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Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport

Published online by Cambridge University Press:  20 August 2015

Sihong Shao ,
Tiao Lu  and
Wei Cai
Sihong Shao*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Tiao Lu*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Wei Cai*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
*
Email:shaosihong@gmail.com
Email:tlu@math.pku.edu.cn
Corresponding author.Email:wcai@uncc.edu
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Abstract

A new adaptive cell average spectral element method (SEM) is proposed to solve the time-dependent Wigner equation for transport in quantum devices. The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for the numerical solutions. The key feature of the proposed method is an analytical relation between the cell averages of the Wigner function in the k-space (local electron density for finite range velocity) and the point values of the distribution, resulting in fast transforms between the local electron density and local fluxes of the discretized Wigner equation via the fast sine and cosine transforms. Numerical results with the proposed method are provided to demonstrate its high accuracy, conservation, convergence and a reduction of the cost using adaptive meshes.

Keywords

65M7065M5042B2045K0581Q05Wigner equationquantum transportspectral element methodsadaptive mesh
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 711 - 739
Copyright
Copyright © Global Science Press Limited 2011

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