A Stochastic Radial Point Interpolation Method for Uncertainty Analysis in Geometry

A time domain method for quantitative analysis of geometrical uncertainty is introduced here by combining polynomial chaos expansion (PCE) with the radial point interpolation method (RPIM). The shape function matrix of RPIM is represented in a stochastic framework. The proposed method is validated in a two dimensional problem and its accuracy is compared with Monte-Carlo (MC) simulation using Kolmogorov Smirnov (KS) test. Time complexity of the proposed method is remarkably better than MC. Since RPIM is an unstructured node based approach, this method can be well adapted for complex curved geometries.