Accurate and Efficient Algorithms for Frequency Domain Scattering from a Thin Wire

This paper contains a systematic study of numerical approximations for solving the exact kernel form of Pocklingtonʹs integro-differential equation for the current induced on a thin wire by an incident time-harmonic electromagnetic field. We consider various Galerkin (h, p, hp, and adaptive h) and collocation schemes and show that a sensible hp refinement strategy provides a very efficient way to solve the problem. We also describe how the kernel (itself a difficult singular integral) can be evaluated reliably and efficiently.