How it works
Finite Element Exterior Calculus
Struphy discretizes fields with B-splines arranged into a de Rham complex: four spline spaces connected by the exact differential operators gradient, curl, and divergence,V₀ --grad--> V₁ --curl--> V₂ --div--> V₃. Every model's variables live in one of these four spaces, chosen so the discretization preserves the underlying vector calculus exactly — not just approximately.
The de Rham complex
Click a space to see which Struphy models place a variable there.
Select a space above.
Scalar potentials — continuous, no derivative constraint.
13 variable(s) across Struphy's models:
Vector fields with a well-defined curl (e.g. electric fields).
10 variable(s) across Struphy's models:
Vector fields with a well-defined divergence (e.g. magnetic fields).
25 variable(s) across Struphy's models:
Densities — no continuity constraint at all.
31 variable(s) across Struphy's models:
B-spline basis functions
Every space above is spanned by B-splines of some degree. Adjust the degree and element count to see how the basis changes — degree p splines are C^(p−1)-continuous across element boundaries, and always sum to exactly 1 everywhere (the "partition of unity").