ISSN:
1572-9265
Keywords:
drift-diffusion equations
;
Gummel-like procedure
;
nonlinear Poisson equation
;
finite elements
;
local scaling
;
iterative methods
;
quasi-Newton algorithm
;
65P05
;
35Q60
;
78A55
;
65H10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019165614860
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