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 > > > >
