Robust integral formulations for electromagnetic scattering from three-dimensional cavities

TL;DR

This paper introduces a new well-conditioned integral equation method for electromagnetic scattering from three-dimensional open cavities, ensuring stable, high-accuracy solutions even at low frequencies, with proven existence and uniqueness.

Contribution

The authors develop a novel integral formulation that remains well-conditioned for scattering from open cavities, including low-frequency regimes, and demonstrate its effectiveness with high-order discretization.

Findings

Stable evaluation of electric and magnetic fields achieved

High-order accuracy demonstrated with Gaussian quadratures

Method proven to have existence and uniqueness

Abstract

Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an infinite, perfectly conducting half-space. The integral representation permits the stable evaluation of both the electric and magnetic field, even in the low-frequency regime, using the continuity equation in a post-processing step. We establish existence and uniqueness results, and demonstrate the performance of the scheme in the cavity-of-revolution case. High-order accuracy is obtained using a Nystrom discretization with generalized Gaussian quadratures.