Implementation and experiments of a hybrid algorithm of the MLFMA-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems

Although the computational complexity of the finite-element boundary-integral (FE-BI) method is significantly reduced by the multilevel fast multipole algorithm (MLFMA), this MLFMA-enhanced FE-BI solution experiences a very slow convergence for some complex inhomogeneous problems. In this paper, a hybrid algorithm, combining direct methods with iterative methods, is designed to speed up the rate of convergence of this MLFMA-enhanced FE-BI solution. This hybrid algorithm is efficiently implemented with the aid of a newly developed package, SuperLU, of the LU decomposition solver. Numerical experiments are performed for a coated Northrop wing to demonstrate the efficiency of this hybrid algorithm. More importantly, the thorough investigation of the numerical experiments clearly shows the better accuracy, stability, and robustness of this hybrid algorithm over the conventional algorithms.