Regular paper
Journal of information and communication convergence engineering 2024; 22(4): 316-321
Published online December 31, 2024
https://doi.org/10.56977/jicce.2024.22.4.316
© Korea Institute of Information and Communication Engineering
Mode Decomposition and Long-Term Solution Prediction for the Vlasov-Poisson Equation
Donghyun Kim 
1*
Correspondence to : Donghyun Kim (E-mail: guru25@kistep.re.kr)
Center for Regional S&T Innovation Policy, Korea Institute of S&T Evaluation and Planning (KISTEP)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Vlasov-Poisson (VP) equation plays an important role in plasma physics. Most numerical methods for the VP equation are based on the finite difference method (FDM) or finite element method (FEM), where the computational costs are high. However, this study focuses on the efficient reconstruction of solutions to the VP equation. We begin by generating short-term solutions to the VP equation using an FDM-type algorithm. Among various versions of FDM schemes, we employ backward semi-Lagrangian-based methods with weighted, essentially non-oscillatory schemes for interpolation. Subsequently, a stable dataset without spurious oscillations is obtained. The spatiotemporal patterns within these snapshot solutions are then analyzed via dynamic mode decomposition (DMD). By projecting solution spaces onto the DMD modes, we efficiently extend the solution to unobserved future time steps. Experimental results indicate that the time cost for the DMD prediction is within one second, showing the efficiency of the proposed algorithm.
Keywords Data-driven, Dynamic mode decomposition, Long-term prediction, Vlasov-Poisson equation
PDF
Standard view
Export citation
Share Article
Regular paper
Journal of information and communication convergence engineering 2024; 22(4): 316-321
Published online December 31, 2024 https://doi.org/10.56977/jicce.2024.22.4.316
Copyright © Korea Institute of Information and Communication Engineering.
Mode Decomposition and Long-Term Solution Prediction for the Vlasov-Poisson Equation
Donghyun Kim 1*
1Center for Regional S&T Innovation Policy, Korea Institute of S&T Evaluation and Planning (KISTEP)
Correspondence to:Donghyun Kim (E-mail: guru25@kistep.re.kr)
Center for Regional S&T Innovation Policy, Korea Institute of S&T Evaluation and Planning (KISTEP)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The Vlasov-Poisson (VP) equation plays an important role in plasma physics. Most numerical methods for the VP equation are based on the finite difference method (FDM) or finite element method (FEM), where the computational costs are high. However, this study focuses on the efficient reconstruction of solutions to the VP equation. We begin by generating short-term solutions to the VP equation using an FDM-type algorithm. Among various versions of FDM schemes, we employ backward semi-Lagrangian-based methods with weighted, essentially non-oscillatory schemes for interpolation. Subsequently, a stable dataset without spurious oscillations is obtained. The spatiotemporal patterns within these snapshot solutions are then analyzed via dynamic mode decomposition (DMD). By projecting solution spaces onto the DMD modes, we efficiently extend the solution to unobserved future time steps. Experimental results indicate that the time cost for the DMD prediction is within one second, showing the efficiency of the proposed algorithm.
Keywords: Data-driven, Dynamic mode decomposition, Long-term prediction, Vlasov-Poisson equation
Article Tools
Stats or Metrics
Share this article on
Related articles in JICCE
-
Differential Authentication Scheme for Electric Charging System through Light Gradient Boosting Machine
Byung-Hyun Lim, Ismatov Akobir, and Ki-Il Kim, Member, KIICE
Journal of information and communication convergence engineering 2024; 22(3): 199-206 https://doi.org/10.56977/jicce.2024.22.3.199
