[petsc-users] Saddle point problem with nested matrix and a relatively small number of Lagrange multipliers

[Matthew Knepley]

On Tue, Sep 8, 2020 at 12:43 PM Olivier Jamond <olivier.jamond at cea.fr>
wrote:

> Thanks for your answer, whereas being 'sad' to me! Do you have any idea
> how the structure FE code geared toward HPC deals with their Lagrange
> multipliers for their BCs?
>
I don't use Lagrange multipliers for Dirichlet conditions, just direct
modification of the approximation space.

> Do they 'accept' that cost?
>
If you have Lagrange multipliers, I think yes.

> To my understanding, I didn't know the Sherman-Morrison formula, and I am
> not sure to see how it applies to my case... Could you please help me on
> that?
>
SM is a formula for inverting a matrix + a rank-one addition. This looks
like your case with the Lagrange multiplier fixing one degree of freedom.

  Thanks,

     Matt

> Many thanks,
> Olivier
>
>
> I am not sure you can get around this cost. In this case, it reduces to
> the well-known
> Sherman-Morrison formula (
> https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula),
> which Woodbury generalized. It seems to have the same number of solves.
>
>
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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