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Initial evaluation of centroidal Voronoi tessellation method for statistical sampling and function integration
Romero, V.J. Burkardt, J.V. Gunzberger, M.D. Peterson, J.S.
Sandia Nat. Labs., Albuquerque, NM;

This paper appears in: Uncertainty Modeling and Analysis, 2003. ISUMA 2003. Fourth International Symposium on
Publication Date: 24-24 Sept. 2003
On page(s): 174-191
Location: College Park, MD,
ISBN: 0-7695-1997-0
INSPEC Accession Number: 8301734
Digital Object Identifier: 10.1109/ISUMA.2003.1236159
Current Version Published: 2003-10-14

Abstract
A recently developed centroidal Voronoi tessellation (CVT) unstructured sampling method is investigated here to assess its suitability for use in statistical sampling and function integration. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-dimensional parameter spaces. It has recently been shown on several 2D test problems to provide superior point distributions for generating locally conforming response surfaces. Its performance as a statistical sampling and function integration method is compared to that of latin-hypercube sampling (LHS) and simple random sampling (SRS) Monte Carlo methods, and Halton and Hammersley quasiMonte-Carlo sequence methods. Specifically, sampling efficiencies are compared for function integration and for resolving various statistics of response in a 2D test problem. It is found that on balance CVT performs best of all these sampling methods on our test problems

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