The hybrid element‐free Galerkin method for three‐dimensional wave propagation problems. (11th September 2018)

• Record Type: Journal Article
• Authors: Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.
• Is Part Of: International journal for numerical methods in engineering. Volume 117:Number 1(2019)
• Page Start: 15
• Page End: 37
• Publication Date: 2018-09-11
• Subjects: dimension split method -- finite difference method -- hybrid element‐free Galerkin method -- improved element‐free Galerkin method -- improved moving least squares approximation -- wave propagation problem; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5944
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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.