AlgebraicJulia / CombinatorialSpaces.jl

Simplicial sets and other combinatorial models of geometric spaces
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Parameterize the Hodge Formulation for Fast DEC operators #76

Open lukem12345 opened 6 months ago

lukem12345 commented 6 months ago

Certain operators such as the interior product between dual 1-forms "hard-code" the choice of GeometricHodge.

Although the interpolation method that this interior product relies on assumes perfect barycentric interpolation, this operator can use the DiagonalHodge formulation. (With the universal caveat that it will be more accurate on "well-structured" meshes.)

These operators should parameterize the choice of Hodge star:

lukem12345 commented 6 months ago

The typo in this doc-string should be amended.

GeorgeR227 commented 6 months ago

For dec_wedge_product_pd and dec_wedge_product_dp instead of calling only.() in the cached function, this should be applied on the flat-sharp matrix beforehand, meaning that we only do matrix multiplication when computing.

lukem12345 commented 6 months ago

Older operators such as the reference Laplacian implementation should also support such parameterization.