Efficient representation of induced currents on large scatterers using complex exponential functions

One of the major challenges in solving large-body scattering problems using rigorous numerical techniques is to overcome the burden of memory and CPU time requirements, arising from the need to employ a large number of unknowns to represent the induced current on the scatterer. Typically, general-purpose and robust techniques such as the method of moments (MoM) with subdomain basis functions are able to handle scatterers whose characteristic dimensions are only a few wavelengths. The author shows that the induced current on the smooth portions a large scatterer may be represented along linear contours on the surface of the scatterer in terms of a series of complex exponential functions comprising of only a handful of terms, typically four or five. Several observations can be made regarding the above approximation: (i) this type of current representation is valid not only for scatterers that are perfect conductors, but also for those coated with absorbers to reduce their RCS; (ii) the complex exponents may be used as entire domain basis functions in a MoM formulation; and, (iii) these numerically-derived basis functions vary slowly and smoothly with the frequency; hence, they may be initially extracted from induced current distributions at lower frequencies, and then extrapolated to higher frequencies for use as entire domain basis functions to drastically reduce the number of unknowns for large scatterers. Illustrative examples presented include a partially coated two-dimensional scatterer modeling a helicopter blade, and a three dimensional problem of a thin plate with edge treatments.