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 <j...@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 <mail2amn...@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 <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!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 <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!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 <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 >
