Hybrid-Precision Block-Jacobi Preconditioned GMRES Solver for Linear System in Circuit Simulation

Abstract: As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and reduced accuracy. In this paper, a hybrid-precision block-Jacobi preconditioned GMRES solver is proposed to solve the large sparse system in circuit simulation. The proposed method capitalizes on the structural sparsity and block properties of circuit matrices, employing a novel hybrid-precision strategy that applies single-precision arithmetic for computationally intensive tasks and double-precision arithmetic for critical accuracy-sensitive computations. Additionally, we use the graph partitioning tools to assist in generating preconditioners, ensuring an optimized preconditioning process. For large-scale problems, we adopt the restart strategy to increase the computational efficiency. Through rigorous mathematical reasoning, the convergence and error analysis of the proposed method are carried out. Numerical experiments on various benchmark matrices demonstrate that our approach significantly outperforms existing solvers, including SuperLU, KLU, and SFLU, in terms of both preconditioning and GMRES runtime. The proposed hybrid-precision preconditioner effectively improves spectral clustering, leading to faster solutions.