Divergence of a two dimensional 3 order tensor

[MasterD]

I want to calculate the divergence of a two dimensional 3 order tensor; e.g.

nabla=(d/dx, d/dy)

and

Ax =
( C D)
( E F),

Ay =
( G H)
( I J)

(it's a 2x2x2 cube).

Index notation:

(nabla)_i = d/dx_i

and elements of A are A_ijk

How do I contract it properly to calculate

Divergence of A (Nabla inner product A)?

Thanks a lot!

 

[MasterD]

Thanks guys.

I got the answer.

You should contract over the first index; so

$(\nabla\cdot\mathbf{A})_{jk}=\frac{d}{dx_i}A{ijk}$