[petsc-users] The exact Jacobian for ASPIN
Lulu Liu
lulu.liu at kaust.edu.sa
Sat Dec 25 23:48:28 CST 2021
Dear Barry,
Yes, J_{I} is the typo, and it should be J_{j}. The exact Jacobian of the
preconditioned Jacobian is
J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-T_{j}) (1)
It seems that PETSc uses the approximate Jacobian,
J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-\sum_{j=1}^{N}T_{j}) (2)
In the RASPEN algorithm, it requires the exact Jacobian of ASPIN in the
equation (1). Currently, the J_{j}(x-T_{i}) is only computed on each
processor in PETSc, how can I get the global term J(x-T_{j})(j=1,2,..N)?
Thanks.
On Tue, Nov 9, 2021 at 11:18 AM Barry Smith <bsmith at petsc.dev> wrote:
>
> Lulu,
>
> Sorry for not responding quicker. This question will take a little
> research to figure out exactly what is needed, I am not sure it is
> possible.
>
> I note below you have a J_{I} is that intentional? If so what does it
> mean, or is a typo that should be J_{j} as in the next equation?
>
> Barry
>
>
> On Nov 6, 2021, at 7:19 AM, Lulu Liu <lulu.liu at kaust.edu.sa> wrote:
>
> Hi,
> For ASPIN, the local problem F_{j}(x-T_{j})=0 (j=1,2,...N) is solved. The
> exact Jacobian of the preconditioned Jacobian is
> J_exact=\sum_{j=1}^{N}J_{I}(x-T_{i})J(x-T_{j}).
>
> It seems that PETSc uses the approximate Jacobian,
> J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-\sum_{j=1}^{N}T_{j}).
>
> I want to implement RASPEN, which requires the exact Jacobian of ASPIN. Is there
> any easy way to compute J(x-T_{j}) (j=1,2,..N)? How can I get the global
> vectors like x-T_{j} ? PETSc only provides the vector x-T_{j} on the
> subdomain now.
>
> Thanks very much!
>
> --
> Best wishes,
> Lulu Liu
>
>
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--
Best wishes,
Lulu Liu
Applied Mathematics and Computational Science
King Abdullah University of Science and Technology
Tel：＋966－0544701599
--
This message and its contents, including attachments are intended solely
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