[petsc-users] Differences between jacobi and bjacobi preconditioner for cg method 1-processor/block

[Jonathan Wong]

Matthew: Thanks for clarifying about the block-jacobi.

Paul: I'm only using bjacobi with PETSc to show that the problem is
solvable, and to provide some "estimation" as to the performance of the
jacobi preconditioner. On the GPU, I am using CUSP to do cg+jacobi which
works fine for this 50k node mesh.


On Mon, May 19, 2014 at 12:07 PM, Paul Mullowney <paulmullowney at gmail.com>wrote:

> I don't think bjacobi is working on GPUs. I know Dominic made a pull
> request a few months ago, but I don't know if its been integrated into next.
> -Paul
>
>
> On Mon, May 19, 2014 at 12:45 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Mon, May 19, 2014 at 1:42 PM, Jonathan Wong <jon.the.wong at gmail.com>wrote:
>>
>>> Thanks for the input. To clarify, I'm trying to compare GPU algorithms
>>> to Petsc, and they only have cg/jacobi for what I'm comparing at the
>>> moment. This is why I'm not using gmres (which also works well).
>>>
>>> I can solve the problem with the GPU (custom code) using CG + jacobi for
>>> all the meshes. On the CPU side, I can solve everything with cg/bjacobi and
>>> almost all of my meshes with cg/jacobi except for my 50k node mesh. I can
>>> solve the problem with my finite element built-in direct solver (just takes
>>> awhile) on one processor. I've been reading that by default the bjacobi pc
>>> uses one block per processor. So I had assumed that for one processor
>>> block-jacobi and jacobi would give similar results. cg+bjacobi works fine.
>>> cg+jacobi does not.
>>>
>>
>> "Jacobi" means preconditioning by the inverse of the diagonal of the
>> matrix. Block-Jacobi means using a preconditioner
>> formed from each of the blocks, in this case 1 block. By default the
>> inner preconditioner is ILU(0), not jacobi. You can
>> make them equivalent using -sub_pc_type jacobi.
>>
>>    Matt
>>
>>
>>>  I'll just look into the preconditioner code and use KSPview to try to
>>> figure out what the differences are for one processor. I'm not sure why the
>>> GPU can consistently solve the problem with cg/jacobi. I'm assuming this is
>>> due to the way round-off or the order of operations differences between the
>>> two.
>>>
>>>
>>> On Mon, May 19, 2014 at 6:35 AM, Jed Brown <jed at jedbrown.org> wrote:
>>>
>>>> Matthew Knepley <knepley at gmail.com> writes:
>>>> > No, Block-Jacobi and Jacobi are completely different. If you are not
>>>> > positive definite, you should be using MINRES.
>>>>
>>>> MINRES requires an SPD preconditioner.
>>>>
>>>
>>>
>>
>>
>> --
>> 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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