[petsc-users] periodic boundary conditions

[Matthew Knepley]

On Tue, Jul 18, 2023 at 11:18 AM Karthikeyan Chockalingam - STFC UKRI <
karthikeyan.chockalingam at stfc.ac.uk> wrote:

> Thanks Matt.
>
>
>
> The mesh is structured (rectilinear), so it is periodic in that sense.
>
>
>
> Can you please explain how I can impose it strongly?
>

Strongly means make those variables equal in a pointwise sense. We do this
in the
LocalToGlobal mapping, so one set is eliminated in the global problem.

  Thanks,

    Matt


> My initial thought was to come up with a relation between the periodic
> nodes:
>
>
>
> x = P x’
>
>
>
> Say for 1-D problem with two elements
>
> (1)-------------(2)------------(3)
>
>
>
> P = [1 0, 0 1, 1 0]
>
> x = [x1 x2 x3]
>
> x’ = [x1 x2]
>
>
>
> and solve
>
> [P^T A P] x’ = P^T b
>
>
>
> I don’t think [P^T A P] is deterministic.
>
>
>
> Kind regards,
>
> Karthik.
>
>
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Tuesday, 18 July 2023 at 14:31
> *To: *Chockalingam, Karthikeyan (STFC,DL,HC) <
> karthikeyan.chockalingam at stfc.ac.uk>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] periodic boundary conditions
>
> On Tue, Jul 18, 2023 at 9:02 AM Karthikeyan Chockalingam - STFC UKRI via
> petsc-users <petsc-users at mcs.anl.gov> wrote:
>
> Hello,
>
>
>
> This is exactly not a PETSc question. I am solving a Poisson equation
> using finite elements. I would like to impose PBC. I am thinking of using
> the Lagrange multiplier method to impose them as constraints. Or do you
> think I could take an alternative approach?
>
>
>
> There are several options:
>
>
>
> 1) Just make a periodic mesh. This is what Plex does by default.
>
>
>
> 2) Impose the conditions strongly. This is what is done if you create the
> ZBox shape in Plex.
>
>
>
> 3) Impose the conditions weakly. This is what you are doing with Lagrange
> multipliers. You could
>
> also do a Nitsche boundary condition for this.
>
>
>
> Since the constraint is so simple, I do not see an advantage to imposing
> it weakly.
>
>
>
>   Thanks,
>
>
>
>      Matt
>
>
>
> Thank you for your help.
>
>
>
> Kind regards,
>
> Karthik.
>
>
>
> --
>
> *Dr. Karthik Chockalingam*
>
> High Performance Software Engineering Group
>
> Hartree Centre | Science and Technology Facilities Council
>
> karthikeyan.chockalingam at stfc.ac.uk
>
>
>
>  [image: signature_3970890138]
>
>
>
>
>
>
> --
>
> 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/>
>


-- 
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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