A HSS Matrix-Inspired Butterfly-Based Direct Solver for Analyzing Scattering from Two-dimensional Objects

TL;DR

This paper introduces a butterfly-based fast direct solver for high-frequency 2D scattering problems, achieving efficient memory and computational scaling for large, complex objects using a randomized butterfly scheme.

Contribution

It presents a novel HSS matrix-inspired butterfly-based direct solver that efficiently handles large-scale 2D scattering problems with reduced memory and computational costs.

Findings

Memory scales as O(N log^2 N)

Computational cost scales as O(N^1.5 log N)

Successfully analyzed objects over ten thousand wavelengths with five million unknowns

Abstract

A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near- and far-field interactions in the discretized forward and inverse electric field integral operators. The observed memory requirements and computational cost of the proposed solver scale as O(Nlog^2N) and O(N^1.5 logN), respectively. The solver is applied to the analysis of scattering from electrically large objects spanning over ten thousand of wavelengths and modeled in terms of five million unknowns.