Two-level direct compression of the plane-wave response matrix without matrix sampling

This paper present the numerical solutions of surface integral equation formulations of time-harmonic electromagnetic radiation and scattering from perfectly conducting targets involve solving linear systems of the form Zx=Fⁱ, (1) where Z is the N-by-N system matrix. If Z is invertible, then the solution to (1) is x=Z^-1Fⁱ. (2). In many cases of practical interest, the incident fields, Fⁱ, can be equivalently represented using a spectrum of plane waves. Following the notation of Adams et al. (2006), we represent the latter observation as Fⁱ =Dfⁱ (3) In (3), fⁱ denotes an incident plane wave spectrum that produces Fⁱ, and D is a discrete representation of the plane wave transform. Combining (2) and (3), x=PFⁱ (4) where P=Z^-1D is the plane wave response matrix (P-matrix).