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Parameterize the Hodge Formulation for Fast DEC operators #76

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lukem12345 opened this issue Apr 26, 2024 · 3 comments
Open
3 tasks

Parameterize the Hodge Formulation for Fast DEC operators #76

lukem12345 opened this issue Apr 26, 2024 · 3 comments
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@lukem12345
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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:

  • Dual Laplacian
  • Interior Product between Dual 1-forms
  • Lie derivative between Dual 1-forms
@lukem12345 lukem12345 self-assigned this Apr 26, 2024
@lukem12345
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The typo in this doc-string should be amended.

@GeorgeR227
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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
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Older operators such as the reference Laplacian implementation should also support such parameterization.

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