Admissible approximations for essential boundary conditions in the reproducing kernel particle method

J. Gosz, Wing K Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In the reproducing kernel particle method (RKPM), and meshless methods in general, enforcement of essential boundary conditions is awkward as the approximations do not satisfy the Kronecker delta condition and are not admissible in the Galerkin formulation as they fail to vanish at essential boundaries. Typically, Lagrange multipliers, modified variational principles, or a coupling procedure with finite elements have been used to circumvent these shortcomings. Two methods of generating admissible meshless approximations, are presented; one in which the RKPM correction function equals zero at the boundary, and another in which the domain of the window function is selected such that the approximate vanishes at the boundary. An extension of the RKPM dilation parameter is also introduced, providing the capability to generate approximations with arbitrarily shaped supports. This feature is particularly useful for generating approximations near boundaries that conform to the geometry of the boundary. Additional issues such as degeneration of shape functions from 2D to 1D and moment matrix conditioning are also addressed.

Original languageEnglish (US)
Pages (from-to)120-135
Number of pages16
JournalComputational Mechanics
Issue number2
StatePublished - Jan 1 1996

ASJC Scopus subject areas

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


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