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A Fast and High Order Algorithm for the Electromagnetic Scattering of Axis-Symmetric Objects

Axis-symmetric objects are an important class of shapes that appear in many electromagnetic applications. By using the separation of variables, we are able to derive a fast and high order numerical algorithm that solves the 3D electromagnetic scattering for an arbitrary axis-symmetric object. The main novelty here is to combine the fast recursion formula for the kernel evaluation along the revolution curve and high order generalized Gaussian quadrature for the singular integrals in integral equations. Numerical experiments show that for a modest sized cylinder, we can easily obtain more than 6 digits accuracy in less than 90 seconds on a personal laptop.