Block Low-rank Algebraic Clustering for Sparse Direct Solvers

Abstract : We will discuss challenges in building clusters for the Block Low-Rank (BLR) approach, for nodes inside separators appearing during the factorization of sparse matrices. We will illustrate limitations for methods that consider only intra-separators connectivity (i.e., k-way and recursive bisection) as well as methods focusing only on reducing the number of updates between separators. The new strategy we propose considers interactions between a separator and its children in the nested dissection. It allows reducing the computational cost of BLR, and the number of off-diagonal blocks. We demonstrate that this method enhances the BLR strategies in the sparse direct supernodal solver PaStiX, and discuss how it can be extended to low-rank formats with more than one level of hierarchy.
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https://hal.inria.fr/hal-01956962
Contributor : Mathieu Faverge <>
Submitted on : Sunday, December 16, 2018 - 11:24:23 PM
Last modification on : Friday, October 25, 2019 - 3:08:01 PM

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  • HAL Id : hal-01956962, version 1

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Grégoire Pichon, Eric Darve, Mathieu Faverge, Pierre Ramet, Jean Roman. Block Low-rank Algebraic Clustering for Sparse Direct Solvers. SIAM Conference on Computational Science and Engineering (CSE19), Feb 2019, Spokane, United States. ⟨hal-01956962⟩

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