CSP: Comprehensively-Sparsified Preconditioner for Efficient Nonlinear Circuit Simulation

Solving sparse linear systems dominates the simulation time for nonlinear integrated circuits. Developing an effective preconditioner is crucial for accelerating the iterative solver when dealing with large-scale circuit matrices, yet this remains a challenging task. In this paper, we introduce an efficient sparsification-based preconditioner method that significantly reduces the number of iterations needed in iterative solvers. Our method transforms nonlinear components into symmetric Laplacian matrices, enabling the inclusion of both nonlinear and linear elements in the sparsification process. We then intersect the generated sparsifier with the original Modified Nodal Analysis (MNA) matrix to further reduce the sparsity, thereby decreasing preconditioner factorization time. Furthermore, we enhance the parallelization of the spectral sparsification strategy by integrating block RMQ and point exclusivity algorithms, which substantially speeds up preprocessing. Experiment results demonstrate acceleration of 2.50x, 13.46x, 2.18x on average in serial, 3.72x, 24.23x, 3.86x on average in parallel, and memory reduction of $21.3 \%, 21.7 \%, 88.0 \%$ on average when solving nonlinear circuit matrices compared to the state-of-the-art solver GPSCP, feGRASS, and direct solver KLU, respectively.