Radial functions are a meshless approximation method that has become popular in computer graphics and scattered data approximation. For a particular species of high order RBFs, Gaussians, we apply Jacobian theta functions, Poisson Summation, and Fourier Transform theory to fill some gaps in theory. We then discuss seven different strategies for approximating derivatives using RBFs, and discuss the prospects and difficulties in using RBFs to provide a meshless, highly adaptive algorithm for solving PDEs in general and fluid flows in particular.
(This is joint work with Lei Wang.)
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