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 <[email protected]> Date: Tuesday, 18 July 2023 at 14:31 To: Chockalingam, Karthikeyan (STFC,DL,HC) <[email protected]> Cc: [email protected] <[email protected]> Subject: Re: [petsc-users] periodic boundary conditions On Tue, Jul 18, 2023 at 9:02 AM Karthikeyan Chockalingam - STFC UKRI via petsc-users <[email protected]<mailto:[email protected]>> 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 [email protected]<mailto:[email protected]> [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/>
