A Structure-Preserving Semi-Lagrangian based bi-fidelity method for the Vlasov--Poisson system with uncertainties
Abstract
Uncertainty quantification for the Vlasov--Poisson (VP) systems entails repeated dynamic simulations, incurring immense computational costs. We develop a structure-preserving Semi-Lagrangian (SL) b-fidelity approximation of macroscopic observables. The MUSCL is used as a low-fidelity solver for pressureless Euler--Poisson system, allowing for a more cost-effective exploration of the stochastic parameter space. A conservative SL scheme combined with high-order discontinuous Galerkin is used as a high-fidelity solver for collisionless VP system, whose mass conservation, positivity preservation, and low numerical dissipation provide a more reliable high-fidelity snapshots for bi-fidelity reconstruction. We further derive a conditional error bound that separates projection, discretization, and model errors. Numerical experiments for both deterministic and uncertain VP problems, including multispecies and higher-dimensional settings, demonstrate that the proposed framework achieves accurate and robust uncertainty propagation.
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BibTeX
@misc{cai2026structurepreserving,
title = {{A Structure-Preserving Semi-Lagrangian based bi-fidelity method for the Vlasov--Poisson system with uncertainties}},
author = {Xiaofeng Cai and Jiaojiao Guo and Liu Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23484},
eprint = {2610.23484},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23484},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Structure-Preserving Semi-Lagrangian based bi-fidelity method for the Vlasov--Poisson system with uncertainties
AU - Xiaofeng Cai
AU - Jiaojiao Guo
AU - Liu Liu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23484
UR - https://arxiv.org/abs/2610.23484
AB - Uncertainty quantification for the Vlasov--Poisson (VP) systems entails repeated dynamic simulations, incurring immense computational costs. We develop a structure-preserving Semi-Lagrangian (SL) b-fidelity approximation of macroscopic observables. The MUSCL is used as a low-fidelity solver for pressureless Euler--Poisson system, allowing for a more cost-effective exploration of the stochastic parameter space. A conservative SL scheme combined with high-order discontinuous Galerkin is used as a high-fidelity solver for collisionless VP system, whose mass conservation, positivity preservation, and low numerical dissipation provide a more reliable high-fidelity snapshots for bi-fidelity reconstruction. We further derive a conditional error bound that separates projection, discretization, and model errors. Numerical experiments for both deterministic and uncertain VP problems, including multispecies and higher-dimensional settings, demonstrate that the proposed framework achieves accurate and robust uncertainty propagation.
ER -