Iterative Physical Optics with Asymptotic Phasefront Extraction for Large Multi-Bounce Scattering Problems

The iterative physical optics algorithm is accelerated with the asymptotic phasefront extraction (APE) method for modeling very electrically large scattering targets. The APE method introduces frequency-scalable basis functions so that a solution obtained at a lower frequency may be extended to much higher frequencies without changing the number of basis functions. INTRODUCTION The iterative physical optics (IPO) method has been shown to be very accurate and efficient for electrically large multi-bounce scattering problems by Obelleiro et al. [1]. However, as the problem size increases the IPO method become computationally cumbersome because the numerical evaluation of the PO integral requires 2-4 sampling points per wavelength. The fast far-field approximation of Lu and Chew [2] has been applied to IPO by Burkholder [3] to reduce the operational count from O(N ) to O(N ). Even so, as the frequency f continues to increase, N can quickly become intractably large because N scales as O(f ). The asymptotic phasefront extraction (APE) method of Kwon et al. [4] was developed for the method of moments (MoM) to deal with the O(f ) dependence of N. It is known that over smooth surfaces this frequency dependence is due to the rapidly varying phase of the surface currents, because the phase must be sampled with several points per wavelength for good accuracy. The basic approach of the APE is to extract the phase variation by expanding the surface currents locally around a point as a sum of a small number of traveling wave functions: J(r) = i Ci(r) exp(-jki r) where Ci(r) is a slowly varying amplitude function and ki is a constant phasefront vector on the surface. The frequency-dependent term in this expansion is the phasefront vector which is linearly proporational to the frequency. APE basis functions are therefore frequency-scalable, i.e., the same set of basis functions may be re-used at arbitrarily high frequencies. Because the amplitude function is slowly varying, the currents may be sampled at far fewer points, and the sampling is very weakly dependent on frequency. This result is consistent with (and derived from) high-frequency asymptotic ray theory, which shows that the fields at a point may be obtained from a small number of geometrical optics (GO) and diffracted wave contributions. The question arises, how does one find the phasefront vectors ki for a given geometry and excitation? One approach is to actually track the GO and diffracted rays to each sample point on the surface, but this may not be practical for a realistically complex geometry. The approach used by Kwon et al. [4] is to solve a particular problem at a frequency that is much lower than the actual frequency, and for which a conventional MoM solution may be reasonably obtained. The phasefront vectors may be obtained from these surface currents because ki has a known linear frequency dependence. A local Fourier expansion approach is used in [4] to find the phasefront vectors at each sample point by considering the surface current solution at neighboring points. The above APE methodology may also be directly applied to the IPO method. In fact, it is easier to apply to IPO than the MoM because edge singularities are not dealt with explicitly in IPO. The APE applied to MoM is only valid away from physical discontinuities such as edges, so regions near edges must be sampled more densely at the higher frequency of interest as shown in Figure 1. This makes the APE method somewhat more cumbersome and less efficient for MoM than for IPO.