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Superalgebraically Converging Galerkin Method for Electromagnetic Scattering by Dielectric Cylinders

The high‐order solutions of the well‐known Green's formulation of the boundary value problems to determine the scattering monochromatic electromagnetic waves by dielectric cylinders are presented. The boundaries are given via infinitely smooth closed contours. That is why the solutions to the transverse electric/transverse magnetic wave scattering problems are obtained by solving the matrix equations, entries of which are Fourier coefficients of the electric field integral equations/magnetic field integral equations kernels obtained via the Fourier transform over the periodic domain on the boundary. This procedure is equivalent to an entire domain Galerkin formulation of the considered problems, with their unknown functions expanded into series with complex exponentials as bases. The algebraic system is solved by truncation, and the superalgebraic convergence of the unknowns is achieved by the suggested algorithm. The numerical results are validated by that of circular cylinders' obtained via a well‐conditioned algorithm based on separation of variables method. Numerical results demonstrate the superalgebraic convergence, owing to the suggested nonsaturated algorithm.