Accesing the fields of a directional derivative in a three-field elasticity problem

Question

Hello,
In a three-field Hu-Washizu variational functional representing nearly incompressible material behaviour like Pi(u,p,theta), the directional derivatives for this would be:

DPi(u,p,theta).dv
DPi(u,p,theta).dp
DPi(u,p,theta).dtheta

After computing these with:

F = derivative(Pi, u, v)

how can I access each component of F.
In other words, does F have three components with for example:

F[0] = DPi(u,p,theta).dv

and therefore, can I manipulate this by e.g., adding a tensor function to it like:

F[0] += some_tensor_function

Answer 1

I believe your Pi is functional. Then F is linear form on mixed space (you did not give its designation so let's say W = MixedSpace([U, P, T])) for components u, p, theta.

Hence you can

• add another linear form corresponding to some subspace, let's say W.sub(0).sub(0) this way

  ux, vx = u[0], v[0]
  F += ux.dx(0)*vx*ds(42) # example, probably stupid
  

• assemble it and then you can access components of resulting vector corresponding to different subspaces of W in principle. This is not a practical way of doing something.

Comments

Thanks Jan, this makes sense to me and I'm sure I can extend it to do what I want. One more question though, did you mean to do W.sub(0).sub(0) or W.sub(0)?

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W.sub(0) is a velocity subspace and W.sub(0).sub(0) is a subspace of a first velocity component.