Fast Multipole Method based Model Order Reduction for Large Scattering Problems

This paper present the fast multipole method (FMM) applied to the model order reduction (MOR) for the fast and efficient treatment of large scattering problems. In the solution of electric field integral equation (EFIE), FMM provides faster matrix filling and matrix-vector multiplication and sparer use of computing resources than method of moments (MoM), while MOR allows reducing the FMM system of equations to a smaller one, whose solution preserves the behavior of the original system. Thus, a so-called reduced order model can be generated, stored and used with other simulation tools for system-level modeling. We show that utilization of FMM in MOR considerably decreases the computational cost in comparison to MOR directly applied to MoM. The novel FMM-MOR approach is successfully validated through its application to the analysis of a dipole antenna of various electrical lengths. The Galerkin method with pulse basis functions is utilized for both FMM and MoM. The generalized minimal residual (GMRES) and MOR based on the Arnoldi algorithm are used for the solution of MoM and FMM matrix equations. Comparisons of MoM, FMM, MoM-MOR and FMM-MOR are provided