@Article{CiCP-9-711,
author = {Sihong Shao, Tiao Lu and Wei Cai},
title = {Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {3},
pages = {711--739},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.080509.310310s},
url = {http://global-sci.org/intro/article_detail/cicp/7518.html}
}