As the resolution continues to increase, the scale of the power grid of the flat panel display (FPD) becomes huge. This imposes a severe computational challenge for analysis and storage. In this paper, based on the highly periodic FPD structure, we present an efficient simulator which contains a novel stamping scheme and a fast structural solver. Experiments on real industrial cases show that compared to the conventional stamping scheme, our proposed stamping scheme achieves up to 118× speedup in 74× less memory; compared to the state-of-art direct solver, Cholmod, our proposed structural solver achieves up to 17× speedup in 5× less memory.

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$1.17\times $speedup compared to AMGPCG in average; compared to the conventional spectral sparsification-based preconditioning techniques, our proposed approach achieves up to$8.53\times $speedup of the factorization,$8.74\times $speedup of the PCG iteration, and$5.6\times $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.

Fast verification for the extremely large-scale power grid is demanding as CMOS technology advances consistently. In this work, we propose ESPSim, an efficient scalable power grid simulator based on a parallel smoothed aggregation-based algebraic multigrid technique. ESPSim has the ability to do fast DC and transient analysis through MPI and adaptive timestep control mechanism. Thanks to the smoother applied on the prolongation operator, ESPSim copes well with the convergence rate on extremely large-scale power grid transient analysis. Extensive experiments are conducted with a variety of serial/parallel solvers. The runtime of ESPSim is linear with case size. With 16 processors, 1,000 timesteps transient analysis of 63.4M nodes can be completed in 22.1 min. Over 22× speedup compared to the well-known direct solver Cholmod is observed.