Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field

Abstract

In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to the stiffness of the problem, in terms of both accuracy and computational cost. The specific difficulty (and the resulting novelty of our approach) stems from the presence of a non-periodic oscillation, which necessitates a careful ad-hoc reformulation of the equations. Our results are illustrated numerically on several examples.

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

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Large-stepsize integrators for charged-particle dynamics over multiple time scales

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Asymptotically Preserving Particle Methods for Strongly Magnetized Plasmas in a Torus

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