To improve the efficiency of direct solution methods in SPICE-accurate integrated circuit simulations, preconditioned iterative solution techniques have been widely studied in the past decades. However, it is still an extremely challenging task to develop robust yet efficient general-purpose preconditioning methods that can deal with various types of large-scale integrated circuit problems. In this work, based on recent graph sparsification research we propose circuit-oriented generalpurpose support-circuit preconditioning (GPSCP) methods to dramatically improve the sparse matrix solution time and reduce the memory cost during SPICE-accurate integrated circuit simulations.
By sparsifying the Laplacian matrix extracted from the original circuit network using graph sparsification techniques, general-purpose support circuits can be efficiently leveraged as preconditioners for solving large Jacobian matrices through Krylov-subspace iterations. Additionally, a performance modelguided graph sparsification framework is proposed to help automatically build nearly-optimal GPSCP solvers. Our experiment results for a variety of large-scale integrated circuit designs show that the proposed preconditioning techniques can achieve up to 18X runtime speedups and 7X memory reduction in DC and transient simulations when compared to state-of-the-art direct solution methods.