Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 1, Pages 44–59 (Mi zvmmf4811)  

This article is cited in 52 scientific papers (total in 52 papers)

Boundary conforming Delaunay mesh generation

K. Gärtner, H. Si, J. Fuhrmann

Berlin, Weierstrass Institute for Applied Analysis and Stochastics
References:
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.
Received: 27.11.2008
Revised: 07.07.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 1, Pages 38–53
DOI: https://doi.org/10.1134/S0965542510010069
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: English
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
\Bibitem{GarSiFuh10}
\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
\mathnet{http://mi.mathnet.ru/zvmmf4811}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2681134}
\elib{https://elibrary.ru/item.asp?id=13044699}
\transl
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 1
\pages 38--53
\crossref{https://doi.org/10.1134/S0965542510010069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-76649143449}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf4811
  • https://www.mathnet.ru/eng/zvmmf/v50/i1/p44
  • This publication is cited in the following 52 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:496
    Full-text PDF :163
    References:51
    First page:5
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024