Tensor Contraction

General
1

Hello,
In the Linear Form of my problem I have a contraction of a third order Tensor with a Vector:
T_{\alpha \beta \gamma} P_\gamma.
Is there some handy way to do this or do I need to write it for each element?
Thanks!

2

Hi Jakob,

there are some options in NGSolve to handle this kind of contraction.
The most generic would be to use Einsum from ngsolve.fem, which is inspired by numpy einsum (numpy.einsum — NumPy v1.26 Manual).

import ngsolve.fem

T = CF( (1,2, 3,4,
         5,6, 7,8), dims=(2,2,2) )
P = CF( (9,0) )
contraction = fem.Einsum('abc,c->ab', T, P)

For the contraction also

contraction2 = T[:,:,P]
contraction3 = T*P

should work fine.

Best,
Michael

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