Finite Element / Boundary Integral Method

In the electromagnetic domain, the finite element method(FEM) be good at solving the electromagnetic problems of complicated structure and the method of moments(MoM) be adept in solving open domain problem. To take advantage the strengths of the both methods a hybrid method is presented, namely the hybrid finite element-boundary integral method(FE-BI). In this paper, a number of methods based on FE-BI are presented for the analysis of electromagnetic scattering problems. The following contributions have been made.Firstly, based on the principle of the hybrid finite element-boundary integral method, the formula of this hybrid method was deduced in detail. The combination of equations of the boundary integral was discussed. There are three current schemes to solve the FE-BI matrix equation. Next, this paper studied the crucial technology of singularity extraction method to evaluate the impedance matrix elements of CFIE in detail. In the developed method, all singularities were extracted and calculated in closed form.Secondly, in order to analysis Frequency Selective Surfaces(FSS) which is loaded by dielectric, finite element tearing and interconnecting method and parallel multilevel fast multipole approach are adopted. For the thin dielectric structure, ill-conditioned sparse FEM matrix destroy the spectral property of the whole FE-BI matrix equation and results in a very slow convergence. For this case, this paper improved the algorithm to solve the final reduced equation. Moreover, for reducing the outer iterative steps, this paper introduced FGMRES into the outer iteration. Through this method, the computational time is reduced.Lastly, with the requirement of unity modeling between target and environment, this paper also studied scattering problems above a lossy half space. Moreover, to compute electromagnetic scattering characteristic of object accurately and quickly in complex circumstance, this paper introducd the multilevel UV methods into FE-BI, the filling time of the impedance matrix elements and memory requirements are both reduced.