The “Interior Resonance” Problem Associated with Surface Integral Equations of Electromagnetics: Numerical Consequences and a Survey of Remedies

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Abstract
It is well known that certain surface integral equations used to describe exterior electromagnetic scattering problems may not produce unique solutions if applied to closed geometries that also represent resonant cavities. This paper explores the numerical consequences of the uniqueness problem. The “interior resonance” problem and several proposed remedies are illustrated using the eigenvalues of the integral operators for circular cylinders. Although an eigenvalue of the continuous integral operator vanishes at a resonance frequency, discretization error may prevent the associated matrix eigenvalue from becoming appreciably small. Inaccurate results are due to an incorrect balance between the excitation and the small matrix eigenvalue near a resonance frequency.

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