[petsc-users] Problems about GMRES restart and Scaling

[Mark Adams]

On Wed, Mar 20, 2019 at 1:18 PM Smith, Barry F. via petsc-users <
petsc-users at mcs.anl.gov> wrote:

>
>
> > On Mar 20, 2019, at 5:52 AM, Yingjie Wu via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
> >
> > Dear PETSc developers:
> > Hi,
> > Recently, I used PETSc to solve a non-linear PDEs for thermodynamic
> problems. In the process of solving, I found the following two phenomena,
> hoping to get some help and suggestions.
> >
> > 1. Because my problem involves a lot of physical parameters, it needs to
> call a series of functions, and can not analytically construct Jacobian
> matrix, so I use - snes_mf_operator to solve it, and give an approximate
> Jacobian matrix as a preconditioner. Because of the large dimension of the
> problem and the magnitude difference of the physical variables involved, it
> is found that the linear step residuals will increase at each restart
> (default 30th linear step) . This problem can be solved by setting a large
> number of restart steps. I would like to ask the reasons for this
> phenomenon? What knowledge or articles should I learn if I want to find out
> this problem?
>
>    I've seen this behavior. I think in your case it is likely the
> -snes_mf_operator is not really producing an "accurate enough"
> Jacobian-Vector product (and the "solution" being generated by GMRES may be
> garbage). Run with -ksp_monitor_true_residual
>

I have found that GMRES is very sensitive. I tried optimizing a smoother by
sending single precision data in MPI and this tanked GMRES. CG was fine
with this.


>
>    If your residual function has if () statements in it or other very
> sharp changes (discontinuities) then it may not even have a true Jacobian
> at the locations it is being evaluated at.  In the sense that the
> "Jacobian" you are applying via finite differences is not a linear operator
> and hence GMRES will fail on it.
>
>     What are you using for a preconditioner? And roughly how many KSP
> iterations are being used.
>
>    Barry
>
> >
> >
> > 2. In my problem model, there are many physical fields (variables are
> realized by finite difference method), and the magnitude of variables
> varies greatly. Is there any Scaling interface or function in Petsc?
> >
> > Thanks,
> > Yingjie
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20190321/50a707aa/attachment-0001.html>