Numerical computation of scattering by very large cylinders

Scattering by a conducting circular cylinder is a classical problem solvable by separation of variables. When the radius of the cylinder is very large, computation of the summation becomes very time consuming. Classically, the harmonic series may be converted into an alternative series by Watson´s transformation. Practically, high frequency scatterings are approximately solved using optical techniques such an geometric optics, physical optics, or geometric theory of diffraction. Direct numerical solutions of electromagnetic scattering in the optical frequency range have never been attempted because the effort would be too expensive and there is no guarantee that the results will be reliable after an astronomical number of arithmetical operations. The measured equation of invariance (MEI) may have just reversed the situation. The advantage of MEI is its ability to terminate finite difference/element meshes very close to the scatterer surface. We demonstrate that the MEI coefficients at high frequency can be obtained by extrapolation of those at low frequencies. So, using the MEI with its coefficient extrapolation the number of arithmetical operations can be drastically reduced and the direct numerical method becomes feasible in the optical frequency range.