Laplacian operator

The Laplacian for a scalar function ϕ is a scalar differential operator defined by del ^2 ϕ = 1/(h_1 h_2 h_3)[d/(du_1)((h_2 h_3)/h_1 d/(du_1)) + d/(du_2)((h_1 h_3)/h_2 d/(du_2)) + d/(du_3)((h_1 h_2)/h_3 d/(du_3))] ϕ, where the h_i are the scale factors of the coordinate system. Note that the operator del ^2 is commonly written as Δ by mathematicians.

Laplacian matrix | tensor Laplacian | vector Laplacian