[Developers] reduction on sphere

Jonathan Thornburg jthorn at aei.mpg.de
Thu Sep 28 05:49:30 CDT 2006

> > it seems a common task for many applications to have some
> > reduction of some value on a sphere (integral, max, min).
> > Would it be useful to implement a general reduction operator
> > or (probably even better) to give existing reduction operators a mask
> > they are confined to work on?

> Thorn SphericalSurface has a way to store spheres.  We recently developed a
> thorn SphericalHarmonics, which performs various integrations and reductions
> over such spheres, among other things.  Maybe this thorn could help in the
> short term?

I'd also like to draw people's attention to Misner, gr-qc/9910044
(= CQG 21, S243), "Spherical Harmonic Decomposition on a Cubic Grid":
  A method is described by which a function defined on a cubic grid (as
  from a finite difference solution of a partial differential equation)
  can be resolved into spherical harmonic components at some fixed
  radius. This has applications to the treatment of boundary conditions
  imposed at radii larger than the size of the grid, following Abrahams,
  Rezzola, Rupright et al.(gr-qc/9709082}. In the method described here,
  the interpolation of the grid data to the integration 2-sphere is
  combined in the same step as the integrations to extract the spherical
  harmonic amplitudes, which become sums over grid points. Coordinates
  adapted to the integration sphere are not needed.


-- Jonathan Thornburg <jthorn at aei.mpg.de>      
   Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
   Golm, Germany, "Old Europe"     http://www.aei.mpg.de/~jthorn/home.html      
   "Washing one's hands of the conflict between the powerful and the
    powerless means to side with the powerful, not to be neutral."
                                      -- quote by Freire / poster by Oxfam

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