Publications

Initial application and evaluation of a promising new sampling method for response surface generation: Centroidal Voronoi tessellation

Romero, Vicente J.; Burkardt, J.; Gunzburger, M.; Peterson, J.; Krishnamurthy, T.

A recently developed Centroidal Voronoi Tessellation (CVT) sampling method is investigated here to assess its suitability for use in response surface generation. CVT is an unstructured sampling method that can generate nearly uniform point spacing over arbitrarily shaped M-dimensional parameter spaces. For rectangular parameter spaces (hypercubes), CVT appears to extend to higher dimensions more effectively and inexpensively than "Distributed" and "Improved Distributed" Latin Hypercube Monte Carlo methods, and CVT does not appear to suffer from spurious correlation effects in higher dimensions and at high sampling densities as quasi-Monte-Carlo methods such as Halton and Sobol sequences typically do. CVT is described briefly in this paper and its impact on response surface accuracy in a 2-D test problem is compared to the accuracy yielded by Latin Hypercube Sampling (LHS) and a deterministic structured-uniform sampling method. To accommodate the different point patterns over the parameter space given by the different sampling methods, Moving Least Squares (MLS) for interpolation of arbitrarily located data points is used. It is found that CVT performs better than LHS in 11 of 12 test cases investigated here, and as often as not performs better than the structured sampling method with its deterministically uniform point placement over the 2-D parameter space.