FE^2 (or computational homogenization)

Question

Hello,

I was successful in installing and running examples of FEniCS in Linux.

Now I wanted to test if I can extend some of the examples, let us say, a simple diffusion equation to solve a computational homogenization type problem. Specifically, I am looking at nested FE or FE^2,

I need to solve a microscale problem at every integration point, by transferring macroscopic gradient at the integration point as a boundary condition to the microscale and then to transfer back the tangent stiffness from the microscale to the macroscale.

Can someone give hints on:
a) how to loop through integration points
b) how to extract macroscopic gradients at the integration points
c) how to extract tangent matrix

Or has some of you already implemented FE^2 approach for any PDEs.

It will take me quite a while to figure this out, so I would be grateful if any one can give me a head start.

Thank you,
Sanny

Answer 1

Hi Sanny, this is not really an answer. I just posted a similar question some days ago and found this post from you. Have you already found the way of implementing the FE^2 in Fenics?
Cheers,
Jonathan