A Kriging interpolation-based boundary face method for 3D potential problems

In this paper, a new implementation of the boundary face method (BFM) is presented and developed for solving 3D potential problems. The BFM is implemented directly based on the boundary representation data structure for geometry modeling to eliminate geometry errors. This study combines the BFM with Kriging interpolation method and the corresponding formulae are derived. The Kriging interpolation is applied instead of the traditional moving least squares (MLS) approximation to overcome the lack of Kronecker delta function property, then essential boundary conditions can be imposed directly and easily. Several numerical examples with different geometry and boundary conditions are presented to illustrate the performance of the present method. The comparisons of accuracy between MLS approximation and Kriging interpolation are studied.