Triangulation of Spatial Elementary Domains
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
| Published: |
Volgograd State University
2015-10-01
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| Series: | Vestnik Volgogradskogo Gosudarstvennogo Universiteta. Serija 1. Mathematica. Physica |
| Subjects: | |
| Online Access: | http://mp.jvolsu.com/index.php/en/component/attachments/download/457 |
| Summary: | 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. |
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| ISSN: | 2222-8896 2409-1782 |