Initial evaluation of centroidal Voronoi tessellation method for statistical sampling and function integration

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