[petsc-users] periodic boundary conditions

[Matthew Knepley]

Jed creates the LocalToGlobal that does this elimination in plexsfc.c

  Thanks,

     Matt

On Tue, Jul 18, 2023 at 12:07 PM Barry Smith <bsmith at petsc.dev> wrote:

>
>    They are never really "eliminated" because extra copies in the global
> vector never exist.
>
> On Jul 18, 2023, at 12:03 PM, Karthikeyan Chockalingam - STFC UKRI <
> karthikeyan.chockalingam at stfc.ac.uk> wrote:
>
> Thank you, Barry. I am using the MPIAIJ format for a Finite Element
> application. So, I am trying to understand what is implemented in DMDA to
> eliminate those extra nodes.
>
> Best,
> Karthik.
>
>
> *From: *Barry Smith <bsmith at petsc.dev>
> *Date: *Tuesday, 18 July 2023 at 16:58
> *To: *Chockalingam, Karthikeyan (STFC,DL,HC) <
> karthikeyan.chockalingam at stfc.ac.uk>
> *Cc: *Matthew Knepley <knepley at gmail.com>, petsc-users at mcs.anl.gov <
> petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] periodic boundary conditions
>
>    If you are using DMDA with periodic boundary conditions for example
> only one "copy" of such nodes exists in the global vector (the vector the
> solvers see) so one does not need to eliminate extra ones
>
>
> On Jul 18, 2023, at 11:51 AM, Karthikeyan Chockalingam - STFC UKRI via
> petsc-users <petsc-users at mcs.anl.gov> wrote:
>
> Yes, I clearly understand I need to eliminate one set of periodic nodes. I
> was hoping to use x = P x’ to eliminate one set. It is a kind of mapping.
>
> Sorry, I am not sure if it is the LocalToGlobal mapping you are referring
> to. Is there an example or reference to show how the LocalToGlobal
> mapping is being used to impose PBC?
>
> Best,
> Karthik.
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Tuesday, 18 July 2023 at 16:38
> *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 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
>
>  <image001.png>
>
>
>
>
> --
> 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/>
>
>
>

-- 
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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