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Article

Medľa, Matej ; Mikula, Karol
Gaussian curvature based tangential redistribution of points on evolving surfaces. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 255-264
MSC: 53C44, 65M08, 65M50
Keywords:
Surface evolution, point redistribution, finite volume method, mean curvature flow
Summary:
There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.
References:
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[2] Húska, M., Medľa, M., Mikula, K., Morigi, S.: Surface quadrangulation. in preparation.
[3] Liu, D., Xu, G.: Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes. In Computer-Aided Design, Volume 39, Issue 6, 2007, pp. 506-517, ISSN 0010-4485, https://doi.org/10.1016/j.cad.2007.01.007 DOI 10.1016/j.cad.2007.01.007
[4] Mikula, K., Remešíková, M., Sarkoci, P., Ševčovič, D.: Manifold evolution with tangential redistribution of points. SIAM J. Scientific Computing, 36, No. 4 (2014), pp. A1384-A1414. DOI 10.1137/130927668 | MR 3226752
[5] Ševčovič, D., Yazaki, S.: Evolution of plane curves with a curvature adjusted tangential velocity. Japan J. Indust. Appl. Math., 28(3) (2011), 413-442. DOI 10.1007/s13160-011-0046-9 | MR 2846183
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