[petsc-users] Rigid body nullspace for Stokes operator

Thu Oct 31 06:41:20 CDT 2024

Just note, GAMG uses these near null space vectors but hypre does not as
far as I know.
Hypre does do elasticity so I would just stick with hypre if you just want
to solve your problem (and move on)

On Thu, Oct 31, 2024 at 1:01 AM Jed Brown <jed at jedbrown.org> wrote:

> There is MatSetNearNullSpace, which is used to ensure an approximation
> property in coarse levels of multigrid. That should always be set when
> dealing with problems like this, regardless of boundary conditions.
> Separately, there is MatSetNullSpace, which you should only use if you are
> solving a singular system with that null space.
>
> Note that you need at least three non-colinear points to constrain the
> null space so if you, for example, have a Dirichlet condition at only one
> point or along one straight line, there will still be a null space.
>
> Amneet Bhalla <mail2amneet at gmail.com> writes:
>
> > I think Mark mentioned this earlier, but I want to make sure that the
> rigid
> > body null vectors should be specified only when Neumann boundary
> conditions
> > are used on all boundaries of the domain, correct? Alternatively, if a
> > Dirichlet boundary condition is used (on any part of the domain boundary)
> > then there is no null space, i.e., the operator is a full rank matrix?
> >
> > If the above is true, then I think I do not need to specify the rigid
> body
> > null modes because I am using Dirichlet boundary conditions for the
> > velocity solver.
> >
> > On Wed, Oct 30, 2024 at 12:28 PM Jed Brown <jed at jedbrown.org> wrote:
> >
> >> Yes to 6 null vectors in 3D, 3 null vectors in 2D. The center of mass
> does
> >> not need to be identified because you can algebraically orthogonalize
> >> (lines 411-420 here).
> >>
> >>
> >>
> https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/dm/impls/plex/plexfem.c?ref_type=heads*L377-425__;Iw!!G_uCfscf7eWS!b0T54ExhpyMjL9O-B63FmKcfUHpYoH0-ixjUnroOoB0PZPSEVH2-LEMb_Yw57sybhA0rknBisFM2erfwfjN2syg$ 
> >>
> >> See also this implementation with raw coordinates. GAMG orthogonalizes
> >> within each aggregate (in a later phase of the algorithm) so global
> >> orthogonalization is not necessary.
> >>
> >>
> >>
> https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/ksp/pc/impls/gamg/agg.c?ref_type=heads*L387__;Iw!!G_uCfscf7eWS!b0T54ExhpyMjL9O-B63FmKcfUHpYoH0-ixjUnroOoB0PZPSEVH2-LEMb_Yw57sybhA0rknBisFM2erfw3-yhJ68$ 
> >>
> >> Amneet Bhalla <mail2amneet at gmail.com> writes:
> >>
> >> > I think the nullspace for the velocity operator is of the form
> >> >
> >> > vnull = U + ω × r
> >> > in which U is a rigid body velocity and ω is the rigid body rotational
> >> > velocity, and r is the radius vector from the center of mass. I
> believe I
> >> > need to construct 6 nullspace vectors in 3D and 3 nullspace vectors in
> >> 2D.
> >> > Sounds correct? Also does the center of mass coordinates matter when
> >> > defining r?
> >> >
> >> > On Wed, Oct 30, 2024 at 7:53 AM Amneet Bhalla <mail2amneet at gmail.com>
> >> wrote:
> >> >
> >> >> @Mark: Is there some document/paper that I can follow to check the
> >> algebra
> >> >> of these zero eigenvectors/null space modes?
> >> >>
> >> >> @Jed : We use a projection method preconditioner to solve the coupled
> >> >> velocity pressure system as described here (
> >> >> https://urldefense.us/v3/__https://www.sciencedirect.com/science/article/pii/S0021999123004205__;!!G_uCfscf7eWS!b0T54ExhpyMjL9O-B63FmKcfUHpYoH0-ixjUnroOoB0PZPSEVH2-LEMb_Yw57sybhA0rknBisFM2erfwvAPghoI$ 
> ).
> >> It
> >> >> is an approximation of the Schur complement. As a part of projection
> >> >> preconditioner, we need to solve just the momentum equation
> separately
> >> >> without considering the pressure part.
> >> >>
> >> >> On Tue, Oct 29, 2024 at 8:03 PM Jed Brown <jed at jedbrown.org> wrote:
> >> >>
> >> >>> And to be clear, we recommend using fieldsplit Schur to separate the
> >> >>> pressure and velocity part (there are many examples). Applying AMG
> >> directly
> >> >>> to the saddle point problem will not be a good solver because the
> >> >>> heuristics assume positivity and do not preserve inf-sup stability
> >> (nor do
> >> >>> standard smoothers).
> >> >>>
> >> >>> Mark Adams <mfadams at lbl.gov> writes:
> >> >>>
> >> >>> > This is linear elasticity and there are 6 "null" vectors (if you
> >> removed
> >> >>> > Dirichlet boundary conditions these are eigenvectors with zero
> >> >>> eigenvalue):
> >> >>> > 3 translations, x, y, z, and three rotatiions xx, yy ,zz.
> >> >>> > x = (1,0,0,1,0,0,1,0 ...)
> >> >>> > and xx is something like (0, z_1, -y_1, 0, z_2, -y_2, ...) where
> z_1
> >> is
> >> >>> the
> >> >>> > z coordinate of the first vertex, etc.
> >> >>> >
> >> >>> > Mark
> >> >>> >
> >> >>> > On Tue, Oct 29, 2024 at 3:47 PM Amneet Bhalla <
> mail2amneet at gmail.com
> >> >
> >> >>> wrote:
> >> >>> >
> >> >>> >> Hi Mark,
> >> >>> >>
> >> >>> >> Thanks! I am not sure how to construct null space and zero energy
> >> modes
> >> >>> >> manually for this operator. Is there some theory or
> documentation I
> >> can
> >> >>> >> follow to figure out what the null space and zero energy modes
> look
> >> >>> like
> >> >>> >> for this operator? Once I know what these are in symbolic form, I
> >> >>> think I
> >> >>> >> should be able to construct them manually.
> >> >>> >>
> >> >>> >> Best,
> >> >>> >> --Amneet
> >> >>> >>
> >> >>> >> On Tue, Oct 29, 2024 at 7:35 AM Mark Adams <mfadams at lbl.gov>
> wrote:
> >> >>> >>
> >> >>> >>> Oh my mistake. You are using staggered grids. So you don't have
> a
> >> >>> block
> >> >>> >>> size that hypre would use for the "nodal" methods.
> >> >>> >>> I'm not sure what you are doing exactly, but try hypre and you
> >> could
> >> >>> >>> create the null space, zero energy modes, manually, attach to
> the
> >> >>> matrix
> >> >>> >>> and try GAMG.
> >> >>> >>> You can run with '-info :pc' and grep on GAMG to see if GAMG is
> >> >>> picking
> >> >>> >>> the null space up (send this output if you can't figure it out).
> >> >>> >>>
> >> >>> >>> Thanks,
> >> >>> >>> Mark
> >> >>> >>>
> >> >>> >>> On Tue, Oct 29, 2024 at 9:28 AM Mark Adams <mfadams at lbl.gov>
> >> wrote:
> >> >>> >>>
> >> >>> >>>> This coordinate interface is just a shortcut for vertex based
> >> >>> >>>> discretizations with 3 dof per vertex, etc. (maybe works in
> 2D).
> >> >>> >>>> You will need to construct the null space vectors manually and
> >> >>> attach it
> >> >>> >>>> to the matrix. Used by GAMG.
> >> >>> >>>>
> >> >>> >>>> Note, for hypre you want to use the "nodal" options and it does
> >> not
> >> >>> use
> >> >>> >>>> these null space vectors. That is probably the way you want to
> go.
> >> >>> >>>> eg: -pc_hypre_boomeramg_nodal_coarsen
> >> >>> >>>>
> >> >>> >>>> I would run with hypre boomerang and -help and grep on nodal to
> >> see
> >> >>> all
> >> >>> >>>> the "nodal" options and use them.
> >> >>> >>>>
> >> >>> >>>> Thanks,
> >> >>> >>>> Mark
> >> >>> >>>>
> >> >>> >>>>
> >> >>> >>>> On Mon, Oct 28, 2024 at 8:06 PM Amneet Bhalla <
> >> mail2amneet at gmail.com
> >> >>> >
> >> >>> >>>> wrote:
> >> >>> >>>>
> >> >>> >>>>> Hi Folks,
> >> >>> >>>>>
> >> >>> >>>>> I am trying to solve the momentum equation in a projection
> >> >>> >>>>> preconditioner using GAMG or Hypre solver. The equation looks
> >> like
> >> >>> for
> >> >>> >>>>> velocity variable *v* looks like:
> >> >>> >>>>>
> >> >>> >>>>>
> >> >>> >>>>>  [image: Screenshot 2024-10-28 at 4.15.17 PM.png]
> >> >>> >>>>>
> >> >>> >>>>> Here, μ is spatially varying dynamic viscosity and λ is
> spatially
> >> >>> >>>>> varying bulk viscosity. I understand that I need to specify
> rigid
> >> >>> body
> >> >>> >>>>> nullspace modes to the multigrid solver in order to accelerate
> >> its
> >> >>> >>>>> convergence. Looking into this routine
> >> >>> MatNullSpaceCreateRigidBody() (
> >> >>> >>>>>
> >> >>>
> >>
> https://urldefense.us/v3/__https://petsc.org/release/manualpages/Mat/MatNullSpaceCreateRigidBody/__;!!G_uCfscf7eWS!bVR6duCoDqPhZrWS-sm1c5qxsFPjZMhdT86AqLpPzWgVy5qoRhd4_Jue2LJOIS6LRrtV2cHGrqger1Yvb-Y5f-0$
> >> >>> >>>>> <
> >> >>>
> >>
> https://urldefense.us/v3/__https://petsc.org/release/manualpages/Mat/MatNullSpaceCreateRigidBody/__;!!G_uCfscf7eWS!eKqgIJjCdMzIU76f7X65AmGxrU_-lC7W02BMWafJ77DNf_IuQk6O1X3qU1x9Ez8NJ20vZEL-mF6T1yNmDnwv0eWa2w$
> >> >>> >),
> >> >>> >>>>> I see that I need to provide the coordinates of each node. I
> am
> >> >>> using
> >> >>> >>>>> staggered grid discretization. Do I need to provide
> coordinates
> >> of
> >> >>> >>>>> staggered grid locations?
> >> >>> >>>>>
> >> >>> >>>>> Thanks,
> >> >>> >>>>> --
> >> >>> >>>>> --Amneet
> >> >>> >>>>>
> >> >>> >>>>>
> >> >>> >>>>>
> >> >>> >>>>>
> >> >>> >>
> >> >>> >> --
> >> >>> >> --Amneet
> >> >>> >>
> >> >>> >>
> >> >>> >>
> >> >>> >>
> >> >>>
> >> >>
> >> >>
> >> >> --
> >> >> --Amneet
> >> >>
> >> >>
> >> >>
> >> >>
> >> >
> >> > --
> >> > --Amneet
> >>
> >
> >
> > --
> > --Amneet
>
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