A Reduced-Order Model for the High-Field Vlasov-Poisson-Fokker-Planck System Based on a Micro-Macro Decomposition
Abstract
We develop a projection-based reduced-order model for the high-field Vlasov-Poisson-Fokker-Planck system. Based on a micro-macro decomposition, the proposed Micro-ROM applies proper orthogonal decomposition (POD)-Galerkin reduction only to the microscopic fluctuation while retaining the macroscopic density on the full spatial grid. The field-dependent Maxwellian and collision operator introduce additional computational costs that cannot be eliminated by Galerkin projection alone. To remove the dependence on the velocity-grid resolution during online simulations, we approximate the projected Maxwellian terms using precomputed Chebyshev expansions of functions of the local electric field and exploit a separable discretization of the collision operator to assemble the reduced collision matrix exactly from precomputed blocks. A first-order implicit-explicit scheme is employed to evolve the reduced coefficients and the density. The resulting method conserves discrete mass and formally recovers a discretization of the limiting high-field model as ε→ 0. Its online computational cost per time step is independent of the velocity-grid resolution. Numerical experiments demonstrate the accuracy and efficiency of the proposed method across a range of parameters, including the high-field regime.
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BibTeX
@misc{zhang2026reducedorder,
title = {{A Reduced-Order Model for the High-Field Vlasov-Poisson-Fokker-Planck System Based on a Micro-Macro Decomposition}},
author = {Shiheng Zhang and Jingwei Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25569},
eprint = {2610.25569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25569},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Reduced-Order Model for the High-Field Vlasov-Poisson-Fokker-Planck System Based on a Micro-Macro Decomposition
AU - Shiheng Zhang
AU - Jingwei Hu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25569
UR - https://arxiv.org/abs/2610.25569
AB - We develop a projection-based reduced-order model for the high-field Vlasov-Poisson-Fokker-Planck system. Based on a micro-macro decomposition, the proposed Micro-ROM applies proper orthogonal decomposition (POD)-Galerkin reduction only to the microscopic fluctuation while retaining the macroscopic density on the full spatial grid. The field-dependent Maxwellian and collision operator introduce additional computational costs that cannot be eliminated by Galerkin projection alone. To remove the dependence on the velocity-grid resolution during online simulations, we approximate the projected Maxwellian terms using precomputed Chebyshev expansions of functions of the local electric field and exploit a separable discretization of the collision operator to assemble the reduced collision matrix exactly from precomputed blocks. A first-order implicit-explicit scheme is employed to evolve the reduced coefficients and the density. The resulting method conserves discrete mass and formally recovers a discretization of the limiting high-field model as ε→ 0. Its online computational cost per time step is independent of the velocity-grid resolution. Numerical experiments demonstrate the accuracy and efficiency of the proposed method across a range of parameters, including the high-field regime.
ER -