A Multilevel Fast Multipole Algorithm for Analyzing Radiation and Scattering From Wire Antennas in a Complex Environment

Abstract

A hybrid VSIE-MLFMA formulation is applied to solve for scattering and radiation solutions from wire antennas, IBC surfaces, and inhomogeneous dielectric objects. Unlike the traditional method of moments, the VSIE-MLFMA formulation has a computational complexity of O( N log N) for both CPU time and memory requirement, where N is the number of unknowns. The surface integral equation part of the formulation is extended to a full curvilinear implementation with the invention of curvilinear junction basis. The curvilinear formulation enables efficient solution for radiation and scattering from highly curved PEC structures. In order to accurately model coaxial feeds for wire antennas, a variational formulation is applied to calculate the input impedances of horizontal and vertical frill sources. Numerical simulations agree well with experimental results after correctly modeling the SMA connector as a horizontal frill source and a lossy transmission line. Moreover, succinct spectral integrals are derived for efficient calculation of the fringe capacitances, which contribute to the main differences of delta-gap and magnetic frill sources in high-frequency simulation. In addition, physics-based preconditioners and basis reduction schemes are developed to reduce iteration counts for iterative solvers. The formulation is then applied for vehicle antenna and photolithography simulations. A fast field calculation based on MLFMA significantly reduces the time for computing near and far fields radiated from vehicle antennas and photomasks.