93 citations · 468 across the 32 of their papers we have counts for
3 papers · 1 filter
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…
Nonlinear Geometric Optics method based multi-scale numerical schemes for highly-oscillatory transport equations
Nicolas Crouseilles, Shi Jin, Mohammed Lemou
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high f…
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…