[petsc-users] Rigid body nullspace for Stokes operator

[Mark Adams]

Interesting. I have seen hypre do fine on elasticity, but do you know if
boomeramg (classical) uses these vectors or is there a smoothed aggregation
solver in hypre?

On Thu, Oct 31, 2024 at 8:32 AM Pierre Jolivet <pierre at joliv.et> wrote:

>
>
> On 31 Oct 2024, at 12:41 PM, Mark Adams <mfadams at lbl.gov> wrote:
>
> Just note, GAMG uses these near null space vectors but hypre does not as
> far as I know.
>
>
> They do:
> https://urldefense.us/v3/__https://petsc.org/release/src/ksp/pc/impls/hypre/hypre.c.html*line266__;Iw!!G_uCfscf7eWS!fgZ28yXAXjJBIqd4SxJehY7SSaYVe_YNHPW4QnnTewSSOxFsPPcBZFPv6Y2IT8PkI3SDEARmixD85cmswwWL0Vk$ 
>
> Thanks,
> Pierre
>
> 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!fgZ28yXAXjJBIqd4SxJehY7SSaYVe_YNHPW4QnnTewSSOxFsPPcBZFPv6Y2IT8PkI3SDEARmixD85cms_bElxqQ$ 
>> <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$>
>> >>
>> >> See also this implementation with raw coordinates. GAMG orthogonalizes
>> >> within each aggregate (in a later phase of the algorithm) so global
>> >> orthogonalization is not necessary.
>> >>
>> >>
>> >>
>> https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/ksp/pc/impls/gamg/agg.c?ref_type=heads*L387__;Iw!!G_uCfscf7eWS!fgZ28yXAXjJBIqd4SxJehY7SSaYVe_YNHPW4QnnTewSSOxFsPPcBZFPv6Y2IT8PkI3SDEARmixD85cmsTsohckA$ 
>> <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$>
>> >>
>> >> Amneet Bhalla <mail2amneet at gmail.com> writes:
>> >>
>> >> > I think the nullspace for the velocity operator is of the form
>> >> >
>> >> > vnull = U + ω × r
>> >> > in which U is a rigid body velocity and ω is the rigid body
>> rotational
>> >> > velocity, and r is the radius vector from the center of mass. I
>> believe I
>> >> > need to construct 6 nullspace vectors in 3D and 3 nullspace vectors
>> in
>> >> 2D.
>> >> > Sounds correct? Also does the center of mass coordinates matter when
>> >> > defining r?
>> >> >
>> >> > On Wed, Oct 30, 2024 at 7:53 AM Amneet Bhalla <mail2amneet at gmail.com
>> >
>> >> wrote:
>> >> >
>> >> >> @Mark: Is there some document/paper that I can follow to check the
>> >> algebra
>> >> >> of these zero eigenvectors/null space modes?
>> >> >>
>> >> >> @Jed : We use a projection method preconditioner to solve the
>> coupled
>> >> >> velocity pressure system as described here (
>> >> >> https://urldefense.us/v3/__https://www.sciencedirect.com/science/article/pii/S0021999123004205__;!!G_uCfscf7eWS!fgZ28yXAXjJBIqd4SxJehY7SSaYVe_YNHPW4QnnTewSSOxFsPPcBZFPv6Y2IT8PkI3SDEARmixD85cmswf1ygKo$ 
>> <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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