Solution of three-dimensional electromagnetic scattering problems by interior source methods

We discuss solving three-dimensional electromagnetic scattering problems by interior source methods, where one looks for solutions as integrals over an auxiliary surface inside the scattering body. Results about existence and uniqueness of solution of the resulting integral equation are presented. The approximate solution of the integral equation is a linear combination of Dirac’s delta-functions; various methods to calculate the coefficients are discussed. If the boundary of the scatterer is analytic, then for specific choices of the auxiliary surface and meshes the convergence is exponential in the number of variables.