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Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady-state conditions. (English) Zbl 1059.82041

Summary: This is an investigative paper which reports the results of comparisons of two numerical techniques for the solution of the Burton-Cabrera-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.

MSC:

82D25 Statistical mechanics of crystals
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References:

[1] Handbook of Crystal Growth, vol. 1a. (ed.). North-Holland: Amsterdam, 1993; 307.
[2] Burton, Philosophical Transactions of Royal Society A 243 pp 299– (1951)
[3] Crystal Growth: an Introduction, (ed.). North-Holland: Amsterdam, 1971; 263.
[4] Rak, Journal of Crystal Growth 197 pp 944– (1999)
[5] Transmission Line Matrix (TLM) Techniques for Diffusion Applications. Gordon and Breach: Reading, U.K., 1998; 167-175.
[6] Numerical Analysis?a Second Course. Academic Press: New York, 1978.
[7] Solid State Devices; A Quantum Physics Approach. Macmillans: London, 1988; 88-90.
[8] Haynes, Physical Reviews 81 pp 835– (1951)
[9] de Cogan, International Journal of Mathematical Algorithms 1 pp 153– (1999)
[10] Solid State Devices; A Quantum Physics Approach. Macmillans: London, 1988; 88-90.
[11] Saleh, International Journal of Numerical Modelling 5 pp 219– (1992)
[12] Transmission Line Matrix (TLM) Techniques for Diffusion Applications. Gordon and Breach: Reading, U.K., 1998; 154-155.
[13] de Cogan, Microelectronics Journal 30 pp 1093– (1999)
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