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Blocking strategy optimizations for sparse direct linear solver on heterogeneous architectures

Abstract : In the context of solving sparse linear systems, an ordering process partitions the matrix graph to minimize both fill-in and computational cost. We found that the ordering strategy used within supernodes might be enhanced to reduce the number of off-diagonal blocks, and then increases block sizes and kernel performance. This turns to be into the same complexity as the factorization algorithm, but allows for more efficient BLAS kernels. On the other side, supernodes that are too large need to be split to create more parallelism. The regular splitting strategy when applied locally impacts significantly the number of off-diagonal blocks and might have negative effect on the efficiency. In this talk, we present both a new strategy to improve supernodes ordering and splitting strategy that both enlarge the off-diagonal block sizes without changing the computational cost of the factorization. Performance improvement gains on the supernodal solver PaStiX are shown on multi-cores and heterogeneous architectures.
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https://hal.inria.fr/hal-01187881
Contributor : Pierre Ramet <>
Submitted on : Thursday, August 27, 2015 - 8:40:32 PM
Last modification on : Thursday, March 5, 2020 - 4:52:22 PM

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  • HAL Id : hal-01187881, version 1

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Mathieu Faverge, Grégoire Pichon, Pierre Ramet, Jean Roman. Blocking strategy optimizations for sparse direct linear solver on heterogeneous architectures. Sparse Days, Jun 2015, Saint Girons, France. ⟨hal-01187881⟩

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