Fast analysis of microwave integrated circuits using preconditioned SMCG method

The analysis and design of planar structures such as microwave monolithic integrated circuits (MMIC) has become a very important topic. Full-wave electromagnetic analysis of microstrip structures is especially significant. Due to the complexity of this scheme, efficient numerical tools are required for their analysis. For these arbitrarily-shaped planar structures, a mixed-potential integral equation (MPIE) formulation with RWG triangular discretization is solved by the method of moments (MoM). One of the most popular techniques for analyzing this scheme is the sparse-matrix/canonical grid (SMCG) method. The impedance matrix of the SMCG method can be decomposed into near-interaction and far-interaction portions. During the iterative process, the near-interaction portion of the matrix-vector multiplication is computed directly as the conventional MPIE formulation. The far-interaction portion of the matrix-vector multiplication is achieved by a Taylor series expansion of the Green's function about the grid point of a uniformly-spaced canonical grid overlaying the triangular discretization (Chan, C.H. et al., 1992). We propose two preconditioned schemes for accelerating iteration of the SMCG method. One method is the inner-outer flexible generalized minimal residual (FGMRES), the other is the approximate inverse of near-interaction.