Broadband MLFMA based on an approximate diagonalization of the three-dimensional Green's function

We present an approximate diagonalization of the three-dimensional Green's function for straightforward broadband implementations of the multilevel fast multipole algorithm. The diagonalization is based on the use of scaled spherical functions and plane waves, leading to approximate but stable expansions for arbitrarily short distances with respect to wavelength. Despite its limited accuracy, the approximate diagonalization is easy to insert into existing MLFMA implementations for converting them into broadband solvers without reprogramming efforts. We demonstrate the effectiveness of the developed implementation on multiscale problems that are difficult to solve without low-frequency stabilizations.