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Journal of Scientific Computing

, Volume 44, Issue 3, pp 286–300

# Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation

• Alfa R. H. Heryudono
• Tobin A. Driscoll
Article

## 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.

## Keywords

Radial basis functions Schwarz-Christoffel mapping Meshfree Interpolation

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## Copyright information

© Springer Science+Business Media, LLC 2010

## Authors and Affiliations

1. 1.Department of MathematicsUniversity of Massachusetts DartmouthDartmouthUSA
2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA