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Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods (2312.07218v1)

Published 12 Dec 2023 in math.NA, cs.NA, math.AP, physics.comp-ph, and physics.plasm-ph

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 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.

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