A fast direct solver for high frequency scattering from a large cavity in two dimensions

TL;DR

This paper introduces a fast direct solver for high-frequency electromagnetic scattering from large, arbitrarily-shaped cavities in two dimensions, utilizing a well-conditioned integral equation and hierarchical matrix factorization.

Contribution

It develops a novel, efficient solver that significantly reduces computation time for complex cavity scattering problems at high frequencies.

Findings

Solver operates in nearly linear time.

Effective for complex cavity geometries.

Works across a wide frequency range.

Abstract

We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily-shaped, large, empty cavity embedded in an infinite perfectly conducting half space. The governing Maxwell equations are reformulated as a well-conditioned second kind integral equation and the resulting linear system is solved in nearly linear time using a hierarchical matrix factorization technique. We illustrate the performance of the scheme with several numerical examples for complex cavity shapes over a wide range of frequencies.