Computing the translation operator for plane wave compression algorithms from sparse samples of the Green function

Efficient numerical simulation of integral formulations of electromagnetic radiation and scattering problems requires the use of a compression algorithm for the underlying Green function. If a simulation domain is subdivided into N elements, a traditional discretization of the integral equation leads to a linear system of the form Ax=b where A contains O(N/sup 2/) nonzero elements. Plane wave compression algorithms (PCAs) have been shown to yield an O(N log N) representation of A when the scatterer is large compared to the wavelength. In the following, we consider an alternate development of a PCA for the free-space Green function. In particular, we outline a procedure to compute the translation operator from sparsely sampled values of the Green function. This approach facilitates the efficient application of PCAs to a more general class of Green functions, including the inverse operator.