HOODESolver.jl: A Julia package for highly oscillatory problems

Mocquard, Yves; Navaro, Pierre; Crouseilles, Nicolas

doi:10.21105/joss.03077

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…To discretize the integrals in (34), we use an Adam-Bashforth type method. We consider here first and second order methods but higher order can be considered as in [9], [29]. Denoting by g(t) a function representing Ĥp,l (t) or Mp,l (t) in (34), we replace g(t) by the following approximations g(t) ≈ g(t n ) (first order approximation),…”

Section: Scheme A: Uniform Accuracy With Respect To εmentioning

confidence: 99%

Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime

Crestetto,

Crouseilles,

Prel

2023

Multiscale Model. Simul.

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This work is devoted to the construction of multiscale numerical schemes efficient in the finite Larmor radius approximation of the collisional Vlasov equation. Following the paper of Bostan and Finot (2019), the system involves two different regimes, a highly oscillatory and a dissipative regimes, whose asymptotic limits do not commute. In this work, we consider a Particle-In-Cell discretization of the collisional Vlasov system which enables to deal with the multiscale characteristics equations. Different multiscale time integrators are then constructed and analysed. We prove asymptotic properties of these schemes in the highly oscillatory regime and in the collisional regime. In particular, the asymptotic preserving property towards the modified equilibrium of the averaged collision operator is recovered. Numerical experiments are then shown to illustrate the properties of the numerical schemes.

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Section: Scheme A: Uniform Accuracy With Respect To εmentioning

confidence: 99%