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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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Geometric Implementation of Spherical Harmonics
by
Robert Bartnik
University of Canberra
Coauthors: Andrew H. Norton (University of Canberra)

Our simulation of the 4-D Einstein equations in the NQS gauge employs various representations for fields defined on the 2-sphere. Central to these representations is the use of spin-weighted spherical harmonics, which provide a geometric generalisation of the familiar spherical, vector and tensor harmonics. Double-FFT's are used to differentiate and to project fields to spherical harmonic subspaces. The geometric operator \edth (``edth'') provides the key to constructing numerically stable derivative evaluations. Edth has particularly simple action on (spin-weighted) spherical harmonics, and this is used as the basis for a preconditioner used in solving a class of 1st-order elliptic equations on the 2-sphere.

Date received: July 30, 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-85.