A broadband stable addition theorem for the two dimensional MLFMA

Integral equations arising from the time-harmonic Maxwell equations contain the Green function of the Helmholtz equation as the integration kernel. The structure of this Green function has allowed the development of so-called fast multipole methods (FMMs), i.e. methods for accelerating the matrix-vector products that are required for the iterative solution of integral equations. Arguably the most widely used FMM is the Multilevel Fast Multipole Algorithm (MLFMA). It allows the simulation of electrically large structures that are intractable with direct or iterative solvers without acceleration. The practical importance of the MLFMA is made all the more clear by its implementation in various commercial EM software packages such as FEKO and CST Microwave studio.