2023/12/12 by Rafael Bailo, Bailo, Rafael, José A. Carrillo +5 · 2 citations
Decision Sciences · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Plasma Physics (physics.plasm-ph) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2312.07218
openalex publication_date 2023/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 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 production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.