Article
MSC:
35K57,
35K65,
53C44,
53C60,
53C80,
65M20,
65N40 | MR 3238852 | Zbl 06362271 | DOI: 10.21136/MB.2014.143867
Full entry |
PDF
(2.2 MB)
Feedback
PDF
(2.2 MB)
Feedback
Keywords:
anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth
anisotropy; mean curvature flow; Finsler metric; fused deposition modeling; epitaxial growth
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.
References:
[1] Bellettini, G., Paolini, M.: Anisotropic motion by mean curvature in the context of Finsler geometry. Hokkaido Math. J. 25 (1996), 537-566. DOI 10.14492/hokmj/1351516749 | MR 1416006 | Zbl 0873.53011
[2] Beneš, M.: Diffuse-interface treatment of the anisotropic mean-curvature flow. Appl. Math. 48 (2003), 437-453. DOI 10.1023/B:APOM.0000024485.24886.b9 | MR 2025297 | Zbl 1099.53044
[3] Deckelnick, K., Dziuk, G.: Discrete anisotropic curvature flow of graphs. M2AN, Math. Model. Numer. Anal. 33 (1999), 1203-1222. DOI 10.1051/m2an:1999141 | MR 1736896 | Zbl 0948.65138
[4] Deckelnick, K., Dziuk, G.: A fully discrete numerical scheme for weighted mean curvature flow. Numer. Math. 91 (2002), 423-452. DOI 10.1007/s002110100322 | MR 1907866 | Zbl 0999.65103
[5] Dziuk, G.: Discrete anisotropic curve shortening flow. SIAM J. Numer. Anal. 36 (1999), 1808-1830. DOI 10.1137/S0036142998337533 | MR 1712165 | Zbl 0942.65112
[6] Hau{ß}er, F., Voigt, A.: A numerical scheme for regularized anisotropic curve shortening flow. Appl. Math. Lett. 19 (2006), 691-698. DOI 10.1016/j.aml.2005.05.011 | MR 2232241 | Zbl 1114.74057
[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
[8] Pozzi, P.: Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: a numerical scheme. Interfaces Free Bound. 10 (2008), 539-576. MR 2465273 | Zbl 1158.65076
[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. DOI 10.1016/j.jcp.2005.09.013 | MR 2208676 | Zbl 1088.74035
[10] Srolovitz, D. J.: On the stability of surfaces of stressed solids. Acta Metallurgica 37 (1989), 621-625. DOI 10.1016/0001-6160(89)90246-0
Search
Partner of
