A hybrid meshless method for the solution of the second order hyperbolic telegraph equation in two space dimensions. (June 2020)

• Record Type: Journal Article
• Authors: Zhou, Yunxu; Qu, Wenzhen; Gu, Yan; Gao, Hongwei
• Is Part Of: Engineering analysis with boundary elements. Volume 115(2020)
• Page Start: 21
• Page End: 27
• Publication Date: 2020-06
• Subjects: Telegraph equation -- Generalized finite difference method -- Houbolt method -- Meshless method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.02.015
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: A hybrid meshless method is developed for hyperbolic telegraph equation. The method is truly meshless and has no reqirement of the mesh generation. A numerical experiment with the complicated domain is efficiently solved. Abstract: A hybrid meshless method is constructed in this paper for the solution of the second order hyperbolic telegraph equation in two space dimensions with Dirichlet or mixed boundary conditions. The temporal derivatives of the physical quantity included in the telegraph equation are approximated into the finite difference formulae by using the Houbolt method. Based on these formulae, the original telegraph problem is then transformed into the modified Helmholtz equation which is efficiently simulated with the generalized finite difference method. The developed hybrid scheme is mathematically simple and truly meshless. We finally provide three numerical examples including one case with a complicated domain, and all numerical results illustrate the good performance of the developed hybrid meshless scheme.