Crate cartan_dec 

cartan-dec

Discrete exterior calculus (DEC) on Riemannian manifolds.

Bridges continuous geometry (cartan-core) to discrete operators for PDE solvers on simplicial meshes. All metric information flows through the Hodge star; topology is encoded in the metric-free exterior derivative.

Modules

Module	Contents
mesh	Mesh<M,K,B> generic simplicial complex; FlatMesh = flat 2D triangular mesh
exterior	ExteriorDerivative — d₀ (0-forms to 1-forms) and d₁ (1-forms to 2-forms)
hodge	HodgeStar — diagonal ⋆₀, ⋆₁, ⋆₂ from primal/dual volumes
laplace	Operators — Laplace-Beltrami, Bochner, and Lichnerowicz Laplacians
advection	Upwind covariant advection for scalar and vector fields
divergence	Discrete covariant divergence of vector and tensor fields
error	DecError — error type for DEC operations

Quick start

use cartan_dec::{FlatMesh, Operators};
use cartan_manifolds::euclidean::Euclidean;
use nalgebra::DVector;

// Build a 4x4 uniform grid on [0,1]^2.
let mesh = FlatMesh::unit_square_grid(4);
let ops = Operators::from_mesh(&mesh, &Euclidean::<2>);

// Apply the scalar Laplacian to a vertex field.
let f = DVector::from_element(mesh.n_vertices(), 1.0);
let lf = ops.apply_laplace_beltrami(&f);

References

• Desbrun et al. “Discrete Exterior Calculus.” arXiv:math/0508341, 2005.
• Hirani. “Discrete Exterior Calculus.” Caltech PhD thesis, 2003.

Re-exports

pub use advection::apply_scalar_advection;

pub use advection::apply_vector_advection;

pub use divergence::apply_divergence;

pub use divergence::apply_tensor_divergence;

pub use error::DecError;

pub use exterior::ExteriorDerivative;

pub use hodge::HodgeStar;

pub use laplace::Operators;

pub use mesh::FlatMesh;

pub use mesh::Mesh;

Modules

advection

Discrete covariant advection operator for scalar and tensor-valued fields.

divergence

Discrete covariant divergence of a vector field.

error

Error type for cartan-dec operations.

exterior

Discrete exterior derivative operators d0 and d1.

hodge

Discrete Hodge star operators star0, star1, star2.

laplace

Discrete Laplace-Beltrami, Bochner, and Lichnerowicz operators.

mesh

Simplicial complex: vertices, (oriented) boundary faces, and simplices.