Multiscale implementation

Question

How can I implement a simple multiscale problem using C++ code and FEniCS?

The idea is to solve a mechanical problem (e.g hyperelasticity or plasticity). The solution should be done in the complete domain (macroscale) with the particularity that the coefficients of the second order term will come from the averaged solution of the same PDE in a mesh representing the local environment of every single quadrature point.

The local solution will have a higher resolution and will capture small oscillations from the microscale nature.

There exist enough algorithmic ideas by Kouznetsova, Babuska, Feyel and others (fast search using keywords homogenization, FE^2 gives enough ideas), but my question is more about a practical implementation using FEniCS.

Is anyone working on simmilar models?

Comments

Hi Jonathan,

I'm also working on a micro-macroscale-problem in the moment and i hope to be able to do the implementation in FEniCS. So, have you found something that helped you??

Best regards,
Lisa

Answer 1

Did you find some hints? I'm just starting to use fenics for a multiscale problem and I wonder how to best calculate a corrector, where the microscale behaviour computed in a representative unit cell needs to be added to the solution of the homogeneous problem, computed on coarse grid and big domain..