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Quasi‐variational inequality and shape optimization for solution of a free boundary problem

J. Abouchabaka (LERMA, Ecole Mohammadia d’Ingénieurs, Université Mohamed V, Rabat‐Agdal, Morocco)
R. Aboulaïch (LERMA, Ecole Mohammadia d’Ingénieurs, Université Mohamed V, Rabat‐Agdal, Morocco)
A. Nachaoui (Département de Mathématiques, Université de Nantes CNRS UMR6629, Nantes, France)
A. Souissi (Département de Mathématiques et Informatique, Université Mohamed V, Rabat‐Agdal, Morocco)

Abstract

Electrical potentials in a junction field transistor can be calculated using a simplified model based on a complete depletion assumption. This gives rise to a free boundary problem. We show here how we can approximate this problem with a quasi‐variational inequality technique and the shape optimization method. A detailed analysis of these methods is presented. Using some numerical experiments we compare our results with the solution of the discrete drift‐diffusion system, accomplished with a Gummel‐like algorithm. The numerical results suggest that the methods proposed here work successfully and that the shape optimization technique provides a reasonably free boundary without excessive iterations.

Keywords

Citation

Abouchabaka, J., Aboulaïch, R., Nachaoui, A. and Souissi, A. (1999), "Quasi‐variational inequality and shape optimization for solution of a free boundary problem", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 18 No. 2, pp. 143-164. https://doi.org/10.1108/03321649910264154

Publisher

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MCB UP Ltd

Copyright © 1999, MCB UP Limited

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