Geodesic
On an algorithm for finding the electric potential distribution in the DG-MOSFET transistor
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 979-1003

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An efficient numerical algorithm for finding the electric potential distribution in the DG-MOSFET transistor is proposed and discussed in detail. The class of hydrodynamic models describing the charge transport in semiconductors includes the Poisson equation for the electric potential. Since the equations of hydrodynamic models are nonlinear and involve small parameters and specific conditions on the boundary of the DG-MOSFET transistor domain, the numerical solution of the Poisson equation meets significant difficulties. An original algorithm is proposed that is based on the stabilization method and the idea of schemes without saturation and helps to cope with these difficulties. 
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     author = {A. M. Blokhin and B. V. Semisalov},
     title = {On an algorithm for finding the electric potential distribution in the {DG-MOSFET} transistor},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {53},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a11/}
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A. M. Blokhin; B. V. Semisalov. On an algorithm for finding the electric potential distribution in the DG-MOSFET transistor. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 979-1003. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a11/