The FEEC stack adds runtime dimension-generic exterior calculus to cartan. Four crates compose a finite element exterior calculus pipeline that runs in any ambient dimension and any form degree . The code derives from luiswirth/formoniq, used with permission and adapted to cartan's sparse and linear-algebra conventions.
| Crate | Layer | Contents |
|---|---|---|
cartan-exterior | algebra | elements, Gramian inner products, multivector terms |
cartan-simplicial | topology and geometry | runtime-dim simplicial complex, boundary chain, Regge metric from edge lengths |
cartan-feec | elements | Whitney forms, cochains, Galerkin Hodge mass , global assembly |
cartan-maxwell | solver | Maxwell evolution on a prescribed evolving Regge background |
edge lengths l_e (cartan-simplicial: Regge metric)
|
|-- per-cell Gramian (cartan-exterior: Lambda^k inner products)
|
|-- Whitney element (cartan-feec: reference Hodge mass M_k)
|
|-- global assembly (cartan-feec: assemble_galmat -> sparse M_k)
|
+-- time evolution (cartan-maxwell: M_1(t), M_2(t), Faraday and Ampere)
Geometry is an input. A driver supplies edge lengths ; the stack validates realizability and assembles the metric-dependent operators. The exterior derivative chain is metric-free and depends only on the abstract complex. Metric and motion enter through the Galerkin Hodge mass .
The Galerkin Whitney Hodge mass is a symmetric positive definite matrix assembled
from per-cell Gramians. It replaces the diagonal circumcentric Hodge star of
cartan-dec, which degrades on meshes that are not well-centered.
[dependencies]
cartan-exterior = "0.6"
cartan-simplicial = "0.6"
cartan-feec = "0.6"
cartan-maxwell = "0.6"