[petsc-dev] Seeking Advice on Petsc Preconditioners to Try
Mark F. Adams
mark.adams at columbia.edu
Fri Dec 2 18:26:12 CST 2011
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
>>
>
More information about the petsc-dev
mailing list