Year: 2019
Author: Tiao Lu, Zhangpeng Sun
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 170–183
Abstract
For the stationary Wigner equation with inflow boundary conditions, the numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution of the stationary Wigner equation is subject to an integral constraint, we prove that the Wigner equation can be written into a form with a bounded operator $\mathcal{B}[V]$, which is equivalent to the operator $\mathcal{A}[V] = Θ[V]/v$ in the original Wigner equation under some conditions. Then the discrete operators discretizing $\mathcal{B}[V]$ are proved to be uniformly bounded with respect to the mesh size. Based on the theoretical findings, a singularity-free numerical method is proposed. Numerical results are provided to show our improved numerical scheme performs much better in numerical convergence than the original scheme based on discretizing $\mathcal{A}[V]$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1711-m2017-0097
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 170–183
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: stationary Wigner equation singularity-free numerical convergence.
Author Details
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