Combining the Ultra-Weak Variational Formulation and the Multilevel Fast Multipole Method

Because of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxwell’s equations, a volume based method using plane wave basis functions, and an overlapping integral representation of the unknown field to obtain an exact artificial boundary condition on an auxiliary surface that can be very close to the scatterer. Combining the new algorithm with a multilevel fast multipole method we obtain an efficient volume based solver with an exact auxiliary boundary condition, but without the need for singular integrals.