Klyachin А.А. Construction of a Triangular Grid for Regions Bounded by Closed Simple Curves
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https://doi.org/10.15688/mpcm.jvolsu.2018.3.3
Aleksey Aleksandrovich Klyachin
Doctor of Physical and Mathematical Sciences, Head of Department
of Mathematical Analysis and Function Theory,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. At present, the triangulation method is widely used in many computational problems, for example, using the finite element method (FEM). The use of triangular grids in the solution of various boundary value problems is also due to the fact that derivatives of any order can be easily approximated on them with sufficient accuracy. In this case, the calculation process, as a rule, can be unified and organized so that the dependence on the grid is minimal [5]. Therefore, the claimed task is to develop algorithms for triangulation of areas that do not require much time for implementation and do not spend a large amount of computer resources. In the work [6] we have presented one such algorithm, based on the process of grinding triangulation triangles. In this paper we describe another approach to constructing a triangular grid for arbitrary planar domains and give an estimate of the minimum sine of the angle of triangles under certain geometric conditions.
Key words: triangulation, triangle, the minimum angle of triangulation, splitting area, Lipschitz condition.
Construction of a Triangular Grid for Regions Bounded by Closed Simple Curves by Klyachin А.А. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 3 2018, pp. 31-38
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