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    High Performance Multi-GPU SpMV for Multi-component PDE-Based Applications

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    Type
    Conference Paper
    Authors
    Abdelfattah, Ahmad cc
    Ltaief, Hatem cc
    Keyes, David E. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Date
    2015-07-25
    Online Publication Date
    2015-07-25
    Print Publication Date
    2015
    Permanent link to this record
    http://hdl.handle.net/10754/565820
    
    Metadata
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    Abstract
    Leveraging optimization techniques (e.g., register blocking and double buffering) introduced in the context of KBLAS, a Level 2 BLAS high performance library on GPUs, the authors implement dense matrix-vector multiplications within a sparse-block structure. While these optimizations are important for high performance dense kernel executions, they are even more critical when dealing with sparse linear algebra operations. The most time-consuming phase of many multicomponent applications, such as models of reacting flows or petroleum reservoirs, is the solution at each implicit time step of large, sparse spatially structured or unstructured linear systems. The standard method is a preconditioned Krylov solver. The Sparse Matrix-Vector multiplication (SpMV) is, in turn, one of the most time-consuming operations in such solvers. Because there is no data reuse of the elements of the matrix within a single SpMV, kernel performance is limited by the speed at which data can be transferred from memory to registers, making the bus bandwidth the major bottleneck. On the other hand, in case of a multi-species model, the resulting Jacobian has a dense block structure. For contemporary petroleum reservoir simulations, the block size typically ranges from three to a few dozen among different models, and still larger blocks are relevant within adaptively model-refined regions of the domain, though generally the size of the blocks, related to the number of conserved species, is constant over large regions within a given model. This structure can be exploited beyond the convenience of a block compressed row data format, because it offers opportunities to hide the data motion with useful computations. The new SpMV kernel outperforms existing state-of-the-art implementations on single and multi-GPUs using matrices with dense block structure representative of porous media applications with both structured and unstructured multi-component grids.
    Citation
    Abdelfattah, Ahmad, Hatem Ltaief, and David Keyes. "High Performance Multi-GPU SpMV for Multi-component PDE-Based Applications." In Euro-Par 2015: Parallel Processing, pp. 601-612. Springer Berlin Heidelberg, 2015
    Publisher
    Springer Nature
    Journal
    Euro-Par 2015: Parallel Processing
    Conference/Event name
    21st International Conference on Parallel and Distributed Computing, Euro-Par 2015
    DOI
    10.1007/978-3-662-48096-0_46
    Additional Links
    http://link.springer.com/chapter/10.1007%2F978-3-662-48096-0_46
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-662-48096-0_46
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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