Vectorial Low-Frequency MLFMA for the Combined Field Integral Equation

A vectorial Low-Frequency Multi-Level Fast Multipole Algorithm (LF-MLFMA) is proposed for acceleration of interactions resultant from the method of moments (MoM) discretization of the combined field integral equation (CFIE). The derivatives relating the scalar Green's function to its dyadic counterparts are defined via recursive identities for scalar wave functions. The method evaluates the matrix vector product in MoM by performing three scalar LF-MLFMA passes. It is demonstrated to be stable for scatterers spanning up to 110 wavelengths in size. As the method does not impose any restrictions on the depth of the MLFMA tree, it is suitable for the solution of both broadband and multiscale problems.