# [petsc-users] Preconditioner for stokes flow with mixed boundary conditions.

Abhinav Singh abhinavrajendra at gmail.com
Mon Apr 19 08:37:23 CDT 2021

>
> What does this mean? Stokes means using an incompressibility constraint,
> for which we often introduce a pressure.

Yes, what I mean is solving the momentum block, say with known pressure.
viscosity is constant however, the momentum equation has both Laplacian and

You should use a good Laplacian preconditioner, like -pc_type gamg or
> -pc_type ml.

I tried gamg and it seems to diverge as the solution is NaN. The KSP
residual message is " 0 KSP Residual norm 1.131782747169e+01  ".
When using -pc_type ml, I get Aggregate Warning and then some faulty

On Mon, 19 Apr 2021 at 12:31, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Apr 19, 2021 at 6:18 AM Abhinav Singh <abhinavrajendra at gmail.com>
> wrote:
>
>> Hello all,
>>
>> I am trying to solve for incompressible stokes flow on a particle based
>> discretization. I use a pressure correction technique along with Particle
>> strength exchange like operators.
>>
>> I call Petsc to solve the Stokes Equation without the pressure term.
>>
>
> What does this mean? Stokes means using an incompressibility constraint,
> for which we often introduce a pressure.
>
> Do you mean you are solving only the momentum block? If so, do you have a
> constant viscosity? If so, then this is just the Laplace equation.
> You should use a good Laplacian preconditioner, like -pc_type gamg or
> -pc_type ml.
>
>   Thanks
>
>      Matt
>
>
>> GMRES usually works great but with dirichlet boundary conditions. When I
>> use a mixed boundary condition in Y, (dirichlet on bottom and Neumann on
>> the top) with periodicity in X,Z. GMRES fails converge when the size of
>> matrix increases. For smaller size (upto 27*27*5), only GMRES works and
>> that too only with the option 'pc_type none'. I was unable to find any
>> preconditioner which worked. Eventually, it also fails for bigger size.
>> UMFPACK works but LU decomposition fails after a certain size and is very
>> slow.
>>
>> It would be great if you could suggest a way or a preconditioner which
>> suits this problem.
>>
>> Kind regards,
>> Abhinav
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their