| Title:
|
Forced anisotropic mean curvature flow of graphs in relative geometry (English) |
| Author:
|
Hoang, Dieu Hung |
| Author:
|
Beneš, Michal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
429-436 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
anisotropy |
| Keyword:
|
mean curvature flow |
| Keyword:
|
Finsler metric |
| Keyword:
|
fused deposition modeling |
| Keyword:
|
epitaxial growth |
| MSC:
|
35K57 |
| MSC:
|
35K65 |
| MSC:
|
53C44 |
| MSC:
|
53C60 |
| MSC:
|
53C80 |
| MSC:
|
65M20 |
| MSC:
|
65N40 |
| idZBL:
|
Zbl 06362271 |
| idMR:
|
MR3238852 |
| DOI:
|
10.21136/MB.2014.143867 |
| . |
| Date available:
|
2014-07-14T08:50:36Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143867 |
| . |
| Reference:
|
[1] Bellettini, G., Paolini, M.: Anisotropic motion by mean curvature in the context of Finsler geometry.Hokkaido Math. J. 25 (1996), 537-566. Zbl 0873.53011, MR 1416006, 10.14492/hokmj/1351516749 |
| Reference:
|
[2] Beneš, M.: Diffuse-interface treatment of the anisotropic mean-curvature flow.Appl. Math. 48 (2003), 437-453. Zbl 1099.53044, MR 2025297, 10.1023/B:APOM.0000024485.24886.b9 |
| Reference:
|
[3] Deckelnick, K., Dziuk, G.: Discrete anisotropic curvature flow of graphs.M2AN, Math. Model. Numer. Anal. 33 (1999), 1203-1222. Zbl 0948.65138, MR 1736896, 10.1051/m2an:1999141 |
| Reference:
|
[4] Deckelnick, K., Dziuk, G.: A fully discrete numerical scheme for weighted mean curvature flow.Numer. Math. 91 (2002), 423-452. Zbl 0999.65103, MR 1907866, 10.1007/s002110100322 |
| Reference:
|
[5] Dziuk, G.: Discrete anisotropic curve shortening flow.SIAM J. Numer. Anal. 36 (1999), 1808-1830. Zbl 0942.65112, MR 1712165, 10.1137/S0036142998337533 |
| Reference:
|
[6] Hau{ß}er, F., Voigt, A.: A numerical scheme for regularized anisotropic curve shortening flow.Appl. Math. Lett. 19 (2006), 691-698. Zbl 1114.74057, MR 2232241, 10.1016/j.aml.2005.05.011 |
| Reference:
|
[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. MR 3238852 |
| Reference:
|
[8] Pozzi, P.: Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: a numerical scheme.Interfaces Free Bound. 10 (2008), 539-576. Zbl 1158.65076, MR 2465273 |
| Reference:
|
[9] Rätz, A., Ribalta, A., Voigt, A.: Surface evolution of elastically stressed films under deposition by a diffuse interface model.J. Comput. Phys. 214 (2006), 187-208. Zbl 1088.74035, MR 2208676, 10.1016/j.jcp.2005.09.013 |
| Reference:
|
[10] Srolovitz, D. J.: On the stability of surfaces of stressed solids.Acta Metallurgica 37 (1989), 621-625. 10.1016/0001-6160(89)90246-0 |
| . |
