Singularity treatment and high-order RWG basis functions for integral equations of electromagnetic scattering.

摘要

Various numerical techniques have been developed to carry out the electromagnetic field simulation. In this dissertation, we consider a mixed potential (vector and scalar potentials) integral equation for electromagnetic scattering and study its numerical methods.; At first we give and prove the approximation properties of traditional RWG basis functions proposed by S. M. Rao, D. R. Wilton and A. W. Glisson [6] and high order basis functions newly developed by W. Cai [7], which show the advantages of high order basis functions in theory. Then we present a novel numerical method for treating singularities of the dyadic Green's functions used in the mixed potential formulation of electromagnetic scattering. At last we compute the electromagnetic scattering of a curved conductor surface with an incident wave Einc by using different order basis functions on flat and curved triangles with the proposed treatment of singularities, and provide different numerical tests and simulations to address various issues of implementing the high order basis function and the treatment of singular integrals.