Application of the preconditioned conjugate-gradient algorithm to the integral equations for microwave circuits

In this Letter, both the banded diagonal matrix and the symmetric successive overrelaxation (SSOR) precondition CG techniques are applied to dense matrix equations from the mixed potential integral equation (MPIE) to enhance computational efficiency. Numerical calculations show that the banded diagonal matrix preconditioned conjugate-gradient (CG) technique is efficient only for the discretization along one dimension, whereas the SSOR scheme is efficient for the discretization in two dimensions. Some typical microstrip discontinuities are analyzed and good results demonstrate the validity of the proposed algorithms.