A boundary cloud method (BCM), for boundary-only analysis of partial differential equations, is presented in this paper for solving potential equations in two dimensions (2-D). The BCM combines a weighted least-squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations. Given a set of scattered points on the surface of an arbitrary object, Hermite-type interpolation functions are constructed by developing a weighted least-squares approach. We also introduce truncated Hermite-type interpolation functions. The boundary integrals are evaluated by using a cell structure. We propose various schemes for evaluating the singular, nearly singular and nonsingular integrals. We also propose a true meshless approach for boundary-only analysis of potential equations. Numerical results, comparing the classical boundary element method and the BCM, are presented for several 2-D potential problems.

Original languageEnglish (US)
Pages (from-to)2337-2370
Number of pages34
JournalComputer Methods in Applied Mechanics and Engineering
Issue number21-22
StatePublished - Mar 15 2002


  • Boundary cloud method
  • Boundary integral method
  • Boundary-only analysis
  • Hermite interpolation
  • Meshless
  • Scattered point interpolation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

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