Fast Poisson Solvers for Graphics Processing Units

Mirko Myllykoski, Tuomo Rossi, Jari Toivanen
Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyvaskyla, Finland
Workshop on State-of-the-Art in Scientific and Parallel Computing (PARA’12), 2012


   title={Fast Poisson Solvers for Graphics Processing Units},

   author={Myllykoski, M. and Rossi, T. and Toivanen, J.},



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Two block cyclic reduction linear system solvers are considered and implemented using the OpenCL framework. The topics of interest include a simplified scalar cyclic reduction tridiagonal system solver and the impact of increasing the radix-number of the algorithm. Both implementations are tested for the Poisson problem in two and three dimensions, using a Nvidia GTX 580 series GPU and double precision floating-point arithmetic. The numerical results indicate up to 6-fold speed increase in the case of the two-dimensional problems and up to 3-fold speed increase in the case of the three-dimensional problems when compared to equivalent CPU implementations run on a Intel Core i7 quad-core CPU.
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