Volume 9, Issue 3
Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport

Sihong Shao, Tiao Lu & Wei Cai

Commun. Comput. Phys., 9 (2011), pp. 711-739.

Published online: 2011-03

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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.

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@Article{CiCP-9-711, author = {}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.080509.310310s}, url = {http://global-sci.org/intro/article_detail/cicp/7518.html} }
TY - JOUR T1 - Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport JO - Communications in Computational Physics VL - 3 SP - 711 EP - 739 PY - 2011 DA - 2011/03 SN - 9 DO - http://doi.org/10.4208/cicp.080509.310310s UR - https://global-sci.org/intro/article_detail/cicp/7518.html KW - AB -

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.

Sihong Shao, Tiao Lu & Wei Cai. (2020). Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport. Communications in Computational Physics. 9 (3). 711-739. doi:10.4208/cicp.080509.310310s
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