Radial basis function methods for meshless PDE computation

Radial basis functions have been used for decades for the interpolation of scattered,

high-dimensional data. Recently they have attracted interest as methods for simulating

partial differential equations as well. RBFs do not require a grid or triangulation, they

offer the possibility of spectral accuracy with local refinement, and their implementation

is very straightforward. A number of theoretical and practical breakthroughs in recent years

has improved our understanding and application of these methods, and they are currently being

tested on real-world applications in shallow water flow on the sphere and tear film evolution

in the human eye.