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I think I was mistaken here. For general curvilinear elements, the redundant computation can't be avoided, as the inverse metric derivatives can vary. The optimization I talk about here is only possible in the affine setting, cf. #161.
This code:
grudge/grudge/op.py
Lines 354 to 359 in 1c44c4b
computes the r,s,t (i.e. reference) derivatives once per dimension. We can compute them once and reuse them. In 3D, that saves a factor of 3 in work.
This is something I should have caught during review of #74.
cc @thomasgibson @lukeolson
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