American Institute of Mathematical Sciences

Advanced
March  2009, 2(1): 81-107. doi: 10.3934/krm.2009.2.81

1D numerical simulation of the mep mathematical model in ballistic diode problem

Alexander Blokhin 1, and  Alesya Ibragimova 2,

1. 

Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2. 

Novosibirsk State University, Novosibirsk, 630090, Russian Federation

Received  April 2008 Revised  November 2008 Published  January 2009

Numerical algorithms for finding approximate solutions of the macroscopic balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999), 307--325; V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12(2000), 31--51] are constructed and discussed for a typical 1D problem.
Keywords: the hydrodynamical models, the stabilization method, moment equations, interpolational cubic spline, Boltzmann Transport Equation, sweep method., the drift-diffusion equations, nonstationary regularization, conservation laws.
Mathematics Subject Classification: Primary: 82D37; Secondary: 65D07, 76M2.
Citation: Alexander Blokhin, Alesya Ibragimova. 1D numerical simulation of the mep mathematical model in ballistic diode problem. Kinetic & Related Models, 2009, 2 (1) : 81-107. doi: 10.3934/krm.2009.2.81
[1]

Takayuki Kubo, Ranmaru Matsui. On pressure stabilization method for nonstationary Navier-Stokes equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2283-2307. doi: 10.3934/cpaa.2018109
[2]

Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic & Related Models, 2010, 3 (1) : 35-58. doi: 10.3934/krm.2010.3.35
[3]

Giacomo Dimarco. The moment guided Monte Carlo method for the Boltzmann equation. Kinetic & Related Models, 2013, 6 (2) : 291-315. doi: 10.3934/krm.2013.6.291
[4]

Dietmar Oelz, Alex Mogilner. A drift-diffusion model for molecular motor transport in anisotropic filament bundles. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4553-4567. doi: 10.3934/dcds.2016.36.4553
[5]

H.J. Hwang, K. Kang, A. Stevens. Drift-diffusion limits of kinetic models for chemotaxis: A generalization. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 319-334. doi: 10.3934/dcdsb.2005.5.319
[6]

Zhiming Chen, Weibing Deng, Huang Ye. A new upscaling method for the solute transport equations. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 941-960. doi: 10.3934/dcds.2005.13.941
[7]

Takayoshi Ogawa, Hiroshi Wakui. Stability and instability of solutions to the drift-diffusion system. Evolution Equations & Control Theory, 2017, 6 (4) : 587-597. doi: 10.3934/eect.2017029
[8]

Gianluca Crippa, Laura V. Spinolo. An overview on some results concerning the transport equation and its applications to conservation laws. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1283-1293. doi: 10.3934/cpaa.2010.9.1283
[9]

C. M. Khalique, G. S. Pai. Conservation laws and invariant solutions for soil water equations. Conference Publications, 2003, 2003 (Special) : 477-481. doi: 10.3934/proc.2003.2003.477
[10]

Martin Burger, José A. Carrillo, Marie-Therese Wolfram. A mixed finite element method for nonlinear diffusion equations. Kinetic & Related Models, 2010, 3 (1) : 59-83. doi: 10.3934/krm.2010.3.59
[11]

Yuchi Qiu, Weitao Chen, Qing Nie. A hybrid method for stiff reaction–diffusion equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6387-6417. doi: 10.3934/dcdsb.2019144
[12]

Raphael Kruse, Yue Wu. A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3475-3502. doi: 10.3934/dcdsb.2018253
[13]

Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007
[14]

T. Ogawa. The degenerate drift-diffusion system with the Sobolev critical exponent. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 875-886. doi: 10.3934/dcdss.2011.4.875
[15]

Ronald E. Mickens. A nonstandard finite difference scheme for the drift-diffusion system. Conference Publications, 2009, 2009 (Special) : 558-563. doi: 10.3934/proc.2009.2009.558
[16]

Claire Chainais-Hillairet, Ingrid Lacroix-Violet. On the existence of solutions for a drift-diffusion system arising in corrosion modeling. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 77-92. doi: 10.3934/dcdsb.2015.20.77
[17]

T. Hillen. On the $L^2$-moment closure of transport equations: The general case. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 299-318. doi: 10.3934/dcdsb.2005.5.299
[18]

T. Hillen. On the $L^2$-moment closure of transport equations: The Cattaneo approximation. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 961-982. doi: 10.3934/dcdsb.2004.4.961
[19]

Stefan Possanner, Claudia Negulescu. Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport. Kinetic & Related Models, 2011, 4 (4) : 1159-1191. doi: 10.3934/krm.2011.4.1159
[20]

Valérie Dos Santos, Bernhard Maschke, Yann Le Gorrec. A Hamiltonian perspective to the stabilization of systems of two conservation laws. Networks & Heterogeneous Media, 2009, 4 (2) : 249-266. doi: 10.3934/nhm.2009.4.249

2018 Impact Factor: 1.38

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences