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Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation

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Abstract

In this paper, Radial Basis Function (RBF) method for interpolating two dimensional functions with localized features defined on irregular domain is presented. RBF points located inside the domain and on its boundary are chosen such that they are the image of conformally mapped points on concentric circles on a unit disk. On the disk, a fast RBF solver to compute RBF coefficients developed by Karageorghis et al. (Appl. Numer. Math. 57(3):304–319, 2007) is used. Approximation values at desired points in the domain can be computed through the process of conformal transplantation. Some numerical experiments are given in a style of a tutorial and MATLAB code that solves RBF coefficients using up to 100,000 RBF points is provided.

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Authors and Affiliations

  1. Department of Mathematics, University of Massachusetts Dartmouth, Dartmouth, MA, 02747, USA

    Alfa R. H. Heryudono

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Tobin A. Driscoll

Authors
  1. Alfa R. H. Heryudono
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  2. Tobin A. Driscoll
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Correspondence to Alfa R. H. Heryudono.

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Heryudono, A.R.H., Driscoll, T.A. Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation. J Sci Comput 44, 286–300 (2010). https://doi.org/10.1007/s10915-010-9380-3

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  • DOI: https://doi.org/10.1007/s10915-010-9380-3

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