Fast electromagnetic analysis of multi-scale models with MLFMA utilizing spherical basis functions

An extension of the scalar Low-Frequency Multi-Level Fast Multipole Algorithm (MLFMA) to the vectorial form suitable for accelerations of matrix-vector product in Rao-Wilton-Glisson (RWG) Method of Moments (MoM) solution of the Combined Field Integral Equation (CFIE) is discussed. The detailed expressions relating vectors of electric and magnetic field to the expansion of the magnetic vector potential over scalar spherical wave functions are presented. The method is shown to be applicable for computational domains spanning 120 wavelengths while imposing no lower bound on the size of the leafy level boxes in the MLFMA's hierarchical space partitioning. This makes the method particularly suitable for broadband electromagnetic modelling of multi-scale geometries.