Re: [Libmesh-users] Periodic BCs for unstructured mesh

[David K. <dav...@ak...>]

On Tue, Aug 7, 2018 at 9:07 AM, Bailey Curzadd <bcu...@gm...> wrote:

> Hi there,
>
> I'm using libMesh to calculate the homogenized properties of
> microstructures with cuboid unit cells. To do this, the boundaries of the
> unit cell require periodic boundary conditions. As far as I can tell,
> though, the PeriodicBoundary class only works with structured meshes, which
> isn't really a feasible option for me. Is this really the case, or have I
> just missed something in my implementation?
>

Good question. I don't recall if PeriodicBoundary requires matching meshes
or not, so I'll leave this part to someone else to answer definitively.



> Currently, I am manually mapping each constrained node on the "far"
> boundary to an element/side pair on the "near" boundary using
> PointLocatorBase and Elem::side_ptr()->contains_point(). Then, I use the
> penalty method to apply a constraint equation with coefficients found using
> FE<2,LAGRANGE>::shape().
>
> The issue I have at the moment most likely concerns preallocation of the
> system matrix. Calls to matrix->add_matrix() are taking a very long time,
> since the DofMap would obviously not expect a node on one side of the mesh
> to be coupled with the nodes on the opposite side. Is there a convenient
> way to make libMesh preallocate extra space beforehand, or does this need
> to be done manually? I'm using PETSc, but I'd like the code to stay
> solver-independent if possible.
>

You can augment the sparsity pattern by telling the system which extra dofs
to couple. For an example of this see miscellaneous_ex9.

Also, note that instead of using a penalty method, you can add dof
constraint rows to the system. This is what PeriodicBoundary does under the
hood.



> I've considered switching to the Lagrange multiplier method using 2
> additional field variables as was suggested for a question I posted earlier
> for a different project. However, this would add 2 DOFs to each node, and
> I'm not even sure this would circumvent the preallocation problem I have
> for the penalty method. Any suggestions concerning the best way to use
> libMesh for this problem would be appreciated.
>

I would not use Lagrange multipliers for this.

If PeriodicBoundary supports non-conforming meshes, then that would be the
best way. If not, then I'd suggest adding constraint rows yourself.

Best,
David