Some Recent Advances In The Development Of Numerically Efficient Computational Electromagnetic Techniques

This paper presents several numerically efficient techniques, in the context of Computational Electromagnetics, for handling a variety of issues that arise in the process of numerical modeling and simulation of electromagnetic scattering and radiation problems. These include: (i) handling the singularity issue in the kernel of the integral when computing the diagonal and near-diagonal Method of Moments (MoM) matrix elements; (ii) dealing with MoM matrices with high condition numbers so as to speed up the convergence of the GMRES algorithm; (iii) solving multiscale problems by utilizing techniques for handling geometries with fine features, in the context of Finite Methods, without using a fine mesh that would significantly increase the computational burden of the Finite Method, and without compromising the accuracy of the solution in the process. Illustrative examples that demonstrate the efficacy of the proposed algorithms are included in the paper for several representative problems