Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

James Brannick, Yao Chen, Xiaozhe Hu, Ludmil Zikatanov
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
arXiv:1302.2547 [math.NA], (11 Feb 2013)

   author={Brannick}, J. and {Chen}, Y. and {Hu}, X. and {Zikatanov}, L.},

   title={"{Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs}"},

   journal={ArXiv e-prints},




   keywords={Mathematics – Numerical Analysis},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.
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