Comparison of Multigrid and Machine Learning-Based Poisson Solvers

Godé H, Kruse C, Angersbach R, Köstler H, Bauerheim M, Rüde U (2025)

Publication Type: Conference contribution

Publication year: 2025

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Science and Business Media Deutschland GmbH

Book Volume: 15581 LNCS

Pages Range: 174-189

Conference Proceedings Title: Lecture Notes in Computer Science

Event location: Ostrava CZ

ISBN: 9783031857027

DOI: 10.1007/978-3-031-85703-4_12

Abstract

We present a comprehensive comparison of the multigrid method and the UNet architecture for solving Poisson’s equation. Those two methods show a lot of similarity and also have the very interesting characteristic that their solving time should scale linearly with the number of mesh nodes. Nevertheless, for Poisson’s equation, an analysis of the number of floating-point operations demonstrates that the multigrid V-Cycle should be faster than the UNet. We have realized a practical comparison of the two methods solving time for different number of mesh nodes on the same computation nodes using GPU.

Authors with CRIS profile

Richard Angersbach Professur für Höchstleistungsrechnen Harald Köstler Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)

Involved external institutions

Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR) Université Fédérale de Toulouse Midi-Pyrénées FR France (FR)

How to cite

APA:

Godé, H., Kruse, C., Angersbach, R., Köstler, H., Bauerheim, M., & Rüde, U. (2025). Comparison of Multigrid and Machine Learning-Based Poisson Solvers. In Roman Wyrzykowski, Jack Dongarra, Ewa Deelman, Konrad Karczewski (Eds.), Lecture Notes in Computer Science (pp. 174-189). Ostrava, CZ: Springer Science and Business Media Deutschland GmbH.

MLA:

Godé, Hadrien, et al. "Comparison of Multigrid and Machine Learning-Based Poisson Solvers." Proceedings of the 15th International Conference on Parallel Processing and Applied Mathematics, PPAM 2024, Ostrava Ed. Roman Wyrzykowski, Jack Dongarra, Ewa Deelman, Konrad Karczewski, Springer Science and Business Media Deutschland GmbH, 2025. 174-189.

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