We have recently presented a boundary cloud method (BCM) [Comput. Meth. Appl. Mech. Engng 191 (2002) 2337], which combines boundary integral formulations with scattered point interpolation techniques. A generalized least-squares approach, which requires information about the outward normal to the boundary, is employed to construct interpolation functions. Since an outward normal is not well defined for geometries with corners for 2D problems (or for corners and edges for 3D problems), points could not be placed at corners when discretizing the surface of the object. In this paper, we introduce a new implementation of the BCM, which uses a varying base interpolating polynomial to construct interpolation functions. The key idea is to define an appropriate polynomial basis which ensures linear completeness. The polynomial basis can change from cloud to cloud depending on the definition of the cloud at each point. The new implementation can handle points at corners and is much simpler and at least an order of magnitude faster compared to our original implementation. The original implementation can be more accurate and can give higher order convergence rates, but is limited because it cannot handle points at corners. Numerical results comparing the original and the new implementation are shown for several potential and electrostatic problems.

Original languageEnglish (US)
Pages (from-to)57-71
Number of pages15
JournalEngineering Analysis with Boundary Elements
Issue number1
StatePublished - Jan 2003


  • Boundary cloud method
  • Cloud by cloud
  • Least-squares approach
  • Meshless method
  • Polynomial basis

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics


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