Hodge Decomposition
Every vector field = gradient (curl-free) + curl (div-free) + harmonic
Original F
Curl-free ∇φ
Div-free ∇×A
Harmonic H
Preset field:
Mixed (source+vortex)
Pure source
Pure vortex
Shear flow
Wave-like
Random
Compute Decomposition
Clear drawing
Hodge theorem:
F = ∇φ + ∇×A + H
∇φ
— curl-free (irrotational)
grad of scalar potential
∇×A
— div-free (solenoidal)
curl of vector potential
H
— harmonic component
both curl-free and div-free
Computed via spectral method (DFT on grid).