Solving the 3D Laplace equation by meshless collocation via harmonic kernels

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

9 Scopus Citations
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Author(s)

  • Y. C. Hon
  • R. Schaback

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1-19
Journal / PublicationAdvances in Computational Mathematics
Volume38
Issue number1
Online published23 Sept 2011
Publication statusPublished - Jan 2013

Abstract

This paper solves the Laplace equation Δu = 0 on domains Ω ⊂ ℝ3 by meshless collocation on scattered points of the boundary ∂Ω. Due to the use of new positive definite kernels K(x, y) which are harmonic in both arguments and have no singularities for x = y, one can directly interpolate on the boundary, and there is no artificial boundary needed as in the Method of Fundamental Solutions. In contrast to many other techniques, e. g. the Boundary Point Method or the Method of Fundamental Solutions, we provide a solid and comprehensive mathematical foundation which includes error bounds and works for general star-shaped domains. The convergence rates depend only on the smoothness of the domain and the boundary data. Some numerical examples are included. © 2011 Springer Science+Business Media, LLC.

Research Area(s)

  • Collocation, Convergence, Error bounds, Harmonic functions, Interpolation, Kernel

Citation Format(s)

Solving the 3D Laplace equation by meshless collocation via harmonic kernels. / Hon, Y. C.; Schaback, R.
In: Advances in Computational Mathematics, Vol. 38, No. 1, 01.2013, p. 1-19.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review