Parallel multigrid preconditioning on graphics processing units (GPUs) for robust power grid analysis

Zhuo Feng, Zhiyu Zeng
Department of ECE, Michigan Technological University, Houghton, MI, 49931
47th ACM/IEEE Design Automation Conference (DAC), 2010, p.661-666


   title={Parallel multigrid preconditioning on graphics processing units (GPUs) for robust power grid analysis},

   author={Feng, Z. and Zeng, Z.},

   booktitle={Design Automation Conference (DAC), 2010 47th ACM/IEEE},






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Leveraging the power of nowadays graphics processing units for robust power grid simulation remains a challenging task. Existing preconditioned iterative methods that require incomplete matrix factorizations can not be effectively accelerated on GPU due to its limited hardware resource as well as data parallel computing. This work presents an efficient GPU-based multigrid preconditioning algorithm for robust power grid analysis. An ELL-like sparse matrix data structure is adopted and implemented specifically for power grid analysis to assure coalesced GPU device memory access and high arithmetic intensity. By combining the fast geometrical multigrid solver with the robust Krylov-subspace iterative solver, power grid DC and transient analysis can be performed efficiently on GPU without loss of accuracy (largest errors < 0.5 mV). Unlike previous GPU-based algorithms that rely on good power grid regularities, the proposed algorithm can be applied for more general power grid structures. Experimental results show that the DC and transient analysis on GPU achieves more than 25X speedups over the best available CPU-based solvers. An industrial power grid with 10.5 million nodes can be accurately solved in 12 seconds.
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