DDFV schemes for semiconductors energy-transport models

Main Article Content

Giulia Lissoni


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

Article Details

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


[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.