How can I add curl conforming boundary constraints to the Multigrid transfer matrices?

[Julian Roth]

Dear all,

I was trying to solve the Eddy Current Problem with Multigrid.

I have curl-conforming boundary constraints, i.e. n x u = 0.

I managed to apply these to the system matrix via

VectorTools::project_boundary_values_curl_conforming_l2()

Unlike step-16 where the same approach has been demonstrated for the LaplaceProblem, I didn't find any method,

which allows me to apply the before mentioned boundary constraints to the MGConstrainedDoFs object.

Thus I computed the curl conforming constraints in assemble_multigrid, when I instantiated the boundary_constraints on each level.

The matrix on the finest grid is the same as the system matrix, which means that my workaround should have worked.

How can I apply my boundary constraints to the transfer matrices between the level meshes, if they are not contained in MGConstrainedDoFs?

Currently I am still using:

MGTransferPrebuilt<VectorType> mg_transfer(mg_constrained_dofs);
mg_transfer.build_matrices(dof_handler);

Obviously this isn't correct though, since the boundary constraints haven't been accounted for.

How can I add curl conforming boundary constraints to the transfer matrices?

Is there any other way that I can deal with the curl conforming boundary conditions, when I am working with Multigrid?

Kind regards,

Julian

P.S. Note that my Multigrid approach is not MatrixFree. Thus I don't think that I can use

MGConstrainedDoFs.add_user_constraints()

since this only applies to MatrixFree methods.

[Timo Heister]

Hi Julian,

you will need to extend MGTransferPrebuilt::prolongate with support for user constraints:

https://github.com/dealii/dealii/blob/70455cc1efde9ad0d5ca4295ea5597fc2fa98171/source/multigrid/mg_transfer_prebuilt.cc#L93

This might be as simple as a call to

  get_user_constraint_matrix(...).distribute(vector)

Can you try and report back?

[Julian Roth]

Hi Timo,

I tried your proposed solution and it looks like the iteration numbers of GMG are similar to what one would expect from the literature.

I will do a more in depth analysis of the results tomorrow, but so far the results look very promising.

Thank you very much!

[Julian Roth]

Hi TImo,

overall I am very happy with the results and I am quite confident that with your advice my Multigrid algorithm now works for the Eddy Current problem.

THANK YOU!

[Timo Heister]

Great, can I convince you to send in a pull request with your changes to deal.II? That would be very much appreciated.
Let us know if you need help with that.

[Julian Roth]

Yes, I will do that and let you know, if I have problems with that

[Julian Roth]

I created a pull request. However, I don't understand why the Travis CI check fails...

On Saturday, May 23, 2020 at 4:53:05 AM UTC+2, Timo Heister wrote: