On Tue, Apr 7, 2015 at 3:16 PM, Manav Bhatia <[email protected]> wrote:
> 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?
>
SCALAR FIRST gives you one dof, SCALAR SECOND gives you two dofs, etc. So
setting the order is one way to add multiple Lagrange multipliers.
> and are they distributed across the mesh?
>
I would say that SCALAR dofs aren't really related to the mesh at all, they
just allow you to add extra dofs to your system (which is of course good
for imposing constraints via Lagrange multipliers).
> 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);
>
>
Yes, that should work.
David
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]> 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
------------------------------------------------------------------------------
BPM Camp - Free Virtual Workshop May 6th at 10am PDT/1PM EDT
Develop your own process in accordance with the BPMN 2 standard
Learn Process modeling best practices with Bonita BPM through live exercises
http://www.bonitasoft.com/be-part-of-it/events/bpm-camp-virtual- event?utm_
source=Sourceforge_BPM_Camp_5_6_15&utm_medium=email&utm_campaign=VA_SF
_______________________________________________
Libmesh-users mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/libmesh-users
