Spin-weighted transforms

[Keaton Burns]

I’ve just added wrappers for the SHTns transforms to Dedalus for use in our spherical, shell, and full-ball spectral methods. Above moderate sizes (lmax > 128), it’s substantially faster than the naive matrix-multiplication transforms we have previously implemented (at least 10x faster at lmax=1024). This is great!

For vector and tensor fields, though, we use spin-weighted spherical harmonics which incorporate the exact polar regularity for components of arbitrary-rank tensor fields. It would be fantastic to have support for these spin-weighted transforms for moderate spin weights (-3 <= s <= 3) on the standard Gauss-Legendre grid in SHTns. I think this would only require minor modifications to the associated Legendre transform routines, as the envelopes and recursions are just slightly perturbed from those for the scalar spherical harmonics (the formulation we use is detailed here: https://arxiv.org/abs/1804.10320). Perhaps even arbitrary spin weights wouldn’t require too much modification.

It this a direction that might be of interest? I think it would certainly get a lot of use in Dedalus and probably by other codes currently using libsharp/ducc for spin-weighted transforms.

[Nathanaël Schaeffer]

Yes, at some point I would also need spin 2 for my own work, so this is something that will be done. I cannot say when though

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