Novel surface integral equation formulation for penetrable bodies

Surface Integral Equations (SIEs) constitute a very powerful method for the analysis of electromagnetic scattering of homogeneous penetrable objects. The discretization of SIEs, however, results in a non-sparse system matrix, expensive to store and solve. In order to consider complex large-scale problems with a high number of unknowns, acceleration methods like the fast multipole method are required, which are based on iterative solution schemes. It is then clear that rapidly converging algorithms are needed, but many of the SIE formulations lead to ill-conditioned slowly converging systems. This paper presents a brief discussion on convergence and accuracy of SIEs, and introduces a new alternative formulation.