Wavelet-based sparse approximate inverse preconditioned CG algorithm for fast analysis of microstrip circuits

In this paper, the wavelet transform technique is used to transform dense matrix equations from the mixed potential integral equation (MPIE) to obtain sparse matrix equations, after dropping elements smaller than the threshold. The multifrontal method is employed to solve the resultant sparse approximate-inverse preconditioning equation for the preconditioned conjugate gradient (CG) algorithm, in order to enhance its computational efficiency. Our numerical calculations show that the preconditioned CG algorithm, with this wavelet-based sparse approximate inverse as preconditioner, can converge 23.43 times faster than the conventional one for 2048 unknowns. Some typical microstrip discontinuities are analyzed and the good results achieved demonstrate the validity of the proposed algorithm.