In this talk we will present a numerical method we introduced recently for the solution of problems of electromagnetic and acoustic wave propagation. Our approach is based on the observation that electromagnetic and acoustic fields behave analytically with respect to variations of a scattering surface, so that they can be represented in the form of convergent power series in a perturbation parameter. We will show that these series expansions can be made into the basis for very efficient numerical algorithms. In fact, a second element in our theory consists of simple recursive formulas which allow us to obtain the power series by considering a sequence of easily solvable scattering problems. The analytic extension of the fields to large perturbations can then be achieved via Padé approximation. We shall present two- and three-dimensional numerical examples that demonstrate that our algorithms lead to accurate predictions for a wide variety of scattering configurations.
This is joint work with Oscar Bruno (Applied Mathematics, Caltech).