Klyachin A.A., Bеlеnikina A.Yu. Triangulation of Spatial Elementary Domains
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http://dx.doi.org/10.15688/jvolsu1.2015.4.1
Klyachin Alеksеy Aleksandrovich
Doctor of Physical and Mathematical Sciences, Head of Department of Mathematical
Analysis and Function Theory,
Volgograd State University
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,
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Bеlеnikina Anzhеlika Yuryevna
Student, Institute of Mathematics and Information Technologies,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. We consider a domain Ω ⊂ R3 that has the form
Ω = {(x,y,z): a<x<b, c<y<d, φ(x,y)<z<ψ(x,y)},
where φ(x,y) and ψ(x,y) are given functions in rectangle [a,b] × [c,d] which satisfy Lipschitz condition. Let a = x0<x1<x2<...<xn=b be a partition of the segment [a,b] and c = y0<y1<y2<...<yn=d be a partition of the segment [c,d]. We put
fτ(x,y) = τψ(x,y) + (1-τ)φ(x,y), τ ∈ [0,1].
We divide the segment [0,1] by points 0 = 0 < 1 < 2 <...< k = 1 and consider the grid in the domain Ω defined points
Aijl(xi, yj, zijl) = (xi, yj, fτl (xi, yj)), i = 0,...,n, j = 0,...,m, l = 0,...,k.
In this paper we built a triangulation of the region Ω of nodes Aijl such that a decrease in the fineness of the partition, and under certain conditions, the dihedral angles are separated from zero to some positive constant.
Key words: triangulation, tetrahedron, dihedral angle, elementary domain, partition of domain, Lipschitz condition.
Triangulation of Spatial Elementary Domains by Klyachin A.A., Bеlеnikina A.Yu. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №4 (29) 2015 pp. 6-12
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