High-Order Structure-Preserving SBP Finite Difference Methods for the Vlasov-Maxwell System on Matrix-Free GPUs
Abstract
In this paper, we present a high-order, stable summation-by-parts (SBP) finite difference method for solving the Vlasov-Maxwell system in a 2D2V phase space. Central SBP operators for the advection terms are not stable when the solution becomes non-smooth and fine-scale filamentary structures develop, as is typical in high-dimensional Vlasov-Maxwell simulations. To address this issue, the method is stabilized using high-order upwind SBP operators. High-order explicit Runge-Kutta methods are employed for time integration. We prove that the fully discrete scheme exactly conserves mass and preserves momentum up to truncation error. Furthermore, we present a matrix-free implementation of the method on modern GPU architectures. A range of challenging benchmark problems is solved to demonstrate the accuracy, robustness, and performance of the proposed scheme.
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BibTeX
@misc{dymer2026highorder,
title = {{High-Order Structure-Preserving SBP Finite Difference Methods for the Vlasov-Maxwell System on Matrix-Free GPUs}},
author = {Robin Dymér and Ken Mattsson and Murtazo Nazarov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06452},
eprint = {2609.06452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-Order Structure-Preserving SBP Finite Difference Methods for the Vlasov-Maxwell System on Matrix-Free GPUs
AU - Robin Dymér
AU - Ken Mattsson
AU - Murtazo Nazarov
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06452
UR - https://arxiv.org/abs/2609.06452
AB - In this paper, we present a high-order, stable summation-by-parts (SBP) finite difference method for solving the Vlasov-Maxwell system in a 2D2V phase space. Central SBP operators for the advection terms are not stable when the solution becomes non-smooth and fine-scale filamentary structures develop, as is typical in high-dimensional Vlasov-Maxwell simulations. To address this issue, the method is stabilized using high-order upwind SBP operators. High-order explicit Runge-Kutta methods are employed for time integration. We prove that the fully discrete scheme exactly conserves mass and preserves momentum up to truncation error. Furthermore, we present a matrix-free implementation of the method on modern GPU architectures. A range of challenging benchmark problems is solved to demonstrate the accuracy, robustness, and performance of the proposed scheme.
ER -