Boundary knot method for 2D and 3D helmholtz and convection-diffusion problems under complicated geometry

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

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  • Y. C. Hon
  • W. Chen

Related Research Unit(s)


Original languageEnglish
Pages (from-to)1931-1948
Journal / PublicationInternational Journal for Numerical Methods in Engineering
Issue number13
Publication statusPublished - 7 Apr 2003


The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.

Research Area(s)

  • Boundary element, Boundary knot method, Dual reciprocity method, Meshless, Method of fundamental solutions, Non-singular general solution, Radial basis function