Sparse supernodal solver using block low-rank compression: Design, performance and analysis
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| Názov: | Sparse supernodal solver using block low-rank compression: Design, performance and analysis |
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| Autori: | Pichon, Grégoire, Darve, Eric, Faverge, Mathieu, Ramet, Pierre, Roman, Jean |
| Prispievatelia: | Pichon, Gregoire |
| Zdroj: | Journal of Computational Science. 27:255-270 |
| Informácie o vydavateľovi: | Elsevier BV, 2018. |
| Rok vydania: | 2018 |
| Predmety: | Sparse linear solver, PaStiX sparse direct solver, Bblock low-rank compression, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO] Computer Science [cs], 0101 mathematics, Multi-threaded architectures, 01 natural sciences |
| Popis: | This paper presents two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver PaStiX. This flat, non-hierarchical, compression method allows to take advantage of the low-rank property of the blocks appearing during the factorization of sparse linear systems, which come from the discretization of partial differential equations. The proposed solver can be used either as a direct solver at a lower precision or as a very robust preconditioner. The first approach, called Minimal Memory, illustrates the maximum memory gain that can be obtained with the BLR compression method, while the second approach, called Just-In-Time, mainly focuses on reducing the computational complexity and thus the time-to-solution. Singular Value Decomposition (SVD) and Rank-Revealing QR (RRQR), as compression kernels, are both compared in terms of factorization time, memory consumption, as well as numerical properties. Experiments on a shared memory node with 24 threads and 128 GB of memory are performed to evaluate the potential of both strategies. On a set of matrices from real-life problems, we demonstrate a memory footprint reduction of up to 4 times using the Minimal Memory strategy and a computational time speedup of up to 3.5 times with the Just-In-Time strategy. Then, we study the impact of configuration parameters of the BLR solver that allowed us to solve a 3D laplacian of 36 million unknowns a single node, while the full-rank solver stopped at 8 million due to memory limitation. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1877-7503 |
| DOI: | 10.1016/j.jocs.2018.06.007 |
| Prístupová URL adresa: | https://hal.inria.fr/hal-01824275/file/blr.pdf https://inria.hal.science/hal-01824275v1 https://doi.org/10.1016/j.jocs.2018.06.007 https://inria.hal.science/hal-01824275v1/document https://www.sciencedirect.com/science/article/abs/pii/S1877750317314497 https://hal.inria.fr/hal-01824275/document https://dblp.uni-trier.de/db/journals/jocs/jocs27.html#PichonDFRR18 https://hal.inria.fr/hal-01824275 https://doi.org/10.1016/j.jocs.2018.06.007 |
| Rights: | Elsevier TDM |
| Prístupové číslo: | edsair.doi.dedup.....92aef672a2519f4ddb31452808f6b6ee |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | This paper presents two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver PaStiX. This flat, non-hierarchical, compression method allows to take advantage of the low-rank property of the blocks appearing during the factorization of sparse linear systems, which come from the discretization of partial differential equations. The proposed solver can be used either as a direct solver at a lower precision or as a very robust preconditioner. The first approach, called Minimal Memory, illustrates the maximum memory gain that can be obtained with the BLR compression method, while the second approach, called Just-In-Time, mainly focuses on reducing the computational complexity and thus the time-to-solution. Singular Value Decomposition (SVD) and Rank-Revealing QR (RRQR), as compression kernels, are both compared in terms of factorization time, memory consumption, as well as numerical properties. Experiments on a shared memory node with 24 threads and 128 GB of memory are performed to evaluate the potential of both strategies. On a set of matrices from real-life problems, we demonstrate a memory footprint reduction of up to 4 times using the Minimal Memory strategy and a computational time speedup of up to 3.5 times with the Just-In-Time strategy. Then, we study the impact of configuration parameters of the BLR solver that allowed us to solve a 3D laplacian of 36 million unknowns a single node, while the full-rank solver stopped at 8 million due to memory limitation. |
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| ISSN: | 18777503 |
| DOI: | 10.1016/j.jocs.2018.06.007 |