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 >> >
