Efficient algorithms for direct resolution of large sparse system on clusters of SMP nodes

Pascal Hénon (1) , Pierre Ramet (1, 2) , Jean Roman (1, 2)

1 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

In previous works, we have described an efficient static scheduling based on a mixed 1D/2D block distribution with local aggregation for a parallel supernodal version of sparse $LL^T$ factorization. In this paper, we present new algorithms suitable for overcoming architectures based on clusters of SMP nodes and also technics to keep a good memory scalability. This algorithms are implemented in the PaStiX library that achieved high performances (resolution of a $26.10^6$ unknown system on 192 ES45 quadriprocessors with 35 percent of peak performance).

Keywords: Sparse

Pascal Hénon, Pierre Ramet, Jean Roman. Efficient algorithms for direct resolution of large sparse system on clusters of SMP nodes. SIAM Conference on Applied Linear Algebra, 2003, Williamsburg, United States. ⟨inria-00346609⟩