A physics-based adaptive low-rank method for 6D Vlasov simulations
Abstract
The numerical simulation of kinetic plasma models in six-dimensional phase space poses significant computational and memory challenges, particularly when considering modern high-performance computing architectures. In this work, we propose an adaptive dynamical low-rank approach for the efficient solution of the 6D Vlasov--Poisson system. Our strategy is an extension of the projector-splitting dynamical low-rank integrator. The algorithm changes the rank based on physical observables (e.g., the electric field and energy) as opposed to controlling the error in the distribution function. Our approach is memory efficient in the sense that only rank r objects are required to implement the scheme. This makes the algorithm suitable for performing high-dimensional computations on graphic processing units. Comparisons with rank adaptive Basis-Update & Galerkin integrators exhibit both significant memory savings and reduction in run time. We show, by presenting a variety of 6D benchmark experiments implemented in the C++/CUDA low-rank framework Ensign, that our technique allows us to run simulations with a significantly smaller rank, while still preserving the physical fidelity. Thus, the approach substantially reduces memory footprint and computational cost and enables simulations that are prohibitively expensive for full-rank or less memory-efficient low-rank schemes.
Related
- A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries
- Rank-Adaptive and Linearly Convergent Frank--Wolfe Method over Spectrahedron via Nonconvex Oracle
- Structure-Preserving Dynamical Low-Rank Approximations for Stochastic Vlasov--Poisson Equations
- A second-order structure- and positivity-preserving convex limiting method for the Vlasov equations
- A Structure-Preserving Semi-Lagrangian based bi-fidelity method for the Vlasov--Poisson system with uncertainties
BibTeX
@misc{cassini2026physicsbased,
title = {{A physics-based adaptive low-rank method for 6D Vlasov simulations}},
author = {Fabio Cassini and Lukas Einkemmer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07107},
eprint = {2611.07107},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07107},
}
RIS
TY - UNPB
TI - A physics-based adaptive low-rank method for 6D Vlasov simulations
AU - Fabio Cassini
AU - Lukas Einkemmer
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07107
UR - https://arxiv.org/abs/2611.07107
AB - The numerical simulation of kinetic plasma models in six-dimensional phase space poses significant computational and memory challenges, particularly when considering modern high-performance computing architectures. In this work, we propose an adaptive dynamical low-rank approach for the efficient solution of the 6D Vlasov--Poisson system. Our strategy is an extension of the projector-splitting dynamical low-rank integrator. The algorithm changes the rank based on physical observables (e.g., the electric field and energy) as opposed to controlling the error in the distribution function. Our approach is memory efficient in the sense that only rank r objects are required to implement the scheme. This makes the algorithm suitable for performing high-dimensional computations on graphic processing units. Comparisons with rank adaptive Basis-Update & Galerkin integrators exhibit both significant memory savings and reduction in run time. We show, by presenting a variety of 6D benchmark experiments implemented in the C++/CUDA low-rank framework Ensign, that our technique allows us to run simulations with a significantly smaller rank, while still preserving the physical fidelity. Thus, the approach substantially reduces memory footprint and computational cost and enables simulations that are prohibitively expensive for full-rank or less memory-efficient low-rank schemes.
ER -