Dimension-splitting data points redistribution for meshless approximation

Abstract

To better approximate nearly singular functions with meshless methods, we propose a data points redistribution method extended from the well-known one-dimensional equidistribution principle. With properly distributed data points, nearly singular functions can be well approximated by linear combinations of global radial basis functions. The proposed method is coupled with an adaptive trial subspace selection algorithm in order to reduce computational cost. In our numerical examples, clear exponential convergence (with respect to the numbers of data points) can be observed.