Multidimensional adaptive sampling for global metamodelling

An adaptive sampling method is presented, which intelligently selects the location of data points in parameter space for multidimensional data interpolation. The method uses a small number of samples to begin, and satisfies the two goals of space-filling updates to explore the domain, and local refinement in areas where the data is nonlinear. A smooth separation function is used to quantify the sample spacing, and the Laplacian is used to indicate nonlinearities. This paper presents an extension of the existing method to improve the computational expense for multidimensional data. A multi-level evaluation grid is assessed using a three-dimensional analytic test case, and it is concluded that significant reduction in the cost of the evaluation procedure can be made without detracting from the performance of the method. In addition, the effect of varying the number of initial points is investigated, and the number of points required to generate a model of given accuracy is reduced by a factor of two. Such findings are encouraging for future work using the method to generate and model aerodynamic loads data, using a minimal number of computational fluid dynamics (CFD) simulations.