# [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

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