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Article Dans Une Revue Numerische Mathematik Année : 2023

Grid-free Weighted Particle method applied to the Vlasov-Poisson equation

Résumé

We study a grid-free particle method based on following the evolution of the characteristics of the Vlasov-Poisson system, and we show that it converges for smooth enough initial data. This method is built as a combination of well-studied building blocks-mainly time integration and integral quadratures-, hence allows to obtain arbitrarily high orders. By making use of the Non-Uniform Fast Fourier Transform (NUFFT), the overall computational complexity is O(P + K^d log K^d), where P is the total number of particles and where we only keep the Fourier modes k ∈ (Z^d)^* such that k_1^2 + • • • + k_d^2 ≤ K^2. Some numerical results are given for the Vlasov-Poisson system in the one-dimensional case.
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Dates et versions

hal-03736227 , version 1 (22-07-2022)

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Yoann Le Henaff. Grid-free Weighted Particle method applied to the Vlasov-Poisson equation. Numerische Mathematik, 2023, 155, pp.289-344. ⟨10.1007/s00211-023-01378-4⟩. ⟨hal-03736227⟩
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