[petsc-users] Store and reuse the factor of matrix

[Jinlei Shen]

Hi Matt,

Thanks for speedy reply.

It seems effective in SNES.

I'm curious about how it works in iterative solver.
Let's say I'm using CG with BJACOBI for modified newton, if I Set lag as 5,
does that mean the ilu decomposition for pc is stored and reused for the
next 4 iterations? Will this setting help to reduce the iteration number of
ksp solver?

Also, I'm wondering how to set the same option for just linear KSP solver
since I have coded the modified newton framework manually.

Thanks

Jinlei





On Thu, Aug 18, 2016 at 10:28 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Thu, Aug 18, 2016 at 9:22 PM, Jinlei Shen <jshen25 at jhu.edu> wrote:
>
>> ​Hi,
>>
>> I'm trying to implement modified newton method to solve the nonlinear
>> finite element using petsc.
>>
>> As well known,  the advantage of modified newton is the Jacobian matrix
>> is always same during the iteration, which means once the J is factorized
>> at the first iteration, we can store the factors and avoid the
>> factorization for next iteration if we use direct solver, e.g. super_lu.
>> Therefore, the option FACTORED in SUPER_LU is quite useful.
>>
>> However, it looks like the option FACTORED is not available in
>> SUPER_LU_DIST in petsc. I tried, and it shows 'unknown option'.
>>
>> Is there alternative way to use the same idea of FACTORED in petsc for
>> super_lu?
>>
>> Also, I'm wondering whether iterative solver in PETSC is also able to
>> apply the same strategy.
>>
>> In other words, in the problem where Jacobian is constant, only residue
>> and solution vectors need to be updated, is there any way to take advantage
>> of such same Jacobian pattern to expedite the computation using iterative
>> solver?
>>
>> Thank you
>>
>> BTW, though using modified newton will increase the iteration number,
>> however, in the case which is much more expensive to factorize the
>> jacobian, more iterations will probably be worthwhile.
>>
>
> You can use
>
>   http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/
> SNESSetLagJacobian.html
>   http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/
> SNESSetLagPreconditioner.html#SNESSetLagPreconditioner
>
> to get fine-grained control over this without writing any code.
>
>    Matt
>
> Bests,
>> Jinlei
>>
>
>
>
> --
> 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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