and
Toby Driscoll
The technique of radial basis functions (RBFs) has been used for years with great success for the approximation of multidimensional data given at scattered data points--as opposed to points on a regular grid. That grid-free nature makes them enticing candidates for the numerical simulation of hyperbolic differential equations, such as Maxwell's, in complicated geometries. However, there are many questions about RBF approximations that need to be answered before such simulations can become useful. I will touch on some of the things that we've found out so far, and on some of the numerous interesting theoretical and practical issues that remain.
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Richard Charles
and Toby Driscoll |
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