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A micro-macro method for a kinetic graphene model in one-space dimension

Nicolas Crouseilles 1, 2, * Shi Jin 3 Mohammed Lemou 4, 2, 5 Florian Méhats 4, 5, 2
* Corresponding author
2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, for the one space dimensional semiclassical kinetic graphene model introduced in [20], we propose a micro-macro decomposition based numerical approach, which reduces the computational dimension of the nonlinear geometric optics method based numerical method for highly oscillatory transport equation developed in [6]. The method solves the highly oscillatory model in the original coordinate, yet can capture numerically the oscillatory space-time quantum solution pointwisely even without numerically resolving the frequency. We prove that the underlying micro-macro equations have smooth (up to certain order of derivatives) solutions with respect to the frequency, and then prove the uniform accuracy of the numerical discretization for a scalar model equation exhibiting the same oscillatory behavior. Numerical experiments verify the theory.
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https://hal.inria.fr/hal-01883237
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Nicolas Crouseilles, Shi Jin, Mohammed Lemou, Florian Méhats. A micro-macro method for a kinetic graphene model in one-space dimension. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2020, 18 (1), pp.444-474. ⟨10.1137/18M1173770⟩. ⟨hal-01883237⟩

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