[petsc-users] The exact Jacobian for ASPIN

Barry Smith bsmith at petsc.dev
Mon Nov 8 21:18:41 CST 2021


    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?


> 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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