71 citations · 176 across the 14 of their papers we have counts for
5 papers · 1 filter
Averaging of nonlinear Schrödinger equations with strong magnetic confinement
Rupert L. Frank, Florian Méhats, Christof Sparber
We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement,…
Averaging of highly-oscillatory transport equations
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent…
Uniformly accurate time-splitting methods for the semiclassical Schrödinger equation Part 1 : Construction of the schemes and simulations
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of new numerical methods for the semiclassical Schrödinger equation. A phase-amplitude reformulation of the equation is described where…
Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
Mohammed Lemou, Florian Méhats, Xiaofei Zhao
We apply the two-scale formulation approach to propose uniformly accurate (UA) schemes for solving the nonlinear Dirac equation in the nonrelativistic limit regime. The nonlinear D…
Uniformly accurate time-splitting methods for the semiclassical linear Schr{ö}dinger equation
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{ö}dinger equation in t…