Iterative solution of the drift-diffusion equations |
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Authors: | Abdeljalil Nachaoui |
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Affiliation: | (1) Département de Mathématiques, Université de Nantes, CNRS UMR6629, 2, rue de la Houssinière, BP 92208, F-44322 Nantes, France |
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Abstract: | The drift-diffusion model can be described by a nonlinear Poisson equation for the electrostatic potential coupled with a system of convection-reaction-diffusion equations for the transport of charge. We use a Gummel-like process [10] to decouple this system. Each of the obtained equations is discretised with the finite element method. We use a local scaling method to avoid breakdown in the numerical algorithm introduced by the use of Slotboom variables. Solution of the discrete nonlinear Poisson equation is accomplished with quasi-Newton methods. The nonsymmetric discrete transport equations are solved using an incomplete LU factorization preconditioner in conjunction with some robust linear solvers, such as (CGS), (BI-CGSTAB) and (GMRES). We investigate the behaviour of these iterative methods to define the effective strategy for this class of problems. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | drift-diffusion equations Gummel-like procedure nonlinear Poisson equation finite elements local scaling iterative methods quasi-Newton algorithm 65P05 35Q60 78A55 65H10 |
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