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Discrete duality finite volume schemes for two-dimensional drift-diffusion and energy-transport models. (English) Zbl 1154.82034

Summary: The drift-diffusion and the energy-transport models appear in the modelling of semiconductor devices. The main difficulty arising in the approximation of the energy transport model by finite volume schemes is the discretization of the Joule heating term in the equation on the density of energy. Following some recent ideas by Domelevo and Omnès for the discretization of the Laplace equation on almost general meshes, we construct a finite volume approximation of the 2-D drift-diffusion and energy transport models. These schemes still hold on almost general meshes. Finally, we present numerical simulations of semiconductor devices.

MSC:

82D37 Statistical mechanics of semiconductors
82C70 Transport processes in time-dependent statistical mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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References:

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