I finally found the answer to my problem. I was not wrongly imposing the
periodic boundary condition but rather was solving a problem (Poisson equation
with PBC), which has an infinite family of solutions. I was recommended to add
an artificial constraint or use a null-space-aware algebraic solver.
Are MUMPS and Hypre null-space-aware algebraic solvers? How can I turn that
option on?
Kind regards,
Karthik.
From: Matthew Knepley <knep...@gmail.com>
Date: Tuesday, 18 July 2023 at 17:22
To: Barry Smith <bsm...@petsc.dev>
Cc: Chockalingam, Karthikeyan (STFC,DL,HC)
<karthikeyan.chockalin...@stfc.ac.uk>, petsc-users@mcs.anl.gov
<petsc-users@mcs.anl.gov>
Subject: Re: [petsc-users] periodic boundary conditions
Jed creates the LocalToGlobal that does this elimination in plexsfc.c
Thanks,
Matt
On Tue, Jul 18, 2023 at 12:07 PM Barry Smith
<bsm...@petsc.dev<mailto:bsm...@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.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@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 <bsm...@petsc.dev<mailto:bsm...@petsc.dev>>
Date: Tuesday, 18 July 2023 at 16:58
To: Chockalingam, Karthikeyan (STFC,DL,HC)
<karthikeyan.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@stfc.ac.uk>>
Cc: Matthew Knepley <knep...@gmail.com<mailto:knep...@gmail.com>>,
petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>
<petsc-users@mcs.anl.gov<mailto:petsc-users@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@mcs.anl.gov<mailto:petsc-users@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 <knep...@gmail.com<mailto:knep...@gmail.com>>
Date: Tuesday, 18 July 2023 at 16:38
To: Chockalingam, Karthikeyan (STFC,DL,HC)
<karthikeyan.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@stfc.ac.uk>>
Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>
<petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>>
Subject: Re: [petsc-users] periodic boundary conditions
On Tue, Jul 18, 2023 at 11:18 AM Karthikeyan Chockalingam - STFC UKRI
<karthikeyan.chockalin...@stfc.ac.uk<mailto: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<mailto:knep...@gmail.com>>
Date: Tuesday, 18 July 2023 at 14:31
To: Chockalingam, Karthikeyan (STFC,DL,HC)
<karthikeyan.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@stfc.ac.uk>>
Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>
<petsc-users@mcs.anl.gov<mailto: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<mailto: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<mailto:karthikeyan.chockalin...@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/>
