Forced anisotropic mean curvature flow of graphs in relative geometry

Dieu Hung Hoang; Michal Beneš

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 2, page 429-436
  • ISSN: 0862-7959

Abstract

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The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.

How to cite

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Hoang, Dieu Hung, and Beneš, Michal. "Forced anisotropic mean curvature flow of graphs in relative geometry." Mathematica Bohemica 139.2 (2014): 429-436. <http://eudml.org/doc/261940>.

@article{Hoang2014,
abstract = {The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.},
author = {Hoang, Dieu Hung, Beneš, Michal},
journal = {Mathematica Bohemica},
keywords = {anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth; anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth},
language = {eng},
number = {2},
pages = {429-436},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Forced anisotropic mean curvature flow of graphs in relative geometry},
url = {http://eudml.org/doc/261940},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Hoang, Dieu Hung
AU - Beneš, Michal
TI - Forced anisotropic mean curvature flow of graphs in relative geometry
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 429
EP - 436
AB - The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.
LA - eng
KW - anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth; anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth
UR - http://eudml.org/doc/261940
ER -

References

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  2. Beneš, M., 10.1023/B:APOM.0000024485.24886.b9, Appl. Math. 48 (2003), 437-453. (2003) Zbl1099.53044MR2025297DOI10.1023/B:APOM.0000024485.24886.b9
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  4. Deckelnick, K., Dziuk, G., 10.1007/s002110100322, Numer. Math. 91 (2002), 423-452. (2002) Zbl0999.65103MR1907866DOI10.1007/s002110100322
  5. Dziuk, G., 10.1137/S0036142998337533, SIAM J. Numer. Anal. 36 (1999), 1808-1830. (1999) Zbl0942.65112MR1712165DOI10.1137/S0036142998337533
  6. Hau{ß}er, F., Voigt, A., 10.1016/j.aml.2005.05.011, Appl. Math. Lett. 19 (2006), 691-698. (2006) Zbl1114.74057MR2232241DOI10.1016/j.aml.2005.05.011
  7. Hoang, D. H., Beneš, M., Oberhuber, T., Numerical simulation of anisotropic mean curvature of graphs in relative geometry, Acta Polytechnica Hungarica 10 (2013), 99-115. (2013) MR3238852
  8. Pozzi, P., Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: a numerical scheme, Interfaces Free Bound. 10 (2008), 539-576. (2008) Zbl1158.65076MR2465273
  9. Rätz, A., Ribalta, A., Voigt, A., 10.1016/j.jcp.2005.09.013, J. Comput. Phys. 214 (2006), 187-208. (2006) Zbl1088.74035MR2208676DOI10.1016/j.jcp.2005.09.013
  10. Srolovitz, D. J., 10.1016/0001-6160(89)90246-0, Acta Metallurgica 37 (1989), 621-625. (1989) DOI10.1016/0001-6160(89)90246-0

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