Geometric selection of centers for radial basis function approximations involved in intensive computer simulations

A method for the selection of centers for radial basis function (RBF) approximation is introduced, which reduces the computational cost of the evaluation of the approximating function. The method takes into consideration:1.the geometric information (arc length and curvature) of the approximating RBF expansion with all data points as centers, in order to retain as centers just those data points that have relevant geometric characteristics;2.the distribution of data points in the function domain do not leave rather large regions of the function domain without centers;3.the approximation error to control the number of centers in such a way that a desired fitting accuracy can be achieved.