Advanced Computational Methods for modeling, simulation and design  

We present a novel "Interpolated Factored Green Function" method (IFGF), including a massively parallel implementation, for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF algorithm evaluates the action of Green function-based integral operators at a cost of O(N log N) operations for an N-point surface mesh. Importantly, the proposed method does not utilize previously-employed acceleration elements such as the Fast Fourier transform (FFT), special-function expansions, high-dimensional linear-algebra factorizations, translation operators, equivalent sources, or parabolic scaling. Instead, the IFGF strategy, which leads to an extremely simple algorithm, capitalizes on slow variations inherent in a certain Green-function "analytic factor", which is analytic up to and including infinity, and which therefore allows for accelerated evaluation of fields produced by groups of sources on the basis of a recursive application of classical interpolation methods. In particular, the IFGF method runs on a small memory footprint, and, as it does not utilize the Fast Fourier Transforms (FFT), it is better suited than other methods for efficient parallelization in distributed-memory computer systems. Related integral equation techniques and associated device-optimization problems will be mentioned, including a novel time-domain scattering solver that effectively solves time-domain problems of arbitrary duration via Fourier transformation in time. (IFGF work in collaboration with graduate student Christoph Bauinger. Device-optimization work in collaboration with former postdoc/USC Prof., Constantine Sideris, and former students Emmanuel Garza and Agustin Fernandez-Lado. Time-domain work, in collaboration with former graduate student/UMich. Postdoc Thomas Anderson.)