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Computational Techniques and Applications Conference and Workshops - CTAC99
September 20-24, 1999
The Australian National University
Canberra, ACT, Australia

Organizers
Mike Osborne, Bob Gingold, Steve Roberts, David Harrar II, Thanh Tran, Bob Anderssen, Henry Gardner, Markus Hegland, Lutz Grosz

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Thin plate spline interpolation on an annulus
by
David R Jenkins
CSIRO Mathematical and Information Sciences

This work demonstrates a method for surface interpolation on an annulus, with the additional constraint that the surface and its normal derivatives are specified on the annulus boundaries. The method is based on a truncated Fourier series solution to the homogeneous biharmonic equation, combined with Green's functions for the point interpolations. The formulation and solution approach is particularly suitable for the annulus geometry because the boundaries are circles, meaning that the boundary constraints are functions of the angle \theta only, and they can be approximated by a truncated Fourier series. The result is that the interpolation method is effectively gridless. The matrix problem resulting from this formulation is highly structured and can be solved in a simple sequential manner. We present results for some test problems to illustrate the effect of the truncation of the Fourier series on the solution and on aspects such as the condition of the matrix problem.

Date received: July 25, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-45.