Thanks for your response, David.
I guess I need to understand the definition of a scalar variable within the
context of libMesh. If I do
system.add_variable ("alpha", FIRST, SCALAR);
then, how many dofs are created for alpha? and are they distributed across the
mesh?
If I have N primary dofs, u_i (i=1,…,N), in the system, and M equations of the
form
f_j (u_i) = 0 (j=1,…,M)
then I would need M Lagrange multipliers. How would I go about adding them?
Would I have to do the following
for (unsigned int i=0; i<M; i++)
system.add_variable (name_of_i_th_multiplier, FIRST, SCALAR);
Thanks,
Manav
> On Apr 7, 2015, at 2:09 PM, David Knezevic <[email protected]> wrote:
>
> On Tue, Apr 7, 2015 at 2:55 PM, Manav Bhatia <[email protected]
> <mailto:[email protected]>> wrote:
> Hi,
>
> I am curious if anyone has any experience/thoughts about addition of
> Lagrange multipliers to handle multi body dynamic constraints.
>
> This would likely need addition of Lagrange variables associated with
> individual constraint equations, as opposed to the example problem (in source
> code) which uses Lagrange multiplier with the incompressible N-S equations,
> requiring a distributed scalar variable.
>
> Any thoughts on how this could be included in the libMesh framework?
>
>
> IIRC at the moment we assume that all dofs in the system can be involved in
> the constraint equation (i.e. SCALAR variables are coupled with all other
> dofs). That is the most general case, and as a result you should be able to
> impose whatever constraint equation you want using a SCALAR Lagrange
> mulitplier, no?
>
> We could be more efficient (i.e. allocate fewer dofs in the sparsity pattern)
> if we knew that the constraint was local to a few dofs. But that's just an
> optimization...
>
> Am I misinterpreting you here?
>
> David
>
>
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