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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)977-989
Journal / PublicationEngineering Analysis with Boundary Elements
Issue number7-8
Online published13 May 2013
Publication statusPublished - Jul 2013


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. © 2013 Elsevier Ltd.

Research Area(s)

  • Convergence analysis, Error estimate, Mesh-free kp-Ritz method, Meshless method, Wave equation