Compression of Translation Operator Tensors in FMM-FFT-Accelerated SIE Solvers via Tucker Decomposition

Abstract

Tucker decompositions (also known as higher order singular value decompositions) are used to lessen the memory requirements of translation operator tensors in fast multipole method-fast Fourier transform accelerated surface integral equation solvers. For many practical examples, the proposed drop-in code enhancement results in over 90% reduction in these tensors' storage requirements while imposing negligible computational overhead, thus significantly enhancing the solvers' application range on fixed computational resources.