New scheme of the discrete sources method for two-dimensional scattering problems by penetrable obstacles

Abstract

A new computational scheme of the Discrete Sources Method (DSM) is developed for the numerical solution of two-dimensional acoustic and electromagnetic transmission boundary-value problems (BVPs) pertaining to the Helmholtz equation. To establish the new DSM scheme, we show that the matrix integral operator, corresponding to the transmission boundary conditions, has a dense range. The approximate solution of the BVP is constructed according to the new DSM scheme and it is proven that it converges uniformly to the exact solution of the BVP. An analytic representation is derived for the calculation of the scattering cross section in terms of the determined DSs amplitudes avoiding an integration over the unit circle. The numerical implementation procedure of the DSM is described and numerical results for the application of the DSM are presented. The new scheme is shown to be accurate and efficient even for highly-elongated scatterers.