[petsc-users] Problems about GMRES restart and Scaling

[Yingjie Wu]

Thanks for all the reply.
The model I simulated is a thermal model that contains multiple physical
fields(eg. temperature, pressure, velocity). In PDEs, these variables are
preceded by some physical parameters, which in turn are functions of these
variables(eg. density is a function of pressure and temperature.). Due to
the complexity of these physical parameter functions, we cannot explicitly
construct Jacobian matrices for this problem. So I use -snes_mf_operator.

My preconditioner is to treat these physical parameters as constants. At
the beginning of each nonlinear step(SNES), the Jacobian matrix is updated
with the result of the previous nonlinear step output(the physical
parameters are updated).


After setting a large KSP restart step, about 60 KSP can converge(ksp_rtol
= 1.e-5).


I have a feeling that my initial values are too large to cause this
phenomenon.


Snes/ex19 is actually a lot like my example, setting up: -da_grid_x 200
-da_grid_y 200 -snes_mf

There will also be a residual rise in step 1290 of KSP

But not all examples will produce this phenomenon.


Thanks, Yingjie

Smith, Barry F. <bsmith at mcs.anl.gov> 于2019年3月21日周四 上午1:18写道：

>
>
> > 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
>
>    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
>
>
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