[petsc-dev] Seeking Advice on Petsc Preconditioners to Try
Dave Nystrom
dnystrom1 at comcast.net
Tue Dec 20 09:33:26 CST 2011
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
> >>
> >
>
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