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—An efficient algorithm combining,the fast multipole method,(FMM) and the discrete complex,image method,(DCIM) is presented for analyzing large-scale microstrip structures.Firstly, the effect of complex images’ locations on the algorithm is discussed in detail.And a simple and efficient scheme,is proposed which greatly enhances the performance of this FMM-DCIM hybrid method. On the other hand, the incomplete LU (ILU) preconditioner with a dual dropping strategy is also tested to study the effect of this preconditioner on the convergence rate of microstrip structures.And experimental results show that this preconditioner reduces the number of iterations substantially.Then the solution is obtained using it in conjunction with the generalized minimal residual (GMRES).The fast multipole method,is used to speed up the matrix-vector product in iterations.Numerical results for microstrip antennas are presented to demonstrate the efficiency and accuracy of this method.

THE FAST MULTIPOLE ALGORITHM FOR ANALYSIS OF LARGE-SCALE MICROSTRIP ANTENNA ARRAYS