An efficiently preconditioned GMRES method for fast parasitic-sensitive deep-submicron VLSI circuit simulation

We propose an efficiently preconditioned generalized minimal residual (GMRES) method for fast SPICE-accurate transient simulation of parasitic-sensitive deep-submicron VLSI circuits. First, when time step-sizes vary within a predefined range, the preconditioned GMRES method is applied to solve circuit matrix equations rather than LU factorization. The preconditioner we use comes directly from the previously factorized L and U matrices. Second, to keep using the same preconditioner during nonlinear iteration, the successive variable chord method is applied as an alternative to the Newton-Raphson method. An improved piecewise weakly nonlinear definition of MOSFET is adopted and the low-rank update technique is implemented to refresh the preconditioner efficiently. With these techniques, the number of required LU factorizations during transient simulation is reduced dramatically. Experimental results on power/ground networks have demonstrated that the proposed method yields SPICE-like accuracy with an about 18× overall CPU time speedup over SPICE3 for circuits with tens of thousands elements.