Benchmark problems for coupling and scattering with cavities of general form

The need for reliable and accurate prediction of electromagnetic wave coupling to, or scattering from, structures arises in many contexts. General-purpose computational codes have been extensively developed in the last few decades as computing power and resources have become widely available; they have had a significant impact in providing numerical solutions and insight into important coupling and scattering mechanisms. However, their accuracy, particularly for objects of some complexity, incorporating edges and re-entrant structures, can be difficult to assess. The strongly resonant features of cavity-backed apertures can present difficulties in accuracy and computational cost for such general-purpose numerical codes. This chapter presents a method of analytically regularizing the underlying integral equation governing diffraction from the structure, so that a well-conditioned system of equations is obtained. It generalizes the process of analytical regularization applied to cavities of spherical and other canonical shape [2, 3] in which the basic equations are transformed to a second-kind Fredholm matrix equation. It applies to axisymmetric bodies, and examples confirm that the condition number of the resultant system is well controlled even near-resonant frequencies and that solutions of guaranteed accuracy can be efficiently obtained.