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 > <[email protected]> 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 <[email protected] <mailto:[email protected]>> > Date: Tuesday, 18 July 2023 at 16:58 > To: Chockalingam, Karthikeyan (STFC,DL,HC) > <[email protected] > <mailto:[email protected]>> > Cc: Matthew Knepley <[email protected] <mailto:[email protected]>>, > [email protected] <mailto:[email protected]> > <[email protected] <mailto:[email protected]>> > 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 <[email protected] <mailto:[email protected]>> 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 <[email protected] <mailto:[email protected]>> > Date: Tuesday, 18 July 2023 at 16:38 > To: Chockalingam, Karthikeyan (STFC,DL,HC) > <[email protected] > <mailto:[email protected]>> > Cc: [email protected] <mailto:[email protected]> > <[email protected] <mailto:[email protected]>> > Subject: Re: [petsc-users] periodic boundary conditions > > On Tue, Jul 18, 2023 at 11:18 AM Karthikeyan Chockalingam - STFC UKRI > <[email protected] > <mailto:[email protected]>> 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 <[email protected] <mailto:[email protected]>> > Date: Tuesday, 18 July 2023 at 14:31 > To: Chockalingam, Karthikeyan (STFC,DL,HC) > <[email protected] > <mailto:[email protected]>> > Cc: [email protected] <mailto:[email protected]> > <[email protected] <mailto:[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]> > > <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/>
