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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 Pocklington's 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.