Sparse supernodal solver using block low-rank compression: Design, performance and analysis

Grégoire Pichon (1, 2) , Eric Darve (3) , Mathieu Faverge (1, 4) , Esragul Korkmaz (1, 2) , Pierre Ramet (1, 2) , Jean Roman (1, 4)

1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 Stanford University
4 Bordeaux INP - Institut Polytechnique de Bordeaux

In this work, we present 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), Rank-Revealing QR (RRQR), and other variants using randomized compression kernels, are compared in terms of factorization time, memory consumption, as well as numerical properties. 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.

Mots clés: Sparse direct solver; Low-rank compression

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Grégoire Pichon, Eric Darve, Mathieu Faverge, Esragul Korkmaz, Pierre Ramet, et al.. Sparse supernodal solver using block low-rank compression: Design, performance and analysis. JOREK development meeting, Nov 2019, Cadarache, France. ⟨hal-02326407⟩