On Tue, Jul 18, 2023 at 11:18 AM Karthikeyan Chockalingam - STFC UKRI < karthikeyan.chockalin...@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 <knep...@gmail.com> > *Date: *Tuesday, 18 July 2023 at 14:31 > *To: *Chockalingam, Karthikeyan (STFC,DL,HC) < > karthikeyan.chockalin...@stfc.ac.uk> > *Cc: *petsc-users@mcs.anl.gov <petsc-users@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@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.chockalin...@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/>