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 <j...@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!ezw7zWJYwCHHUvoAmPZ4JT-HJ8l8V8aC3pq3VbTRke4EO6i5Z_AxjqmaJ1M_6BS6b99zSzfvl8FQIhZEjNHJ84-m6w$ > > > 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!ezw7zWJYwCHHUvoAmPZ4JT-HJ8l8V8aC3pq3VbTRke4EO6i5Z_AxjqmaJ1M_6BS6b99zSzfvl8FQIhZEjNFr-J8G0w$ > > > 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!ezw7zWJYwCHHUvoAmPZ4JT-HJ8l8V8aC3pq3VbTRke4EO6i5Z_AxjqmaJ1M_6BS6b99zSzfvl8FQIhZEjNFHB5gzxg$ > >> ). > 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 > -- --Amneet
