A novel procedure for an efficient and rigorous solution of electromagnetic scattering problems is presented. It is based on the use of universal bases that are obtained by applying the SVD procedure to PO-derived basis functions. These bases, constructed by totally bypassing any matrix-type approach, can be used for all angles of incidence and their use leads to a matrix with relatively small dimensions. The method enables us to solve 2D scattering problems in a computationally efficient and numerically rigorous manner.

A major step in the numerical solution of electromagnetic scattering problems involves the computation of the convolution based reaction integrals. In this paper a procedure based on the analytical Fourier transform is introduced which allows us to calculate the convolution-based reaction integrals in the spectral domain without evaluating any convolution products directly. A numerical evaluation of the computational cost is presented to show the efficiency of the method when handling electrically large problems.