Tucker decomposition for compressing translation operator tensors in FMM-FFT accelerated SIE solvers

Fast multipole method - Fast Fourier transform (FMM-FFT) accelerated surface integral equation (SIE) solvers allow for accurate and efficient analysis of electromagnetic (EM) scattering from and radiation by complex and large scale structures (R. L. Wagner et. al., IEEE Trans. Antennas Propagat., 45(2), 235–245, 1997). These solvers (and their multilevel extensions) provide an increasingly appealing avenue for solving EM scattering problems involving hundreds of millions (and billions) of unknowns (Taboada et. al., IEEE Antennas Propagat. Mag., 51(6), 20–28, 2009; Taboada et. al., Progress in Electromagnetics Research, 105, 15–30, 2010). When used on present high-performance computers to solve practical problems of current interest, these solvers tend to be memory as opposed to CPU-limited. The solvers´ memory requirements directly depends on the storage requirements for (i) near-field interaction matrices, (ii) matrices that hold the far-field signatures of basis functions, and (iii) tensors that hold FFT´ed translation operator values on a structured grid. In past, the memory requirements of the first two data structures were successfully reduced by singular value decomposition (SVD) (Kapur and Long, IEEE Comp. Sci. Eng., 5(4), 60–67, 1998; Rodriguez et. al., IEEE Trans. Antennas Propagat., 56(8), 2325–2334, 2008). To date, no compression scheme has been reported to reduce the memory requirements of translation operator tensors.