[petsc-users] Stokes-Brinkmann equation preconditioner

[Matthew Knepley]

On Thu, Oct 3, 2019 at 6:34 PM Salazar De Troya, Miguel via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> I am trying to solve the Stokes equation with the Brinkman term to
> simulate a solid material. My intention is to implement the preconditioner
> in this paper: https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.426
> <https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.426section%202.6>
> (section 2.6)
>

Link does not work for me.


> where they solve for the velocity and substitute that expression in the
> pressure equation. They end up solving a system of the type B K^-1 B^T,
> i.e. the Schur complement of the problem. For this system of equations,
> they argue that the preconditioner in page 11 is perfect for a given
> constant Brinkman penalty term.
>
>
>
> Because I am solving for velocity and pressure without doing any
> substitution, I thought I could use a PC fieldsplit type Schur (full
> factorization)
>

Yes, this will form the exact factorization and a matrix-free form of the
Schur complement.


> and provide the preconditioner in the paper to solve the Schur complement.
>

Yes, you can provide a user-defined PC for the Schur complement.


> My question is, should I provide this preconditioner through
> PCFieldSplitSetSchurPre or through fieldsplit_1_pc_type (probably through
> the Firedrake interface as in
> https://www.firedrakeproject.org/demos/stokes.py.html) ?
>

The name PCFieldSplitSetSchurPre seems to be very misleading. You do not
use it to provide a _preconditioner_. You use it to determine
the _preconditioning matrix_ from which the actual preconditioner is built.
The preconditioner itself is defined using -fieldpslit_1_pc_type.
Since I do not know what the preconditioner looks like, I cannot say what
preconditioner matrix you would want. Since Firedrake can construct
any operator for you, you might not care about the matrix we pass to you.

  Thanks,

    Matt


> Thanks
>
> Miguel
>
>
>
> Miguel A. Salazar de Troya
>
> Postdoctoral Researcher, Lawrence Livermore National Laboratory
>
> B141
>
> Rm: 1085-5
>
> Ph: 1(925) 422-6411
>


-- 
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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