The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Jin S, Zhu Y, Zuazua Iriondo E (2022)

Publication Language: English

Publication Type: Journal article

Publication year: 2022

Journal

Numerische Mathematik Springer Verlag (Germany)

DOI: 10.1007/s00211-021-01257-w

Open Access Link: https://doi.org/10.1007/s00211-021-01257-w

Abstract

We consider the Vlasov-Fokker-Planck equation with random electric field where the random field is parametrized by countably many infinite random variables due to uncertainty. At the theoretical level, with suitable assumption on the anisotropy of the randomness, adopting the technique employed in elliptic PDEs [5], we prove the best N approximation in the random space breaks the dimension curse and the convergence rate is faster than the Monte Carlo method. For the numerical method, based on the adaptive sparse polynomial interpolation (ASPI) method introduced in [2], we develop a residual based adaptive sparse polynomial interpolation (RASPI) method which is more efficient for multi-scale linear kinetic equation, when using numerical schemes that are time dependent and implicit. Numerical experiments show that the numerical error of the RASPI decays faster than the Monte-Carlo method and is also dimension independent

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Shanghai Jiao Tong University / 上海交通大学 CN China (CN) University of Wisconsin - Madison US United States (USA) (US)

How to cite

APA:

Jin, S., Zhu, Y., & Zuazua Iriondo, E. (2022). The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term. Numerische Mathematik. https://doi.org/10.1007/s00211-021-01257-w

MLA:

Jin, Shi, Yuhua Zhu, and Enrique Zuazua Iriondo. "The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term." Numerische Mathematik (2022).

BibTeX: Download