Export an api for differential forms?

[Antoinemarteau]

I understand the package leverages differential calculus internally to compute integral of correct unit over domain of correct dimension, do you have any plan to export an API for a differential form defined on a mesh/domain to enable doing computation with them before integrating ?

[JoshuaLampert]

Hi @Antoinemarteau! Thanks for your interest. Yes, we do have plans to expand the support for dealing with differential forms. Recently, @kylebeggs continued the initiative and started looking into switching from finite difference formulas to compute the differential to automatic differentiation. See #35 for an issue tracking the progress. We plan to upstream an API for differential forms to Meshes.jl (see also #115 (comment) for our plan). Until we finished this effort, you can already use the exported function jacobian(geometry, ts; ε=1e-6) (see the documentation for more info) and the non-exported function differential(geometry, ts), see

MeshIntegrals.jl/src/differentiation.jl

Lines 85 to 90 in 6c8cd1f

	"""
	differential(geometry, ts)
	Calculate the differential element (length, area, volume, etc) of the parametric
	function for `geometry` at arguments `ts`.
	"""

As mentioned above, these use a central finite difference formula (and an analytical derivative for the special case of a BezierCurve).