On 6/24/19 3:59 AM, Félix Bunel wrote:
> 
> Fortunately for me, the dealII doc has an answer for everything

:-)


> 1 - Is there a simpler way to solve my stokes problem than using a Schur 
> Preconditioner and the augmented lagrangian method ?

There are plenty of simpler methods, such as just using a direct solver for 
the matrix, or using some kind of ILU decomposition as a preconditioner. The 
problem is just that these are not very efficient (ILU) or don't scale to 
large problems (direct solvers) or don't easily work in parallel (both). But 
if all you want to do is play with the equations, then start with a direct 
solver and replace it by something else when you go to large problems where 
the direct solver is no longer sufficient. I often advise to use the direct 
solver in the beginning because it's a 5-line piece of code that always work.


> 2 - Will the augmented Lagrangien Method also works for my terms ? I don't 
> see 
> an issue from the theory... In the tutorial and in the paper referenced it's 
> used to solve the antisymetric terms that comes from the advectiv terms.

I don't know enough about this topic to say for sure, but my understanding is 
that the penalty term step-57 is adding just improve the spectrum of the 
matrix to make the (iterative) solver more efficient. This may or may not work 
for your equations -- it's worth playing with it.


> 3 - In my case I have eta  = 1 in comparison to step 57 ?

Yes.


> 4 - I don't understand how I should choose the gamma parameter and why its 
> value does not change the results of the resolution. In step 57, it's value 
> is 
> set to 1 and does not change at all...

I don't know enough about that as well. You might want to look into Timo 
Heister's PhD thesis.


> 5 - Why is the Stokes FE is always set to :
>      stokes_fe(FE_Q<2>(degree+1), 2,
>                FE_Q<2>(degree), 1)
> 
> 
> Can it work with  :
> 
>      stokes_fe(FE_Q<2>(degree), 2,
>                FE_Q<2>(degree), 1)

You will want to read up on the theory of saddle point problems (of which the 
Stokes system is one). There, it is necessary to satisfy the so-called inf-sup 
(or LBB, or Babuska-Brezzi) condition for the solution to be stable. Using the 
first of the choice above, this condition is satisfied, but for the second 
choice it is not.


> I'm asking this because my main interest is in phi and with the degree+1, I 
> have 8 times more dofs describing the flow than the ones describing phi.

Then use degree+1 for phi as well :-) That's what we do in several of our codes.

Best
  W.


-- 
------------------------------------------------------------------------
Wolfgang Bangerth          email:                 [email protected]
                            www: http://www.math.colostate.edu/~bangerth/

-- 
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see 
https://groups.google.com/d/forum/dealii?hl=en
--- 
You received this message because you are subscribed to the Google Groups 
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To view this discussion on the web visit 
https://groups.google.com/d/msgid/dealii/5ed53f3b-d29f-a0ef-8981-7af82ec32c2d%40colostate.edu.
For more options, visit https://groups.google.com/d/optout.

Reply via email to