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RBF as MFS approximations in higher dimension

Alves, Carlos J. S.

8th World Congress on Computational Mechanics (WCCM8), ECCOMAS, Barcelona (2008), (CD-Rom)

Some of the most common scalar PDEs have fundamental solutions that have a radial feature. There-fore, the method of fundamental solutions (MFS) is usually associated to radial basis functions (RBF) as a particular case, when the basis functions have radial property. Here we will present a missing counterpart – some of the most common RBF approximation methods are just a particular case of the MFS boundary approximation when applied in a higher dimension. This idea was presented in [1]. In thispresentation we will consider the relation between MFS boundary interpolation in dimension d+1 and RBF domain interpolation in dimension d, for the most commonly used RBF basis functions.