Electric Field Integral Equation Fast Frequency Sweep for Scattering of Nonpenetrable Objects via the Reduced-Basis Method

A reduced-basis approximation to solve for the electromagnetic scattering from nonpenetrable targets in a frequency band of interest is studied in detail. Perfect electric scatterers in homogeneous media are considered. Even though the frequency behavior can be complicated, the electromagnetic scattering does not arbitrarily change in the frequency band of interest. Thus, instead of using computationally inefficient, large-dimension numerical approximation scenarios, such as the method of moments, to solve for integral equations in the band of interest, a low-dimension reduced-basis space is identified to approximate the smooth evolution of the electromagnetic scattering itself as frequency changes. As a result, the frequency-parameter scattering problem is solved within a reduced-order model approach. The electric field integral equation formulation is addressed and properly selected electric currents are considered to span the reduced-basis space in the frequency band of interest. The involved frequency dependence in the integral equation due to the wave propagation phenomena described in the free-space Green's function has traditionally limited the applicability of reduced-basis approximations for fast frequency sweep in integral equation methods in electromagnetics. In this article, we focus on this difficulty and propose a physics-based approach where the frequency-parameter dependence shows an affine behavior in the integral equation, without relying on rather complicated interpolation schemes. As a result, a fast frequency sweep for integral equation problems in electromagnetics is proposed. Finally, real-life applications will illustrate the capabilities of this methodology.