Asymptotic Spectral Insights Behind Fast Direct Solvers for High-Frequency Electromagnetic Integral Equations on Non-Canonical Geometries

TL;DR

This paper evaluates the effectiveness of a high-frequency fast direct solver for electromagnetic integral equations on complex geometries, using semiclassical microlocal analysis to justify its applicability and efficiency.

Contribution

It provides a rigorous analysis combining microlocal results to validate and understand the solver's performance on non-canonical geometries at high frequencies.

Findings

The solver is effective for complex geometries in high-frequency regimes.

Microlocal analysis justifies the solver's assumptions and accuracy.

The approach reduces computational costs significantly.

Abstract

Integral-equation-based fast direct solvers for electromagnetic scattering can substantially reduce computational costs, especially in the presence of multiple excitations. We recently proposed a new high-frequency fast direct solver strategy that combines preconditioning techniques with acceleration algorithms. However, the validity of this approach applied to non-canonical geometries requires further justification. In this contribution, we collect relevant semiclassical microlocal results and use them to assess the legitimacy and effectiveness of the proposed fast direct solver in the high-frequency regime.