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A micro-macro method for a kinetic graphene model in one-space dimension
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.
Cited literature [22 references]
https://hal.inria.fr/hal-01883237
Contributor : Nicolas Crouseilles <>
Submitted on : Thursday, September 27, 2018 - 8:28:03 PM
Last modification on : Wednesday, January 27, 2021 - 4:06:30 PM
Long-term archiving on: : Friday, December 28, 2018 - 3:08:25 PM
Contributor : Nicolas Crouseilles <>
Submitted on : Thursday, September 27, 2018 - 8:28:03 PM
Last modification on : Wednesday, January 27, 2021 - 4:06:30 PM
Long-term archiving on: : Friday, December 28, 2018 - 3:08:25 PM
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graphene_vfinal.pdf
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