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An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Numerical Simulation of Anisotropic Surface Diffusion of Graphs

Authors : D. H. Hoang, M. Beneš

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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Abstract

The aim of this contribution is the numerical simulation of anisotropic surface diffusion of graphs in the context of the epitaxial growth of quantum dots. The numerical scheme is based on the method of lines where the spatial derivatives are approximated by finite differences (Beneš, Appl Math, 48:437–453, 2003). We then solve the resulting ODE system by means of the adaptive Runge-Kutta-Merson method. Finally, we show computational results with various anisotropy settings leading to singular behaviour.

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previous chapter A Numerical Remark on the Time Discretization of Contact Problems in Nonlinear Elasticity
next chapter A Special Multiwavelet Basis for Unbounded Product Domains
Literature
1.
G. Bellettini and M. Paolini, Anisotropic motion by mean curvature in the context of finsler geometry, Hokkaido Mathematical Journal, 25 (1996), pp. 537–566.
2.
M. Beneš, Diffuse-interface treatment of the anisotropic mean-curvature flow, Applications of Mathematics, 48 (2003), pp. 437–453.
3.
_______, Numerical solution for surface diffusion on graphs, in Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, M. Beneš, M. Kimura, and T. Nakaki, eds., vol. 3 of COE Lecture Note, 2005, pp. 9–25.
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D. Bimberg, M. Grundmann, and N. Ledentsov, Quantum dot heterostructures, John Wiley, 1999.
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W. T. Tekalign and B. J. Spencer, Evolution equation for a thin epitaxial film on a deformable substrate, Journal of Applied Physics, 96 (2004), pp. 5505–5512.
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Metadata
Title
Numerical Simulation of Anisotropic Surface Diffusion of Graphs
Authors
D. H. Hoang
M. Beneš
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_19

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