The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems

Abstract

In this paper, the moving least-squares (MLS) approximation and the interpolating moving least-squares (IMLS) method proposed by Lancaster are discussed first. A new method for deriving the MLS approximation is presented, and the IMLS method is improved. Compared with the IMLS method proposed by Lancaster, the shape function of the improved IMLS method in this paper is simpler so that the new method has higher computing efficiency. Then combining the shape function of the improved IMLS method with Galerkin weak form of the potential problem, the interpolating element-free Galerkin (IEFG) method for the two- dimensional potential problem is presented, and the corresponding formulae are obtained. Compared with the conventional element-free Galerkin (EFG) method, the boundary conditions can be applied directly in the IEFG method, which makes the computing efficiency higher. For the purposes of demonstration, some selected numerical examples are solved using the IEFG method.