“Interpolated Factored Green Function” method for accelerated solution of scattering problems

This paper presents a novel Interpolated Factored Green Function method (IFGF) for the accelerated evaluation of integral operators in scattering theory and other areas. Like existing acceleration methods these fields, IFGF algorithm evaluates action function-based at cost O(Nlog⁡N) operations an N-point surface mesh. The strategy, which leads to extremely simple algorithm, capitalizes on slow variations inherent certain function analytic factor, is up including infinity, therefore allows fields produced by groups sources basis recursive application classical interpolation methods. Unlike approaches, does not utilize Fast Fourier Transform (FFT), thus better suited than efficient parallelization distributed-memory computer systems. Only serial implementation considered this paper, however, whose efficiency terms memory speed illustrated means variety numerical experiments—including 43 min., single-core operator (on 10 GB peak memory), with relative error 1.5×10−2, problem acoustic size 512 wavelengths.