libMesh/libmesh — pull request #54 by benkirk (2013-03-18 20:39:01+00:00)
Title: Radial basis meshfree interpolation

This patchset provides the initial capability for radial basis meshfree interpolation. This provides a smoother alternative to the inverse distance capability.

At the moment the coefficient construction requires solving a dense NxN linear system, so clearly it does not scale particularly well.

We will be experimenting with O(N log N) and better speedup techniques borrowing from tree-code technology, but at the moment the implementation is naive.

For some inspiring examples of application see https://github.com/benkirk/Documents/raw/master/articles/RBF-carr-beatson-etal-siggraph01.pdf In addition to the obvious use of interpolating an unordered set of points, this could be used for example as a CAD surrogate to provide smooth surfaces for refinement.