Compression of Far-Fields in the Fast Multipole Method via Tucker Decomposition

TL;DR

This paper introduces Tucker decomposition to efficiently compress far-field data in the fast multipole method, significantly reducing memory use and accelerating computations in electromagnetic simulations.

Contribution

It presents a novel application of Tucker decomposition to compress far-fields in FMM, improving memory efficiency and computational speed for surface integral equation simulations.

Findings

Reduces far-field memory requirement by over 87%.

Speeds up aggregation and disaggregation stages by over 15 times.

Demonstrates effectiveness on a 30λ-diameter sphere in electromagnetic analysis.

Abstract

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which are stored in three-dimensional (3-D) arrays (or tensors). The compressed tensors are then used to perform fast tensor-vector multiplications during the aggregation and disaggregation stages of the FMM. For many practical scenarios, the proposed Tucker decomposition yields a significant reduction in the far-fields' memory requirement while dramatically accelerating the aggregation and disaggregation stages. For the electromagnetic scattering analysis of a 30{\lambda}-diameter sphere, it reduces the memory requirement of the far-fields more than 87% while it expedites the aggregation and disaggregation stages by a factor of 15.8 and 15.2, respectively, where {\lambda} is the wavelength in free space.