Volume 5, Issue 2
Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

Jia Deng

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 278-296.

Published online: 2012-05

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  • Abstract

As is known, the numerical stiffness arising from the small mean free path is one of the main  difficulties in the kinetic equations. In this paper, we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling. In the two schemes, the anisotropic collision operator is realized by the ``BGK"-penalty method, which is proposed by Filbet and Jin [F. Filbet and S. Jin, J. Comp. Phys. 229(20), 7625-7648, 2010] for the kinetic equations and the related problems having stiff sources. According to the numerical results, both of the schemes are shown to be uniformly convergent and asymptotic-preserving. Besides, numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.

  • Keywords

linear semiconductor Boltzmann equation drift-diffusion limit diffusive relaxation system ``BGK"-penalty method

  • AMS Subject Headings

35Q20 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-278, author = {Jia Deng}, title = {Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {2}, pages = {278--296}, abstract = {

As is known, the numerical stiffness arising from the small mean free path is one of the main  difficulties in the kinetic equations. In this paper, we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling. In the two schemes, the anisotropic collision operator is realized by the ``BGK"-penalty method, which is proposed by Filbet and Jin [F. Filbet and S. Jin, J. Comp. Phys. 229(20), 7625-7648, 2010] for the kinetic equations and the related problems having stiff sources. According to the numerical results, both of the schemes are shown to be uniformly convergent and asymptotic-preserving. Besides, numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m1045}, url = {http://global-sci.org/intro/article_detail/nmtma/5939.html} }
TY - JOUR T1 - Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime AU - Jia Deng JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 278 EP - 296 PY - 2012 DA - 2012/05 SN - 5 DO - http://dor.org/10.4208/nmtma.2012.m1045 UR - https://global-sci.org/intro/article_detail/nmtma/5939.html KW - linear semiconductor Boltzmann equation KW - drift-diffusion limit KW - diffusive relaxation system KW - ``BGK"-penalty method AB -

As is known, the numerical stiffness arising from the small mean free path is one of the main  difficulties in the kinetic equations. In this paper, we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling. In the two schemes, the anisotropic collision operator is realized by the ``BGK"-penalty method, which is proposed by Filbet and Jin [F. Filbet and S. Jin, J. Comp. Phys. 229(20), 7625-7648, 2010] for the kinetic equations and the related problems having stiff sources. According to the numerical results, both of the schemes are shown to be uniformly convergent and asymptotic-preserving. Besides, numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.

Jia Deng. (1970). Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime. Numerical Mathematics: Theory, Methods and Applications. 5 (2). 278-296. doi:10.4208/nmtma.2012.m1045
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