Preconditioners for Batched Iterative Linear Solvers on GPUs

Isha Aggarwal; Pratik Nayak; Aditya Kashi; Hartwig Anzt

doi:10.1007/978-3-031-23606-8_3

Preconditioners for Batched Iterative Linear Solvers on GPUs

Isha Aggarwal, Pratik Nayak, Aditya Kashi, Hartwig Anzt

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Batched iterative solvers can be an attractive alternative to batched direct solvers if the linear systems allow for fast convergence. In non-batched settings, iterative solvers are often enhanced with sophisticated preconditioners to improve convergence. In this paper, we develop preconditioners for batched iterative solvers that improve the iterative solver convergence without incurring detrimental resource overhead and preserving much of the iterative solver flexibility. We detail the design and implementation considerations, present a user-friendly interface to the batched preconditioners, and demonstrate the convergence and runtime benefits over non-preconditioned batched iterative solvers on state-of-the-art GPUs for a variety of benchmark problems from finite difference stencil matrices, the Suitesparse matrix collection and a computational chemistry application.

Original language	English
Title of host publication	Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers
Editors	Kothe Doug, Geist Al, Swaroop Pophale, Hong Liu, Suzanne Parete-Koon
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	38-53
Number of pages	16
ISBN (Print)	9783031236051
DOIs	https://doi.org/10.1007/978-3-031-23606-8_3
State	Published - 2022
Externally published	Yes
Event	Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022 - Virtual, Online Duration: Aug 24 2022 → Aug 25 2022

Publication series

Name	Communications in Computer and Information Science
Volume	1690 CCIS
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022
City	Virtual, Online
Period	08/24/22 → 08/25/22

Funding

2 This work was performed on the HoreKa supercomputer funded by the Ministry of Science, Research and the Arts Baden-Württemberg and by the Federal Ministry of Education and Research. This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

Funders	Funder number
Office of Science
National Nuclear Security Administration
Bundesministerium für Bildung und Forschung
Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg

Keywords

Batched preconditioners
Batched solvers
GPU
Ginkgo
Sparse linear systems

Access to Document

10.1007/978-3-031-23606-8_3

Cite this

Aggarwal, I., Nayak, P., Kashi, A., & Anzt, H. (2022). Preconditioners for Batched Iterative Linear Solvers on GPUs. In K. Doug, G. Al, S. Pophale, H. Liu, & S. Parete-Koon (Eds.), Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers (pp. 38-53). (Communications in Computer and Information Science; Vol. 1690 CCIS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-23606-8_3

Aggarwal, Isha ; Nayak, Pratik ; Kashi, Aditya et al. / Preconditioners for Batched Iterative Linear Solvers on GPUs. Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers. editor / Kothe Doug ; Geist Al ; Swaroop Pophale ; Hong Liu ; Suzanne Parete-Koon. Springer Science and Business Media Deutschland GmbH, 2022. pp. 38-53 (Communications in Computer and Information Science).

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abstract = "Batched iterative solvers can be an attractive alternative to batched direct solvers if the linear systems allow for fast convergence. In non-batched settings, iterative solvers are often enhanced with sophisticated preconditioners to improve convergence. In this paper, we develop preconditioners for batched iterative solvers that improve the iterative solver convergence without incurring detrimental resource overhead and preserving much of the iterative solver flexibility. We detail the design and implementation considerations, present a user-friendly interface to the batched preconditioners, and demonstrate the convergence and runtime benefits over non-preconditioned batched iterative solvers on state-of-the-art GPUs for a variety of benchmark problems from finite difference stencil matrices, the Suitesparse matrix collection and a computational chemistry application.",

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author = "Isha Aggarwal and Pratik Nayak and Aditya Kashi and Hartwig Anzt",

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Aggarwal, I, Nayak, P, Kashi, A & Anzt, H 2022, Preconditioners for Batched Iterative Linear Solvers on GPUs. in K Doug, G Al, S Pophale, H Liu & S Parete-Koon (eds), Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers. Communications in Computer and Information Science, vol. 1690 CCIS, Springer Science and Business Media Deutschland GmbH, pp. 38-53, Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Virtual, Online, 08/24/22. https://doi.org/10.1007/978-3-031-23606-8_3

Preconditioners for Batched Iterative Linear Solvers on GPUs. / Aggarwal, Isha; Nayak, Pratik; Kashi, Aditya et al.
Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers. ed. / Kothe Doug; Geist Al; Swaroop Pophale; Hong Liu; Suzanne Parete-Koon. Springer Science and Business Media Deutschland GmbH, 2022. p. 38-53 (Communications in Computer and Information Science; Vol. 1690 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Aggarwal I, Nayak P, Kashi A, Anzt H. Preconditioners for Batched Iterative Linear Solvers on GPUs. In Doug K, Al G, Pophale S, Liu H, Parete-Koon S, editors, Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation - 22nd Smoky Mountains Computational Sciences and Engineering Conference, SMC 2022, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2022. p. 38-53. (Communications in Computer and Information Science). doi: 10.1007/978-3-031-23606-8_3