Applying multigrid to one part of the domain

[Nihar Bhardwaj Darbhamulla]

I am trying to develop a Stokes-Darcy solver. In this regard, I would like to apply geometric multigrid as a preconditioner to the Darcy part of the domain. Overall, I'm treating the Stokes-Darcy system discretization using an hp::FECollection object, and attaching it to a dof handler. 

Following step-56, I would like to attach a darcy_dof_handler to the darcy degrees of freedom. However, this is not possible through the existing distribute_mg_dofs() functionality, as hp::FECollection is not supported through the DoFHandler. 

I can understand why applying geometric multigrid to a part of the existing grid would be challenging, as we do not discriminate between Cartesian and generalized domains within the deal.II framework. 

Are there any work-arounds which do not require me to setup dofs for the entire FESystem everywhere on the mesh, and apply constraints on individual parts of the domain?

[Peter Munch]

You can try out MGTransferGlobalCoarsening  (see https://dealii.org/developer/doxygen/deal.II/step_75.html). The infrastructure is quite flexible.

Best,
Peter

[Nihar Bhardwaj Darbhamulla]

I believe MGTransferGlobalCoarsening does not work with hp::FECollection. I use hp::FECollection for a variable number of dofs on two different parts of the domain. One part has Q2-Q1 elements, and the other has Q2 elements, with interface conditions. As an alternative, I have set up two triangulations with two dof_handlers. The only thing which remains is setting up the off-diagonal blocks which couple these matrices. How can I go about this ?

Nihar