The Adaptive Delaunay Tessellation: A neighborhood covering meshing technique

Alexandru Constantiniu; Paul Steinmann; Tom Bobach; Gerald Farin; Georg Umlauf

doi:10.1007/s00466-008-0265-3

The Adaptive Delaunay Tessellation: A neighborhood covering meshing technique

Alexandru Constantiniu, Paul Steinmann, Tom Bobach, Gerald Farin, Georg Umlauf

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper we propose an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. The mesh is automatically obtained in a bounded period of time by transforming an initial Delaunay tessellation. Novel types of polygonal interpolants are used for interpolation applications and the geometric qualities of the elements make them also useful for discretization schemes. The approach proves to be superior to classical Delaunay one in a finite element context.

Original language	English (US)
Pages (from-to)	655-669
Number of pages	15
Journal	Computational Mechanics
Volume	42
Issue number	5
DOIs	https://doi.org/10.1007/s00466-008-0265-3
State	Published - Oct 2008

Keywords

Adaptive Delaunay Tessellation
Generalized barycentric coordinates
Polygonal finite elements
Polygonal interpolation
Scattered data interpolation

ASJC Scopus subject areas

Computational Mechanics
Ocean Engineering
Mechanical Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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keywords = "Adaptive Delaunay Tessellation, Generalized barycentric coordinates, Polygonal finite elements, Polygonal interpolation, Scattered data interpolation",

author = "Alexandru Constantiniu and Paul Steinmann and Tom Bobach and Gerald Farin and Georg Umlauf",

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AU - Steinmann, Paul

AU - Bobach, Tom

AU - Farin, Gerald

AU - Umlauf, Georg

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AB - In this paper we propose an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. The mesh is automatically obtained in a bounded period of time by transforming an initial Delaunay tessellation. Novel types of polygonal interpolants are used for interpolation applications and the geometric qualities of the elements make them also useful for discretization schemes. The approach proves to be superior to classical Delaunay one in a finite element context.

KW - Adaptive Delaunay Tessellation

KW - Generalized barycentric coordinates

KW - Polygonal finite elements

KW - Polygonal interpolation

KW - Scattered data interpolation

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The Adaptive Delaunay Tessellation: A neighborhood covering meshing technique

Abstract

Keywords

ASJC Scopus subject areas

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