An Element-Free Galerkin Method Based on Complex Variable Moving Kriging Interpolation for Potential Problems

The moving Kriging interpolation (MKI) is an accurate approximation method that has the interpolating property. However, it is rarely used in meshless methods because of its low efficiency. In this paper, we proposed an efficient MKI method, the complex variable moving Kriging interpolation (CVMKI) method, for "domain" type meshless method. Further, we proposed the CVMKI-based element-free Galerkin (CVMKIEFG) method for 2D potential problems. CVMKIEFG is an efficient meshless method and can impose the essential boundary conditions directly and easily. We proposed two formulations for CVMKIEFG: the conventional formulation and the cell-based formulation. The latter formulation is proposed for higher efficiency. Three 2D example problems are presented to demonstrate the efficiency and accuracy of CVMKIEFG.