Parallel power grid analysis using preconditioned GMRES solver on CPU-GPU platforms

In this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU-GPU platforms. The new solver is very robust and can be applied to power grids with different structures and other applications like thermal analysis. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU (ILU) based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and GMRES convergence rate can be achieved for the best overall performance. Such a tunable feature makes this algorithm very adaptive to different problems. Furthermore, we properly partition the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPU, which further boosts performance of the proposed method. Experimental results on the set of published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver UMFPACK. GPU-GMRES can also deliver 3-10× speedup over the CPU implementation of the same GMRES method on transient analysis.