Abstract
To improve the efficiency of direct solution methods in SPICE-accurate integrated circuit (IC) 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 IC problems. In this paper, based on recent graph sparsification research we propose circuit-oriented general-purpose support-circuit preconditioning (GPSCP) methods to dramatically improve the sparse matrix solution time and reduce the memory cost during SPICE-accurate IC 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 model-guided graph sparsification framework is proposed to help automatically build nearly-optimal GPSCP solvers. Our experiment results for a variety of large-scale IC designs show that the proposed preconditioning techniques can achieve up to $18 {\times }$ runtime speedups and $7 {\times }$ memory reduction in DC and transient simulations when compared to state-of-the-art direct solution methods.
Published Version
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