A meshless collocation method based on the differential reproducing kernel interpolation

Yung Ming Wang, Syuan Mu Chen, Chih Ping Wu

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

A differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving partial differential equations governing a certain physical problem. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the DRK interpolation function, without directly differentiating the DRK interpolation function. In addition, the shape function of the DRK interpolation function at each sampling node is separated into a primitive function processing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied. A point collocation method based on the present DRK interpolation is developed for the analysis of one-dimensional bar problems, two-dimensional potential problems, and plane problems of elastic solids. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach, with excellent accuracy and fast convergence rate.

Original languageEnglish
Pages (from-to)585-606
Number of pages22
JournalComputational Mechanics
Volume45
Issue number6
DOIs
Publication statusPublished - 2010 May

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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