# [petsc-users] periodic boundary conditions

Karthikeyan Chockalingam - STFC UKRI karthikeyan.chockalingam at stfc.ac.uk
Tue Jul 18 10:18:10 CDT 2023

```Thanks Matt.

The mesh is structured (rectilinear), so it is periodic in that sense.

Can you please explain how I can impose it strongly?

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<mailto: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

Kind regards,
Karthik.

--
Dr. Karthik Chockalingam
High Performance Software Engineering Group
Hartree Centre | Science and Technology Facilities Council
karthikeyan.chockalingam at stfc.ac.uk<mailto:karthikeyan.chockalingam at stfc.ac.uk>

[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/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20230718/8226a86d/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image001.png
Type: image/png
Size: 18270 bytes
Desc: image001.png
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20230718/8226a86d/attachment-0001.png>
```