The explicit functional form of the projection operator in 3D is found from the Helmholtz Theorem: Π Π S F ( r ) = 1 4 π π ∇ ∇ × × ∫ ∫ ∇ ∇ ′ ′ × × F ( r ′ ) | r − − r ′ | d V ′ , Π Π I = 1 − − Π Π S with a similar structure in 2D. Thus the governing equation is an integro-differential equation similar to Coulomb and Biot–Savart law, not convenient for numerical computation.