A Fast Complex Variable Element-Free Galerkin Method for Three-Dimensional Wave Propagation Problems

In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin (ICVEFG) method, we present a fast ICVEFG method for three-dimensional wave propagation problems. Using the dimension splitting method, the equations of three-dimensional wave propagation problems are translated into a series of two-dimensional ones in another one-dimensional direction. The new Galerkin weak form of the dimension splitting method for three-dimensional wave propagation problems is obtained. The improved complex variable moving least-square (ICVMLS) approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions, finite difference method is used in the one-dimensional direction, then the formulae of the ICVEFG method for three-dimensional wave propagation problems are obtained. The convergence and the corresponding parameters in the ICVEFG method are discussed. Some numerical examples are given to show that the new method has higher computational precision, and can improve the computational efficiency of the conventional meshless methods for three-dimensional problems greatly.