An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

An efficient multilevel fast multipole algorithm (MLFMA) formalism to model radiation and scattering by/from large planar microwave structures is presented. The technique relies on an electric field integral equation (EFIE) formulation and a series expansion for the Green dyadic, based on the use of perfectly matched layers (PML). In this way, a new PML-MLFMA is developed to efficiently evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. The computational complexity of the new algorithm scales down to O(N) for electrically large structures. The theory is validated by means of several illustrative, numerical examples.