Discrete Differential Geometry: Discrete Exterior Calculus

[bollu]

• A new type to model discrete k-forms for (0 <= k <= n) on a simplicial complex of dimension n.
• A k-form is a function from the k-dimensional faces of the simplicial complex to a Z-module R.
• The exterior derivative operator d to integrate a k-form to build a (k+1)-form over a simplicial complex
• A chain complex structure for the collection of differential forms over a simplicial complex. https://doc.sagemath.org/html/en/reference/homology/sage/homology/chain_complex.html

References

• Discrete exterior calculus: https://arxiv.org/abs/math/0508341
• Keenan Crane's textbook, chapter 3: https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf

Component: geometry

Keywords: discrete, differential geometry

Issue created by migration from https://trac.sagemath.org/ticket/30196

[mkoeppe]

comment:2

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.