Co-Author(s): N. Crouseilles, S. Jin, M. Lemou, F. Mehats
Abstract:
We propose a numerical method that combines micro-macro decomposition techniques with nonlinear geometric optics based methods to solve a highly oscillatory kinetic graphene model. The method solves the highly oscillatory model in the original coordinates, 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. We finally present some numerical experiments to illustrate the theory.