Hybrid matrix compression for high-frequency problems

TL;DR

This paper introduces a hybrid matrix compression technique for high-frequency boundary element problems, combining analytic and algebraic methods to improve efficiency and compression quality.

Contribution

A novel hybrid approach that merges analytic and algebraic directional compression methods for boundary element matrices in high-frequency Helmholtz problems.

Findings

Hybrid method achieves better compression than purely analytic approaches.

Combines speed and robustness of analytic methods with superior compression of algebraic methods.

Applicable to large-scale high-frequency boundary element problems.

Abstract

Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for high-frequency problems. Currently there are two approaches to directional compression: analytic methods approximate the kernel function, while algebraic methods approximate submatrices. Analytic methods are quite fast and proven to be robust, while algebraic methods yield significantly better compression rates. We present a hybrid method that combines the speed and reliability of analytic methods with the good compression rates of algebraic methods.