A hybrid meshless method for the solution of the second order hyperbolic telegraph equation in two space dimensions

被引：21
|
作者：
Zhou, Yunxu [1 ,2 ]
Qu, Wenzhen [1 ,3 ]
Gu, Yan [1 ,3 ]
Gao, Hongwei [1 ]
机构：
[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Peoples R China
[2] Qingdao Univ, Int Off, Qingdao 266071, Peoples R China
[3] Qingdao Univ, Inst Mech Multifunct Mat & Struct, Qingdao 266071, Peoples R China
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2020年 / 115卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Telegraph equation; Generalized finite difference method; Houbolt method; Meshless method; FINITE-DIFFERENCE METHOD; SINGULAR BOUNDARY METHOD; FUNDAMENTAL-SOLUTIONS; GALERKIN METHOD; INTERPOLATION; SIMULATION; DIRICHLET; SCHEME; SOLVE;
D O I：
10.1016/j.enganabound.2020.02.015
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
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.
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页码：21 / 27
页数：7
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