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Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady‐state conditions
Author(s) -
de Cogan D.,
Rak M.
Publication year - 2005
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/jnm.568
Subject(s) - mathematics , convergence (economics) , mathematical analysis , poisson's equation , laplace transform , supersaturation , steady state (chemistry) , physics , chemistry , thermodynamics , economics , economic growth
This is an investigative paper which reports the results of comparisons of two numerical techniques for the solution of the Burton Cabrera and Frank (BCF) equation for the growth on crystal surfaces under steady state conditions. A successive over‐relaxation (SOR) scheme for the equivalent finite difference equation gives rapid convergence to the static solution. It is known that a suitable choice of scattering parameters in a transmission line matrix (TLM) network analogue of the Laplace equation yields ultra‐fast convergence. The results of numerical experiments which are reported here suggests that a similar situation also applies to the solution of the Poisson equation with shunt losses (the BCF equation), although the choice of optimum conditions appears to be different for different spatial positions within the solution space. Copyright © 2005 John Wiley & Sons, Ltd.