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SOLUTION OF THE COUPLED POISSON–SCHRÖDINGER EQUATIONS USING THE MULTIGRID METHOD
Author(s) -
Cole Eric A. B.,
Snowden Christopher M.,
BOETTCHER TOBIAS
Publication year - 1997
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(199703)10:2<121::aid-jnm271>3.0.co;2-#
Subject(s) - multigrid method , poisson distribution , mathematics , poisson's equation , schrödinger's cat , discrete poisson equation , mathematical analysis , mathematical physics , physics , partial differential equation , laplace's equation , statistics
This paper presents a multigrid method for numerically solving the coupled Poisson–Schrödinger equations in one dimension for a multilayered HEMT device structure. It is shown that this method produces a good speed‐up factor over the non‐multigrid approach. This should make it suitable for incorporating into the two‐dimensional HEMT model involving coupled Poisson, Schrödinger, current continuity and energy transport equations, with the Schrödinger equation being solved in slices perpendicular to the layer structure. The time taken to produce a multigrid solution depends on the size of the coarse grid and on the number of grids used. A method of predicting the time taken for any combination of these values is presented. The method is demonstrated for a 4‐layer device. © 1997 by John Wiley & Sons, Ltd.