Sparse Supernodal Solver Using Block Low-Rank Compression: design, performance and analysis

Abstract : 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 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 com- putational 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 single 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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https://hal.inria.fr/hal-01660665
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Submitted on : Monday, December 11, 2017 - 11:25:08 AM
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Grégoire Pichon, Eric Darve, Mathieu Faverge, Pierre Ramet, Jean Roman. Sparse Supernodal Solver Using Block Low-Rank Compression: design, performance and analysis. [Research Report] RR-9130, Inria Bordeaux Sud-Ouest. 2017, pp.1-32. ⟨hal-01660665⟩

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