface waves and cross-polarization effects.

---

Keywords

---