A new approach to solving second kind integral equations

Many problems in applied electromagnetics can be formulated in terms of solving a boundary integral equation of the second kind. Much success has been achieved in solving these type equations through the Method of Moments (MOM) or related approaches by which the integral equation is reduced to solving a matrix equation. However, for problems involving long range interactions such as rough surface scattering, propagation over irregular terrain, or even large complicated structures, the MOM leads to intractable matrices. These problems have been overcome for two dimensional geometries through methods such as Forward-Backward or the Method of Ordered Multiple Interactions but the extension to three dimensions is still prohibitive. For this reason, there remains a need for a new approach to solving integral equations of the second kind.