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

Yoann Le Henaff 1, 2, 3 
1 MINGUS - Multi-scale numerical geometric schemes
ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
Abstract : 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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Submitted on : Friday, July 22, 2022 - 10:44:13 AM
Last modification on : Saturday, July 23, 2022 - 3:53:09 AM


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  • HAL Id : hal-03736227, version 1


Yoann Le Henaff. Grid-free Weighted Particle method applied to the Vlasov-Poisson equation. 2022. ⟨hal-03736227⟩



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