Efficient Surface Integral Equation Using Hierarchical Vector Bases for Complex EM Scattering Problems

A set of hierarchical divergence-conforming vector basis functions based on curved triangular patches is presented for method of moment (MoM) solutions of surface integral equations in this paper. The higher order method of combined-field integral equation (CFIE) solves perfect electric conductor electromagnetic scattering problems, the higher order electric-magnetic current combined-field integral equation (JMCFIE) formulations solves dielectric objects, and their combination is able to efficiently analyzes the scattering of hybrid PEC-dielectric objects. The expressions of the divergence- conforming hierarchical basis functions up to order 3.5 are reported in this paper. The multilevel fast multipole algorithm (MLFMA) is then employed to reduce the memory requirements and computational complexity. Numerical experiments indicate that the proposed hierarchical vector basis functions can provide well-conditioned linear system for iterative solution.