Electromagnetic Scattering from a Zero-Thickness PEC Disk: A Note on the Helmholtz-Galerkin Analytically Regularizing Procedure

Recently, a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, has been proposed to analyze the electromagnetic scattering from a zero-thickness perfectly electrically conducting disk. The convergence of the discretization scheme is guaranteed and of exponential type, i.e., few expansion functions are needed to achieve highly accurate solutions. However, it leads to the numerical evaluation of improper integrals of asymptotically oscillating and slowly decaying functions. Asymptotic acceleration techniques allow to obtain faster decaying integrands without overcoming the problem of the oscillating nature of the integrands themselves, i.e., the convergence of the integrals becomes slower and slower as the accuracy required for the solution is higher. In this paper, by means of algebraic manipulations and a suitable integration procedure in the complex plane, an alternative expression for the scattering matrix coefficients involving only fast converging properintegrals isdevised. Asshown in thenumerical resultssection, theproposedtechnique is very effective and drastically outperforms the classical analytical asymptotic acceleration technique.