On a High-Frequency Analysis of Some Relevant Integral Equations in Electromagnetics

TL;DR

This paper investigates the spectral properties of boundary integral operators in computational electromagnetics, focusing on high-frequency regimes and their impact on numerical solution accuracy through theoretical and numerical analysis.

Contribution

It provides a detailed spectral analysis of boundary integral operators and their discretizations, revealing deviations at high frequencies and their effects on numerical methods.

Findings

Spectral deviations increase at high frequencies.

Eigenvalues of discrete operators differ from continuous ones.

Numerical results confirm theoretical predictions.

Abstract

In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular, a comparison with the eigenvalues of the continuous operators will be presented that highlights deviations in the high frequency regime and impacts, in a peculiar way, the accuracy of the numerical solutions of each formulation. A study and a proactive analysis of numerical results from standard boundary element solvers and the predictions from the theoretical analysis will corroborate the analytical framework employed and the validity of our observations.