The Dimension Splitting Interpolating Element-Free Galerkin Method for Solving 3D Wave Equations

Abstract

Based on the idea of dimension splitting method, a dimension splitting interpolating element-free Galerkin (DSIEFG) method for 3D wave propagation problems is proposed. In the splitting direction, the 3D domain of a problem is divided into a series of related 2D subdomains. Using the improved interpolating moving least-squares (IMLS) method to acquire the shape function in the 2D subdomains, the discretized equations are formed based on Galerkin weak form of 2D problem. The discretized equations are coupled by using the difference method in the splitting direction. Then, the final equations of the DSIEFG method for 3D wave propagation problems are obtained. Numerical examples are given to study the effects of node distribution, number of split layers, influence domain parameters, splitting direction, and time step on the computational accuracy of the DSIEFG method. The results of numerical examples show that the DSIEFG method is more efficient and accurate compared with the improved EFG method for 3D wave equations.