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!b_U_d3oTZckny15inoAStJf_DkxTjYjj_yN7UJJPIs82UiIP-TYpBuEhMzrLsOWU6-Zv4dvrTgU9VJWe_WVwhigemQ$ > ). 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
