On Tue, Apr 7, 2015 at 9:45 PM, grandrabbit <[email protected]> wrote:

> I see. But is there a way to remove the nulspace explicitly in libmesh
> other than forcing the presure value at one node, such as substraction the
> average pressure value?
>

This is what we do in systems_of_equations_ex3. In that case we constrain
the average value of the pressure, rather than pinning it at a single node.
The constraint is imposed using a SCALAR variable as a Lagrange multiplier.

David







>
> ------------------ Original ------------------
> From:  "Roy Stogner";<[email protected]>;
> Date:  Apr 7, 2015
> To:  "grandrabbit"<[email protected]>;
> Cc:  "libmesh-users"<[email protected]>;
> Subject:  Re: [Libmesh-users] Pin presure in lid-cavity case
>
>
>
>
> On Tue, 7 Apr 2015, grandrabbit wrote:
>
> > Later I found in systems_of_equations_ex2, even I comment out the part
> of pinning pressure,
> > the code still can give a reasonable cavity flow, any body can show me
> why? Thanks a lot.
>
> Without pinning the pressure, you have a non-invertible matrix.  But
> it's not an overconstrained system with no solutions, it's an
> underconstrained system with an infinity of solutions, and in that
> case many iterative linear solvers will still find some solution to
> the system, one in which the final values of any underconstrained
> modes are just indirectly determined by the initial iterate.
> ---
> Roy
>
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