[petsc-users] Problems about GMRES restart and Scaling

[Smith, Barry F.]

> 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