DDFV schemes for semiconductors energy-transport models
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Abstract
We propose a Discrete Duality Finite Volume scheme (DDFV for short) for an energy transport model for semiconductors. As in the continuous case, thanks to a change of variables into the so-called "entropic variables", we are able to prove a discrete entropy-dissipation estimate, which gives a priori estimates for the problem. We perform some numerical tests for the 2D ballistic diode, by comparing the Chen model and the Lyumkis model
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How to Cite
Lissoni, G.
(2020).
DDFV schemes for semiconductors energy-transport models.
Proceedings Of The Conference Algoritmy, , 31 - 40.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1550/812
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References
[1] B. Andreianov, F. Boyer, and F. Hubert, Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D-meshes, Num. Meth. for PDEs, 23(1):145-195, 2007.
[2] M. Bessemoulin-Chatard, C. Chainais-Hillairet and H. Mathis, Numerical schemes for semiconductors energy-transport models, to appear in FVCA IX, Springer Proceedings in Mathematics and Statistics.
[3] C. Chainais-Hillairet, Discrete duality finite volume schemes for two dimensional drift-diffusion and energy-transport models, International Journal for Numerical Methods in Fluids 59(3):239 - 257, 2009.
[4] C. Chainais-Hillairet and Y. -J. Peng, Finite Volume Scheme for Semiconductor Energy-transport Model, pages 139-146. Birkäuser Basel, Basel, 2005.
[5] P. Degond, S. Génieys and A. Jungel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl., 1997.
[6] P. Degond, A. Jungel and P. Pietra, Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure, SIAM Journal on Scientific Computing, 2000.
[7] K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN Math. Model. Numer. Anal., 39(6):1203-1249, 2005.
[8] M. Fournié, Numerical discretization of energy-transport model for semiconductors using high-order compact schemes, Appl. Math. Lett., 15(6):721-726, 2002.
[9] F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., 160(2):481-499, 2000.
[10] S. Holst, A. Jungel and P. Pietra, A mixed Finite-Element Discretization of the Energy- Transport model for semiconductors, SIAM Journal on Scientific Computing, 2003.
[11] A. Jungel, Quasi-hydrodynamic semiconductor equations Birkhäuser, 2001.
[12] A. Jungel, Transport equations for semiconductors, Lecture Notes in Physics, 773, 2009.
[13] S. Krell, Schémas Volumes Finis en mécanique des fluides complexes, PhD thesis, Univ. de Provence, 2010.
[2] M. Bessemoulin-Chatard, C. Chainais-Hillairet and H. Mathis, Numerical schemes for semiconductors energy-transport models, to appear in FVCA IX, Springer Proceedings in Mathematics and Statistics.
[3] C. Chainais-Hillairet, Discrete duality finite volume schemes for two dimensional drift-diffusion and energy-transport models, International Journal for Numerical Methods in Fluids 59(3):239 - 257, 2009.
[4] C. Chainais-Hillairet and Y. -J. Peng, Finite Volume Scheme for Semiconductor Energy-transport Model, pages 139-146. Birkäuser Basel, Basel, 2005.
[5] P. Degond, S. Génieys and A. Jungel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl., 1997.
[6] P. Degond, A. Jungel and P. Pietra, Numerical discretization of energy-transport models for semiconductors with non-parabolic band structure, SIAM Journal on Scientific Computing, 2000.
[7] K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN Math. Model. Numer. Anal., 39(6):1203-1249, 2005.
[8] M. Fournié, Numerical discretization of energy-transport model for semiconductors using high-order compact schemes, Appl. Math. Lett., 15(6):721-726, 2002.
[9] F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., 160(2):481-499, 2000.
[10] S. Holst, A. Jungel and P. Pietra, A mixed Finite-Element Discretization of the Energy- Transport model for semiconductors, SIAM Journal on Scientific Computing, 2003.
[11] A. Jungel, Quasi-hydrodynamic semiconductor equations Birkhäuser, 2001.
[12] A. Jungel, Transport equations for semiconductors, Lecture Notes in Physics, 773, 2009.
[13] S. Krell, Schémas Volumes Finis en mécanique des fluides complexes, PhD thesis, Univ. de Provence, 2010.