A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems

A novel hybridization of the finite element (FE) and boundary integral methods is presented for an efficient and accurate numerical analysis of electromagnetic scattering and radiation problems. The proposed method derives an adaptive numerical absorbing boundary condition (ABC) for the finite element solution based on boundary integral equations. Unlike the standard finite element-boundary integral approach, the proposed method is free of interior resonance and produces a purely sparse system matrix, which can be solved very efficiently. Unlike the traditional finite element-absorbing boundary condition approach, the proposed method uses an arbitrarily shaped truncation boundary placed very close to the scatterer/radiator to minimize the computational domain; and more importantly, the method produces a solution that converges to the true solution of the problem. To demonstrate its great potential, the proposed method is implemented using higher order curvilinear vector elements. A mixed functional is designed to yield both electric and magnetic fields on an integration surface, without numerical differentiation, to be used in the calculation of the adaptive ABC. The required evaluation of boundary integrals is carried out using the multilevel fast multipole algorithm, which greatly reduces both the memory requirement and CPU time. The finite element equations are solved efficiently using the multifrontal algorithm. A mathematical analysis is conducted to study the convergence of the method. Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.