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Add SimplexTree for enforcing a DeltaSet to be a Complex #92

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jpfairbanks opened this issue May 28, 2024 · 0 comments
Open

Add SimplexTree for enforcing a DeltaSet to be a Complex #92

jpfairbanks opened this issue May 28, 2024 · 0 comments
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@jpfairbanks
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Based on our discussion today. Owen is going to implement the geometric maps in terms of the simplex tree data structure, which is just a Trie on the sorted vertices of the simplex.

struct SimplicialComplex{D}
  delta_set::D
  complexes::Trie{Int, Int}
end

Then GeometricMap is a morphism between SimplicialComplexes

struct GeometricPoint
  simplex::Int
  coords::Vector{Float64}
end

struct GeometricMap
  dom::SimplicialComplex
  codom::SimplicialComplex
  values::Vector{GeometricPoint}
end

Then we also need the pullback maps

function pullback(f::GeometricMap, u::Form)::Form
  dom(u) == codom(f) || error("Must pullback along the geometric map")
  ...
  # return value is a form over the domain(f)
end

Source on Whitney Forms and Interpolation for the pullbacks: https://www.sciencedirect.com/science/article/pii/S0377042721001394?via%3Dihub

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