Modified Superformula Contours Optimized via Genetic Algorithms for Fastly Converging 2D Solutions of EFIE

Abstract

It is known that solutions of the integral equations converge at the smoothness rate of the parametrical function representing the boundary contour. Thus using an infinitely smooth parametrical representation with derivatives of all orders results into exponentially converging solutions. A version of superformula tailored for this purpose is exposed to optimization of its parameters via genetic algorithms to obtain smooth parameterization for desired boundaries in two dimensional problems. The convergence of the resulting solutions of the electric-field integral equation will be presented.