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Research Article
Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady-state conditions
Article first published online: 20 JAN 2005
DOI: 10.1002/jnm.568
Copyright © 2005 John Wiley & Sons, Ltd.
Issue
1099-1204/asset/cover.gif?v=1&s=0f28842dc1cec015c761d199ee080528b22ef746 "International Journal of Numerical Modelling: Electronic Networks, Devices and Fields")
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Volume 18, Issue 2, pages 133–148, March/April 2005
Additional Information
How to Cite
de Cogan, D. and Rak, M. (2005), Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady-state conditions. Int. J. Numer. Model., 18: 133–148. doi: 10.1002/jnm.568
Publication History
- Issue published online: 7 FEB 2005
- Article first published online: 20 JAN 2005
- Manuscript Accepted: 1 NOV 2004
- Manuscript Received: 1 JUN 2004
- Abstract
- References
- Cited By
Keywords:
- crystallography models;
- BCF model;
- TML
Abstract
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.