We describe heterogeneous multi-CPU and multi-GPU implementations of Jacobi's iterative method for the 2-D Poisson equation on a structured grid, in both single- and double-precision. Properly tuned, our best implementation achieves 98% of the empirical streaming GPU bandwidth (66% of peak) on a NVIDIA C1060. Motivated to find a still faster implementation, we further consider "wildly asynchronous" implementations that can reduce or even eliminate the synchronization bottleneck between iterations. In these versions, which are based on the principle of a chaotic relaxation (Chazan and Miranker, 1969), we simply remove or delay synchronization between iterations, thereby potentially trading off more flops (via more iterations to converge) for a higher degree of asynchronous parallelism. Our relaxed-synchronization implementations on a GPU can be 1.2-2.5x faster than our best synchronized GPU implementation while achieving the same accuracy. Looking forward, this result suggests research on similarly "fast-and-loose" algorithms in the coming era of increasingly massive concurrency and relatively high synchronization or communication costs.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/29728 |
| Date | 18 May 2009 |
| Creators | Venkatasubramanian, Sundaresan |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Thesis |
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