[petsc-users] Problem about Scaling

[Matthew Knepley]

On Tue, Sep 24, 2019 at 11:17 AM Yingjie Wu via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Respected Petsc developers
> Hi,
> I am currently using SNES to solve some non-linear PDEs. The model is a
> two-dimensional X-Y geometry. Because the magnitude of different physical
> variables is too large, it is difficult to find the direction in Krylov
> subspace, and the residual descends very slowly or even does not converge.
> I think my PDEs need scaling. I need some help to solve the following
> quentions.
>
> 1. I use - snes_mf_operator, so instead of providing Jacobian matrix, I
> only set up an approximate Jacobian matrix for precondition. For my model,
> do I just need to magnify the residuals to the same level? Is there any
> need to modify the precondition matrix?
> 2. I have seen some articles referring to the non-dimensional method. I
> don't know how to implement this method in the program and how difficult it
> is to implement.
>

That answer to 1 and 2 is the same. Nondimensionalize your system, and in
the the process scale your unknowns so that
they are about the same magnitude. Here is a great article on this process

  https://epubs.siam.org/doi/pdf/10.1137/16M1107127

  Thanks,

    Matt


> Thanks,
> Yingjie
>
>

-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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