Numerical study of the three-dimensional wave equation using the mesh-free kp-Ritz method

This paper deals with numerical modeling of three-dimensional linear wave propagation based on the mesh-free kp-Ritz method. The mesh-free kernel particle estimate is employed to approximate the 3D displacement field. A system of discrete equations is obtained through application of the Ritz minimiz...

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Bibliographic Details
Published inEngineering analysis with boundary elements Vol. 37; no. 7-8; pp. 977 - 989
Main Authors Liew, K.M., Cheng, R.J.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2013
Subjects
Convergence analysis
Error estimate
Mesh-free kp-Ritz method
Meshless method
Wave equation
Wave equation
Mesh-free kp-Ritz method
Meshless method
Error estimate
Convergence analysis
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Summary:This paper deals with numerical modeling of three-dimensional linear wave propagation based on the mesh-free kp-Ritz method. The mesh-free kernel particle estimate is employed to approximate the 3D displacement field. A system of discrete equations is obtained through application of the Ritz minimization procedure to the energy expressions. Convergence analysis and error estimates of the kp-Ritz method for three-dimensional wave equation are also presented in the paper. From the error analysis, we found that the error bound between the numerical and the exact solution is directly related to the radii of weight functions and the time step length. Effectiveness of the kp-Ritz method for three-dimensional wave equation is investigated by three numerical examples.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2013.04.001