快速振荡磁场下带电粒子动力学的一致高阶精度格式
Uniformly higher order accurate schemes for dynamics of charged particles under fast oscillating magnetic fields
AI总结：
本文针对快速振荡磁场下等离子体Vlasov模型，提出并分析了一致高阶精度时间积分器，其精度不依赖小参数，并构建了退化为能量保持格式的扩展，数值实验验证了方法有效性。
摘要：
本文研究在Vlasov模型中，由快速振荡磁场效应（参见\\(\cite{Bostan2012}\\)）约束的等离子体的数值逼近问题。该磁场的存在使得特征方程的解在时间上产生振荡。由于其多尺度特性，标准的时间离散化将导致求解器效率低下。本文针对一类高度振荡的微分系统，推导并分析了时间积分器。我们证明了这些时间积分器的一致精度性质，即精度不依赖于小参数\\(\varepsilon\\)。此外，我们构建了该格式的一种扩展，当\\(\varepsilon\to 0\\)时，它退化为平均模型的能量保持数值格式。多个数值结果展示了该方法的性能。
英文摘要：
This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in time) to the solution of the characteristic equations. Due to its multiscale character, a standard time discretization would lead to an inefficient solver. In this work, time integrators are derived and analyzed for a class of highly oscillatory differential systems. We prove the uniform accuracy property of these time integrators, meaning that the accuracy does not depend on the small parameter $\varepsilon$. Moreover, we construct an extension of the scheme which degenerates towards an energy preserving numerical scheme for the averaged model, when $\varepsilon\to 0$. Several numerical results illustrate the capabilities of the method.
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