Abstract
The paper presents a brief survey of the available methods of automatic triangulation of two-dimensional regions. A technique proposed for nonhomogeneous regions of complex structure ensures compact representation of the input data and generates nearly uniform triangular meshes. This technique is applied to an example.
Similar content being viewed by others
Literature cited
Yu. N. Babich and A. S. Tsybenko, Methods and Algorithms for Automatic Generation of a Mesh of Triangular Elements [in Russian], Inst. Probl. Prochnosti Akad. Nauk UkrSSR, Kiev (1978).
K. Bate and E. Wilson, Numerical Methods of Analysis and Finite-Element Method [Russian translation], Stroiizdat, Moscow (1982).
V. G. Borovik, “An indexing algorithm for nodal unknowns in the finite-element method,” Probl. Prochnosti, No. 2, 81–82 (1980).
Bule and Bush, “A survey of finite-element mesh generation methods,” Trans. AAME,95, Ser. C, No. 1 (1973).
P. P. Voroshko, A. L. Kvitka, and O. N. Petrenko, “A program for triangulation of a plane region using given vertex coordinates,” in: Algorithms and Programs for the Analysis of the Stress-Strain State and Strength Calculations of Construction Elements [in Russian], Naukova Dumka, Kiev (1978), pp. 37–47.
P. P. Voroshko, A. L. Kvitka, and S. É. Umanskii, “On automating data specification in the finite-element method,” Probl. Prochnosti, No. 3, 42–46 (1975).
P. P. Voroshko and O. N. Petrenko, “Semiautomatic triangulation of a plane region using given nodes,” in: Algorithms and Programs for Strength Calculations and Analysis of the Stress-Strain State of Construction Elements [in Russian], Naukova Dumka, Kiev (1979), pp. 123–132.
Ch. Dzhanybekov, Mathematical Modeling of Groundwater Motion in Stratified Media [in Russian], Ilim, Fruzne (1982).
A. Yu. Eremin and N. Ya. Mar'yashkin, FEMS Program Package for Solving Elliptic Boundary-Value Problems by the Finite-Element Method [in Russian], VTs AN SSSR, Moscow (1981).
L. A. Zaslotskaya and S. É. Umanskii, “A program package for calculating the three-dimensional thermal stress state of turbine blades,” Probl. Prochnosti, No. 3, 34–39 (1983).
Kh. A. Kamel' and G. K. Éizenshtein, “Automatic mesh generation in two- and three-dimensional composite regions,” in: Calculation of Elastic Structures by Computer [in Russian], Vol. 2, Sudostroenie, Leningrad (1974), pp. 21–35.
A. L. Kvitka, P. P. Voroshko, S. D. Bobrovitskaya, and V. I. Kravchenko, “Application of the finite-element method to analyze the thermal stress state of pistons in internal combustion engines,” Probl. Prochnosti, No. 8, 21–25 (1976).
A. L. Kvtika, P. P. Voroshko, and L. A. Zaslotskaya, “Calculating turbine blades by the finite-element method,” Probl. Prochnosti, No. 6, 60–64 (1976).
S. V. Kobel'skii and V. I. Kravchenko, “Description of FEM programs for solving plane and axisymmetric problems of thermoelasticity on the ES-1020 computer,” in: Algorithms and Programs for the Analysis of the Stress-Strain State and Strength Calculations of Construction Elements [in Russian], Naukova Dumka, Kiev (1978), pp. 8–37.
S. V. Kobel'skii and V. I. Kravchenko, “Fragmentation program for stress state improvement in local zones of a plane region,” in: Algorithms and Programs for Strength Calculations and Analysis of the Stress-Strain State of Construction Elements [in Russian], Naukova Dumka, Kiev (1979), pp. 14–29.
W. Crawly, “FLAG — a free-Lagrangian method for simulation of two-dimensional hydrodynamic flows,” in: Numerical Methods in Fluid Mechanics [Russian translation], Mir, Moscow (1973), pp. 135–145.
I. I. Lyashko and L. I. Yushchuk, “A system for processing of geometrical information for boundary-value problems,” Programmirovanie, No. 1, 76–81 (1984).
V. M. Mitkevich and V. I. Okorokov, “Automatic preparation of input data for solving two-dimensional problems with the use of triangular elements,” Probl. Mashinostr., No. 2, 16–21 (1976).
A. I. Sakovich and I. A. Kholmyanskii, “Minimizing the band width for the system of equations in the finite-element method,” Probl. Prochnosti, No. 1, 120–122 (1981).
Yu. M. Temis and M. V. Sobornov, “Computer-aided design of rotor parts with calculation of the stress-strain state by the finite-element method,” Probl. Prochnosti, No. 8, 26–30 (1982).
S. É. Umanskii, “An algorithm and a program for triangulation of a two-dimensional region of an arbitrary shape,” Probl. Prochnosti, No. 6, 83–87 (1978).
S. É. Umanskii, Optimization of Approximate Methods of Solution of Boundary-Value Problems of Mechanics [in Russian], Naukova Dumka, Kiev (1983).
S. É. Umanskii and I. A. Duvidzon, “Automatic subdivision of an arbitrary two-dimensional region into finite elements,” Probl. Prochnosti, No. 6, 89–92 (1977).
S. É. Umanskii and I. A. Duvidzon, “Triangulation algorithms for two-dimensional regions of arbitrary shape,” in: Algorithms and Programs for Strength Calculations and Analysis of the Stress-Strain State of Construction Elements [in Russian], Naukova Dumka, Kiev (1981), pp. 104–110.
A. S. Tsybenko, N. G. Vashchenko, and N. G. Krishchuk, “Efficient computer implementation of the finite-element method in application to plane problems of elasticity theory for bodies of piecewise-variable thickness,” Probl. Prochnosti, No. 6, 110–115 (1980).
O. C. Zienkiewicz and D. V. Phillips, “An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates,” Int. J. Numer. Methods in Engineering,3, No. 4, 519–528 (1971).
Author information
Authors and Affiliations
Additional information
Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 74–83, 1987.
Rights and permissions
About this article
Cite this article
Yushchuk, L.I. Automatic triangulation of plane regions of complex logical structure for solution of boundary-value problems by the finite-element method. J Math Sci 63, 465–470 (1993). https://doi.org/10.1007/BF01849532
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01849532