Unleashing the Power of Graph Spectral Sparsification for Power Grid Analysis via Incomplete Cholesky Factorization.

Graph spectral sparsification-based preconditioning technique has shown promising results for power grid analysis. However, the conventional methods converge slowly for high-accuracy requirement. In this work, we propose an efficient approach to address this issue. Instead of using the Cholesky factorization, we employ the incomplete Cholesky factorization to factorize the spectral sparsifier. We also propose a concept of graph spectral pattern, which can further reduce the preconditioned conjugate gradient (PCG) iterations using less number of nonzeros. Experiments show that under 10(-6) relative tolerance, our proposed preconditioning technique achieves 1.17x speedup compared to AMGPCG in average; compared to the conventional spectral sparsification-based preconditioning techniques, our proposed approach achieves up to 8.53x speedup of the factorization, 8.74x speedup of the PCG iteration, and 5.6x speedup of the total time. Moreover, the speedup of the total time continues to enlarge for higher-accuracy requirement, e.g., 10(-12). Finally, but not least, our method is compatible with existing graph spectral sparsification algorithms for power grid analysis.