Work

Uncertainty Quantification for the Homogeneous Landau–Fokker–Planck Equation via Deterministic Particle Galerkin Methods

Year: 2025

Type: article

Abstract: . 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.

Source: Multiscale Modeling and Simulation

DOI: 10.1137/23m1623653

Authors: Rafael Bailo, José A. Carrillo, Andrea Medaglia, Mattia Zanella

Institutions: Eindhoven University of Technology, University of Oxford, University of Pavia

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green