Grid-free Weighted Particle method applied to the Vlasov-Poisson equation
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.
Domains
Numerical Analysis [math.NA]| Origin | Files produced by the author(s) |
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