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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 1, Pages 44–59 (Mi zvmmf4811)  

This article is cited in 30 scientific papers (total in 30 papers)

Boundary conforming Delaunay mesh generation

K. Gärtner, H. Si, J. Fuhrmann

Berlin, Weierstrass Institute for Applied Analysis and Stochastics

Abstract: A boundary conforming Delaunay mesh is a partitioning of a polyhedral domain into Delaunay simplices such that all boundary simplices satisfy the generalized Gabriel property. It's dual is a Voronoi partition of the same domain which is preferable for Voronoi-box based finite volume schemes. For arbitrary 2D polygonal regions, such meshes can be generated in optimal time and size. For arbitrary 3D polyhedral domains, however, this problem remains a challenge. The main contribution of this paper is to show that boundary conforming Delaunay meshes for 3D polyhedral domains can be generated efficiently when the smallest input angle of the domain is bounded by $\arccos1/3\approx 70.53^\circ$. In addition, well-shaped tetrahedra and appropriate mesh size can be obtained. Our new results are achieved by reanalyzing a classical Delaunay refinement algorithm. Note that our theoretical guarantee on the input angle $(70.53^\circ)$ is still too strong for many practical situations. We further discuss variants of the algorithm to relax the input angle restriction and to improve the mesh quality.

Key words: Delaunay mesh, Voronoi partitions, partitions of polyhedra.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:1, 38–53

Bibliographic databases:

UDC: 519.63
Received: 27.11.2008
Revised: 07.07.2009
Language:

Citation: K. Gärtner, H. Si, J. Fuhrmann, “Boundary conforming Delaunay mesh generation”, Zh. Vychisl. Mat. Mat. Fiz., 50:1 (2010), 44–59; Comput. Math. Math. Phys., 50:1 (2010), 38–53

Citation in format AMSBIB
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\by K.~G\"artner, H.~Si, J.~Fuhrmann
\paper Boundary conforming Delaunay mesh generation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 1
\pages 44--59
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2681134}
\elib{https://elibrary.ru/item.asp?id=13044699}
\transl
\jour Comput. Math. Math. Phys.
\yr 2010
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\pages 38--53
\crossref{https://doi.org/10.1134/S0965542510010069}
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    Citing articles on Google Scholar: Russian citations, English citations
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    2. Lelievre P.G., Farquharson C.G., Hurich Ch.A., “Inversion of first-arrival seismic traveltimes without rays, implemented on unstructured grids”, Geophysical Journal International, 185:2 (2011), 749–763  crossref  adsnasa  isi  scopus
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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