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Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization

Esragul Korkmaz 1 Mathieu Faverge 1 Grégoire Pichon 2 Pierre Ramet 1 
1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest
2 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Low-rank compression techniques are very promising for reducing memory footprint and execution time on a large spectrum of linear solvers. Sparse direct supernodal approaches are one of these techniques. However, despite providing a very good scalability and reducing the memory footprint, they suffer from an important flops overhead in their unstructured low-rank updates. As a consequence, the execution time is not improved as expected. In this paper, we study a solution to improve low-rank compression techniques in sparse supernodal solvers. The proposed method tackles the overprice of the low-rank updates by identifying the blocks that have poor compression rates. We show that the fill-in levels of the graph based block incomplete LU factorization can be used in a new context to identify most of these non-compressible blocks at low cost. This identification enables to postpone the low-rank compression step to trade small extra memory consumption for a better time to solution. The solution is validated within the PASTIX library with a large set of application matrices. It demonstrates sequential and multithreaded speedup up to 8.5×, for small memory overhead of less than 1.49× with respect to the original version.
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https://hal.inria.fr/hal-03361299
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Submitted on : Friday, October 1, 2021 - 12:12:13 PM
Last modification on : Friday, July 1, 2022 - 3:51:47 AM
Long-term archiving on: : Sunday, January 2, 2022 - 6:50:07 PM

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Esragul Korkmaz, Mathieu Faverge, Grégoire Pichon, Pierre Ramet. Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization. HiPC 2021 - 28th IEEE International Conference on High Performance Computing, Data, and Analytics, Dec 2021, Bangalore, India. pp.1-10, ⟨10.1109/HiPC53243.2021.00024⟩. ⟨hal-03361299⟩

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