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Parallel Guaranteed Quality Planar Delaunay Mesh Generation by Concurrent Point Insertion

 

Andrey Chernikov and Nikos Chrisochoides.

 

Published in 14^th Annual Fall Workshop on Computational Geometry, Cambridge, MA, November, 2004

 

Abstract

 

We develop a theoretical framework for constructing parallel guaranteed quality Delaunay planar meshes using commercial o®-the shelf software (COTS). We call two points Delaunay-independent if they can be inserted concurrently without destroying the conformity and Delaunay properties of the mesh. First, we present a sufficient condition of Delaunay-independence. It is based on the distance between points, can be verified very efficiently and used in practice. Second, we show that a simple block mesh decomposition can be utilized in order to guarantee a-priori Delaunay-independence of points in certain regions. Third, we derive an expression which relates three mesh quality and size parameters that allow to conduct the preprocessing step of our approach using a sequential Delaunay refinement algorithm. We conclude with our current work in progress that includes extending the presented approach to generate nonuniform graded meshes.