Uncertainty quantification for the homogeneous Landau-Fokker-Planck equation via deterministic particle Galerkin methods

Journal article

We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a stochastic Galerkin (sG) representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy dissipation. We provide a regularity result for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.

Authors: Bailo, R; Carrillo, JA; Medaglia, A; Zanella, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
• Volume: 23
• Issue: 2
• Pages: 687-710
• Publication date: 2025-04-02
• Acceptance date: 2024-11-27
• DOI: 10.1137/23m1623653
• EISSN: 1540-3467
• ISSN: 1540-3459
• Language: English
• Keywords: plasma physics; Landau–Fokker–Planck equation; deterministic particle methods; uncertainty quantification; stochastic Galerkin methods