THE METHOD OF FUNDEMENTAL SOLUTIONS FOR THE MULTI-DIMENSIONAL WAVE EQUATIONS

Authors

Meng-Huang Gu, Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei 10617, Taiwan. R.O.C.
Chia-Ming Fan, Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C.
Der-Liang Young, Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei 10617, Taiwan. R.O.C.Follow

Abstract

In this paper, a meshless method is developed for solving multi-dimensional wave equations. The proposed method is based on the method of particular solution (MPS), the method of fundamental solutions (MFS) and the Houbolt finite difference (FD) method. The wave equation is considered as a Poisson-type equation with the time-dependent source term. The Houbolt method is applied to avoid the difficult problems for dealing with the initial conditions in forming the linear algebra system. The works of space discretization are dependent on the method of particular solution and the method of fundamental solutions. There are three numerical examples considered in this paper, such as the string vibration and wave vibration problems. Numerical validations have proven that the proposed method is a highly efficient and accurate meshless numerical tool for solving wave equations in engineering and sciences by comparing with analytical solution and other numerical solutions.

Recommended Citation

Gu, Meng-Huang; Fan, Chia-Ming; and Young, Der-Liang (2011) "THE METHOD OF FUNDEMENTAL SOLUTIONS FOR THE MULTI-DIMENSIONAL WAVE EQUATIONS," Journal of Marine Science and Technology: Vol. 19: Iss. 6, Article 2.
DOI: 10.51400/2709-6998.2200
Available at: https://jmstt.ntou.edu.tw/journal/vol19/iss6/2