The hybrid element-free Galerkin method for three-dimensional wave propagation problems

This paper presents a hybrid element-free Galerkin (HEFG) method for solving wave propagation problems. By introducing the dimension split method, the three-dimensional wave propagation problems are transformed into a series of two-dimensional ones in other one-dimensional directions. The two-dimensional problems are solved using the improved element-free Galerkin (IEFG) method, and the finite difference method is used in the one-dimensional splitting direction and the time space. Then, the formulas of the HEFG method for three-dimensional wave propagation problems are obtained. Numerical examples are selected to show the effectiveness and the advantage of the HEFG method. The convergence and error analysis of the HEFG method are discussed according to the numerical results under different splitting directions, weight functions, node distributions, scale parameters of the influence domain, penalty factors, and time steps. The numerical results are given to show the convergence and advantages of the HEFG method over the IEFG method. Comparing with the IEFG method, the HEFG method has greater computational precision and speed for three-dimensional wave propagation problems.