A Concise and Efficient MLFMA Scheme for Electromagnetic Surface Integral Equations From Dielectric Objects

In the surface field integral equations (SIEs) from three-dimensional homogeneous dielectric objects, the equivalence electric and magnetic currents on the discontinuous interfaces between different homogeneous media are two independent sources. When the SIEs are iteratively solved, as indicated by the published literatures, the multilevel fast multipole algorithm (MLFMA) needs to be implemented respectively for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) with these two currents, and hence a few MLFMA implementations are necessary for each homogeneous medium. In this paper, a concise and efficient scheme is proposed for reducing the implementations of the SIEs-MLFMA. First, the summation of the EFIE and MFIE-MLFMA implementations with the two currents can be simplified into one EFIE or MFIE-MLFMA implementation with integrating electric and magnetic currents at the lowest-level aggregation stage. Secondly, the common matrix frameworks consisting of the EFIE and MFIE-MLFMA implementations used in the SIEs can be simplified into one MLFMA implementation with two lowest-level diaggregations. The enhanced MLFMA scheme has excellent applicability to eight kinds of SIEs in wide use. In this way, the resulted SIE-MLFMA scheme performs only once for each homogeneous medium when transforming outgoing wave expansions of the two currents into incoming wave expansions for bottom cubes. Compared with the widely-used implementation approach of the MLFMA one by one for the two currents, it reduces the computation complexity by one half without sacrificing accuracy and adding a little memory requirement. Some examples are presented to validate the enhanced MLFMA scheme.