A Higher Order Multilevel Fast Multipole Algorithm for Scattering from Mixed Conducting/Dielectric Bodies

Abstract

A higher order multilevel fast multipole algorithm (MLFMA) is presented for computing electromagnetic scattering from three-dimensional bodies comprising both conducting and dielectric objects. The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) approach for multiple homogeneous dielectric objects and the combined-field approach for conducting objects. The resultant integral equations are discretized by the method of moments (MoM), in which the conducting and dielectric surfaces/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions. Such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling. An implicit matrix-filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions. The resultant numerical system is then solved by MLFMA, which is tailored to accommodate the material properties of dielectric scatterers, and the solution is accelerated using an incomplete LU decomposition preconditioner. Numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems.