Hi Mark, I would like to try GAMG on some of my linear solves. Could you suggest how to get started? Is it more complicated than something like:
-ksp_type cg -pc_type gamg I'm guessing I should first try it on one of my easier linear solves. I have 5 of them that would have a block size of 1. Are the other GAMG option defaults good to start with or should I be trying to configure them as well? If so, I'm not familiar enough with multigrid to know off hand how to do that. Thanks, Dave Mark F. Adams writes: > > On Dec 2, 2011, at 6:06 PM, Dave Nystrom wrote: > > > Mark F. Adams writes: > >> It sounds like you have a symmetric positive definite systems like du/dt - > >> div(alpha(x) grad)u. The du/dt term makes the systems easier to solve. > >> I'm guessing your hard system does not have this mass term and so is > >> purely elliptic. Multigrid is well suited for this type of problem, but > >> the vector nature requires some thought. You could use PETSc AMG -pc_type > >> gamg but you need to tell it that you have a system of two dof/vertex. > >> You can do that with something like: > >> > >> ierr = MatSetBlockSize( mat, 2 ); CHKERRQ(ierr); > >> > >> For the best results from GAMG you need to give it null space information > >> but we can worry about that later. > > > > Hi Mark, > > > > I have been interested in trying some of the multigrid capabilities in > > petsc. I'm not sure I remember seeing GAMG so I guess I should go look for > > that. > > GAMG is pretty new. > > > I have tried sacusp and sacusppoly but did not get good results on > > this particular linear system. > > In particular, sacusppoly seems broken. I > > can't get it to work even with the petsc > > src/ksp/ksp/examples/tutorials/ex2.c > > example. Thrust complains about an invalid device pointer I believe. > > Anyway, I can get the other preconditioners to work just fine on this petsc > > example problem. When I try sacusp on this matrix for the case of > > generating > > a rhs from a known solution vector, the computed solution seems to diverge > > from the exact solution. We also have an interface to an external agmg > > package which is not able to solve this problem > > but works well on the other 5 > > linear solves. So I'd like to try more from the multigrid toolbox but do > > not > > know much about how to supply the extra stuff that these packages often > > need. > > > > So, it sounds like you are suggesting that I try gamg and that I could at > > least try it out without having to initially supply lots of additional > > info. > > So I will take a look at gamg. > > > > There are many things that can break a solver but most probably want to know > that its a system so if you can set the block size and try gamg then that > would be a good start. > > Mark > > > Thanks, > > > > Dave > > > >> Mark > >> > >> On Nov 30, 2011, at 8:15 AM, Matthew Knepley wrote: > >> > >>> On Wed, Nov 30, 2011 at 12:41 AM, Dave Nystrom <dnystrom1 at > >>> comcast.net> wrote: > >>> I have a linear system in a code that I have interfaced to petsc that is > >>> taking about 80 percent of the run time per timestep. This linear > >>> system is > >>> a symmetric block banded matrix where the blocks are 2x2. The matrix > >>> looks > >>> as follows: > >>> > >>> 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 > >>> 1X X Y Y Y > >>> 2X X X Y Y Y > >>> 3 X X X Y Y Y > >>> 4 X X X Y Y Y > >>> 5 X X X Y Y Y > >>> 6 X X X Y Y Y > >>> 7 X X X Y Y Y > >>> 8 X X X Y Y Y > >>> 9 X X X Y Y Y > >>> 0 X X X Y Y Y > >>> 1 X X X Y Y Y > >>> 2 X X X Y Y Y > >>> 3Z X X X Y Y Y > >>> 4Z Z X X X Y Y Y > >>> 5Z Z Z X X X Y Y Y > >>> 6 Z Z Z X X X Y Y Y > >>> 7 Z Z Z X X X Y Y Y > >>> 8 Z Z Z X X X Y Y Y > >>> 9 Z Z Z X X X Y Y Y > >>> 0 Z Z Z X X X Y Y Y > >>> > >>> So in my diagram above, X, Y and Z are 2x2 blocks. The symmetry of the > >>> matrix requires that X_ij = transpose(X_ji) and Y_ij = transpose(Z_ji). > >>> So > >>> far, I have just input this matrix to petsc without indicating that it > >>> was > >>> block banded with 2x2 blocks. I have also not told petsc that the > >>> matrix is > >>> symmetric. And I have allowed petsc to decide the best way to store the > >>> matrix. > >>> > >>> I can solve this linear system over the course of a run using -ksp_type > >>> preonly -pc_type lu. But that will not scale very well to larger > >>> problems > >>> that I want to solve. I can also solve this system over the course of a > >>> run > >>> using -ksp_type cg -pc_type jacobi -vec_type cusp -mat_type aijcusp. > >>> However, over the course of a run, the iteration count ranges from 771 to > >>> 47300. I have also tried sacusp, ainvcusp, sacusppoly, ilu(k) and icc(k) > >>> with k=0. The sacusppoly preconditioner fails because of a thrust error > >>> related to an invalid device pointer, if I am remembering correctly. I > >>> reported this problem to petsc-maint a while back and have also reported > >>> it > >>> for the cusp bugtracker. But it does not appear that anyone has really > >>> looked into the bug. For the other preconditioners of sacusp, ilu(k) and > >>> icc(k), they do not result in convergence to a solution and the runs > >>> fail. > >>> > >>> All preconditioners are custom. Have you done a literature search for PCs > >>> known to work for this problem? Can yu say anything about the spectrum > >>> of the > >>> operator? conditioning? what is the principal symbol (if its a PDE)? The > >>> pattern > >>> is not enough to recommend a PC. > >>> > >>> Matt > >>> > >>> I'm wondering if there are suggestions of other preconditioners in petsc > >>> that > >>> I should try. The only third party package that I have tried is the > >>> txpetscgpu package. I have not tried hypre or any of the multigrid > >>> preconditioners yet. I'm not sure how difficult it is to try those > >>> packages. Anyway, so far I have not found a preconditioner available in > >>> petsc that provides a robust solution to this problem and would be > >>> interested > >>> in any suggestions that anyone might have of things to try. > >>> > >>> I'd be happy to provide additional info and am planning on packaging up a > >>> couple of examples of the matrix and rhs for people I am interacting > >>> with at > >>> Tech-X and EMPhotonics. So I'd be happy to provide the matrix examples > >>> for > >>> this forum as well if anyone wants a copy. > >>> > >>> Thanks, > >>> > >>> Dave > >>> > >>> -- > >>> Dave Nystrom > >>> > >>> phone: 505-661-9943 (home office) > >>> 505-662-6893 (home) > >>> skype: dave.nystrom76 > >>> email: dnystrom1 at comcast.net > >>> smail: 219 Loma del Escolar > >>> Los Alamos, NM 87544 > >>> > >>> > >>> > >>> -- > >>> What most experimenters take for granted before they begin their > >>> experiments is infinitely more interesting than any results to which > >>> their experiments lead. > >>> -- Norbert Wiener > >> > > >