Re: [Libmesh-users] Non-symmetric constrained element matrices in case of recursive constraints

[Roy S. <roy...@ic...>]

On Sun, 14 Jan 2018, Jonas Ballani wrote:

> I have a question regarding constrained dofs that are themselves constrained by other dofs within the same element. Apparently, this leads to a non-symmetric constrained element matrix which I illustrate here by a small example:
>
> I consider an element with dof indices = (0,1,2,3). I impose the following contraint rows
>
> {
>  constrained_dof_index = 0;
>  constraint_row[1] = 1.0;
>  constraint_row[2] = -1.0;
> }
> {
>  constrained_dof_index = 1;
>  constraint_row[0] = 1.0;
>  constraint_row[3] = -1.0;
> }

So x0 = x1 - x2 is the first constraint, and
x1 = x0 - x3 is the second constraint?

You're constraining DoF 0 in terms of DoF 1, *and* you're constraining
DoF 1 in terms of DoF 0?

I'm afraid we don't support constraint equations with cycles.  You can
have a sequence in which you constrain a DoF with respect to a second
DoF which is itself constrained with respect to a third DoF and so on
indefinitely, *except* that you can never end up at a constraint which
was already referenced earlier in that sequence.

I don't think that limitation would be easy to change, either.  It
would turn DofMap::enforce_constraints_exactly() from a simple sweep
into an outright linear solve.
---
Roy