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Grid generation and optimization based on centroidal Voronoi tessellations. (English) Zbl 1024.65118
Summary: Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, and optimal allocation of resources.
In this paper, we explore the use of CVTs in grid generation in connection with finite element approximations of partial differential equations. We describe these tessellations and methods for their determination. We then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations.

##### MSC:
 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Qhull; Voronoi
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