On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere

@article{Fornberg2008OnCA,
  title={On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere},
  author={Bengt Fornberg and C{\'e}cile Piret},
  journal={J. Comput. Physics},
  year={2008},
  volume={227},
  pages={2758-2780}
}
Radial basis function (RBF) approximations have been used for some time to interpolate data on a sphere (as well as on many other types of domains). Their ability to solve, to spectral accuracy, convection-type PDEs over a sphere has been demonstrated only very recently. In such applications, there are two main choices that have to be made: (i) which type of radial function to use, and (ii) what value to choose for their shape parameter (denoted by e, and with flat basis functions – stretched… CONTINUE READING