Modified Superformula Contours Optimized via Genetic Algorithms for Exponentially Converging 2D Solutions of MFIE

An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of magnetic field integral equation (MFIE) in 2D either for TM or TE polarized excitations. A version of superformula modified for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the MFIE kernel and convergence of the solution will be presented

Analytical regularization of the Dirichlet diffraction problem for screen of revolution

A rigorous and numerically efficient approach, based on the Analytical Regularization Method, has been developed for the Dirichlet scalar diffraction problem of a smooth arbitrarily shaped open screen of revolution. The initial integral equation of the first kind is transformed so that the integral kernel is decomposed into a singular canonical part and a smooth remainder. Then the technique of dual series equations involving Jacoby polynomials reduces the problem to the infinite system of linear algebraic equations of the second kind. This provides desired solution accuracy depending on the truncation number alone. The numerical tests are presented for an open prolate spheroid and some open screens obtained by the revolution of the “Cassini Oval” and ”Pascal Lima¸con” curves. A high accuracy, efficiency and potential of the approach are shown.20 page(s

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

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