Speaker: David Yuen
The RBF method was introduced by Rolland Hardy in the 70s as a new interpolation technique, but it is not until the 90s that Ed Kansa used this method to numerically solve PDEs. It has three major advantages: it is meshfree, easy to implement in any number of dimensions and spectrally accurate for certain types of radial functions. In the context of solving PDEs, its accuracy depends on three things: the type of the radial function, the value of the RBF shape parameter (which controls how steep or how flat a radial function will be), and for time-dependent problems, also the integration time. In this presentation, I will introduce the method in both contexts of interpolation and of solving PDEs. I will then focus on the solution of hyperbolic equations around the surface of the sphere, with a quick overview on the RBF-QR method, introduced by Fornberg and Piret in 2007 to go around an important numerical conditioning issue of the RBF method, encountered in this context.