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!bc0A2Vc5CGCuDQuOVZRyBUNTEbK3NZvHNmZUECNwUBwJPj0Pvv0CW2rGfEzeSxVXdWkjCE-D5jl2sonSQN8$ 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!bc0A2Vc5CGCuDQuOVZRyBUNTEbK3NZvHNmZUECNwUBwJPj0Pvv0CW2rGfEzeSxVXdWkjCE-D5jl20dv2S0M$ Amneet Bhalla <mail2amn...@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 <mail2amn...@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!bc0A2Vc5CGCuDQuOVZRyBUNTEbK3NZvHNmZUECNwUBwJPj0Pvv0CW2rGfEzeSxVXdWkjCE-D5jl2BQDymOU$ >> ). 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 <j...@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 <mfad...@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 <mail2amn...@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 <mfad...@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 <mfad...@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 <mail2amn...@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
