Complexity analysis and scalability of a matrix-free extrapolated geometric multigrid solver for curvilinear coordinates representations from fusion plasma applications

Leleux P, Schwarz C, Kühn MJ, Kruse C, Rüde U (2025)

Publication Language: English

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Parallel and Distributed Computing Elsevier

Book Volume: 205

Article Number: 105143

DOI: 10.1016/j.jpdc.2025.105143

Abstract

Tokamak fusion reactors are promising alternatives for future energy production. Gyrokinetic simulations are important tools to understand physical processes inside tokamaks and to improve the design of future plants. In gyrokinetic codes such as Gysela, these simulations involve at each time step the solution of a gyrokinetic Poisson equation defined on disk-like cross sections. The authors of [14,15] proposed to discretize a simplified differential equation using symmetric finite differences derived from the resulting energy functional and to use an implicitly extrapolated geometric multigrid scheme tailored to problems in curvilinear coordinates. In this article, we extend the discretization to a more realistic partial differential equation and demonstrate the optimal linear complexity of the proposed solver, in terms of computation and memory. We provide a general framework to analyze floating point operations and memory usage of matrix-free approaches for stencil-based operators. Finally, we give an efficient matrix-free implementation for the considered solver exploiting a task-based multithreaded parallelism which takes advantage of the disk-shaped geometry of the problem. We demonstrate the parallel efficiency for the solution of problems of size up to 50 million unknowns.

Authors with CRIS profile

Ulrich Rüde Technische Fakultät

Involved external institutions

Laboratory for Analysis and Architecture of Systems (LAAS) / Laboratoire d'Analyse et d'Architecture des Systèmes FR France (FR) Universität Bayreuth DE Germany (DE) Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) / German Aerospace Center DE Germany (DE) Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR)

How to cite

APA:

Leleux, P., Schwarz, C., Kühn, M.J., Kruse, C., & Rüde, U. (2025). Complexity analysis and scalability of a matrix-free extrapolated geometric multigrid solver for curvilinear coordinates representations from fusion plasma applications. Journal of Parallel and Distributed Computing, 205. https://doi.org/10.1016/j.jpdc.2025.105143

MLA:

Leleux, Philippe, et al. "Complexity analysis and scalability of a matrix-free extrapolated geometric multigrid solver for curvilinear coordinates representations from fusion plasma applications." Journal of Parallel and Distributed Computing 205 (2025).

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