Discrete de Rham sequence

The FEEC layer makes the sequence explicit in code and diagnostics.

Sequence

On triangulated surfaces:

0 -> Λh0 --d0--> Λh1 --d1--> Λh2 -> 0

where:

• Λh0: vertex DOFs,
• Λh1: oriented edge DOFs,
• Λh2: oriented face DOFs.

API

• build_whitney_complex(mesh, geom)
• build_de_rham_sequence(mesh, geom)
• de_rham_report(complex)
• verify_subcomplex(complex)

What de_rham_report provides

• DOF counts (ndofs0, ndofs1, ndofs2),
• sparsity metrics (nnz_d0, nnz_d1, nnz_M*),
• exactness residual ||d1*d0||,
• mass symmetry and basic positivity diagnostics.

Minimal example

using FrontIntrinsicOps

mesh = generate_torus(1.0, 0.35, 12, 10)
geom = compute_geometry(mesh)

W = build_de_rham_sequence(mesh, geom)
println(verify_subcomplex(W; atol=1e-12))
println(de_rham_report(W).exactness_residuals)

Limitations and non-goals

• This is an explicit lowest-order sequence layer.
• No higher-order P_r / P_r^- families yet.
• No replacement of existing DEC core operators.