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luiswirth / formoniq

Finite Element Exterior Calculus on Coordinate-Free Simplicial Manifolds in Rust
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exterior algebra: k-vectors and k-forms #32

Open luiswirth opened 4 months ago

luiswirth commented 4 months ago

We need to implement data structures for k-{vectors,forms}. These data structures are similar to nalgebra datastructures like na::{Vector, Matrix}. We need to decide on an ordering of the standard bases of these linear spaces of k-{vectors, forms} and then we can store the coefficients/coordinates of these objects. By choosing an ordering we can store a list of coefficients in a vector or we can store the objects as actual tensors using nD arrays.

These exterior algebras need of course common operations like wedge product, hodge star, sharp and flat. And for forms we additionally need exterior derivative and evaluation.

It would of course be nice to abstracts over vectors and forms and just have an ExteriorAlgebra.

luiswirth commented 1 month ago

it's not clear if this is needed for the computation of the element matrices... it seems to me that is not really required, but i'm not sure.