Parallel Incomplete LU Factorization Based Iterative Solver for Fixed-Structure Linear Equations in Circuit Simulation
Lingjie Li, Zhiqiang Liu, Kan Liu, Shan Shen, Wenjian Yu · 2023
A series of fixed-structure sparse linear equations are solved in a circuit simulation process. We propose a parallel incomplete LU (ILU) preconditioned GMRES solver for those equations. A new subtree-based scheduling algorithm for ILU factorization and forward/backward substitution is adopted to overcome the load-balancing and data locality problem of the conventional levelization-based scheduling. Experimental results show that the proposed scheduling algorithm can achieve up to 2.6X speedup for ILU factorization and 3.1X speedup for forward/backward substitution compared to the levelization-based scheduling. The proposed ILU-GMRES solver achieves around 4X parallel speedup with 8 threads, which is up to 2.1X faster than that based on the levelization-based scheme. The proposed parallel solver also shows remarkable advantage over existing methods (including HSPICE) on transient simulation of linear and nonlinear circuits.