[petsc-users] Questions about residual function can't be reduced

[Matthew Knepley]

On Thu, Sep 6, 2018 at 4:47 AM Yingjie Wu <yjwu16 at gmail.com> wrote:

> Dear Petsc developer:
> Hi,
> Thank you for your previous help.
> I recently modeled on PETSc's SNES example and wrote a computer program
> myself. This program is mainly for solving nonlinear equations of thermal
> hydraulics.
>
> ∇·（λ∇T） - ∇_y（ρ*Cp*u） - T_source = 0
>
> w*ρ*u = ρg - ∇_y（P）
>
>      ∇·（ 1/w * ∇P ） =  - ∇（ ρg / w ）
>
> Where P, T and u are variables, the distribution represents pressure,
> temperature and velocity. The rest are nonlinear physical parameters and
> constants.
>
> Because the program is very preliminary, so I use - snes_mf so that I can
> save the part of writing to calculate the Jacobian matrix.
>
> After compiling and passing, I found that the residual function had not
> dropped to a small enough level, but the program stopped, as follows:
>
> Setting Up: -snes_mf  -snes_monitor  -draw_pause  10  -snes_view
>
>
First, do not use -snes_mf. It is not for testing, but for sophisticated
use. The first option you
might try is

   -snes_fd -pc_type lu

That uses a full Jacobian and LU factorization for a direct solve. Always
run the solve using

  -snes_view -snes_converged_reason -snes_monitor -ksp_converged_reason
-ksp_monitor_true_residual

When that gets too expensive, you can try

  -snes_fd_color -snes_fd_color_use_mat -mat_coloring_type greedy

but that requires you to preallocate the Jacobian matrix correctly.

  Thanks,

    Matt

> 0 SNES Function norm 3.724996516631e+09
>
>   1 SNES Function norm 2.194322909557e+09
>
>   2 SNES Function norm 1.352051559826e+09
>
>   3 SNES Function norm 1.522311916217e+08
>
> SNES Object: 1 MPI processes
>
>   type: newtonls
>
>   maximum iterations=50, maximum function evaluations=10000
>
>   tolerances: relative=1e-08, absolute=1e-50, solution=1e-08
>
>   total number of linear solver iterations=1298
>
>   total number of function evaluations=11679
>
>   norm schedule ALWAYS
>
>   SNESLineSearch Object: 1 MPI processes
>
>     type: bt
>
>       interpolation: cubic
>
>       alpha=1.000000e-04
>
>     maxstep=1.000000e+08, minlambda=1.000000e-12
>
>     tolerances: relative=1.000000e-08, absolute=1.000000e-15,
> lambda=1.000000e-08
>
>     maximum iterations=40
>
>   KSP Object: 1 MPI processes
>
>     type: gmres
>
>       restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>
>       happy breakdown tolerance 1e-30
>
>     maximum iterations=10000, initial guess is zero
>
>     tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
>
>     left preconditioning
>
>     using PRECONDITIONED norm type for convergence test
>
>   PC Object: 1 MPI processes
>
>     type: none
>
>     linear system matrix = precond matrix:
>
>     Mat Object: 1 MPI processes
>
>       type: mffd
>
>       rows=300, cols=300
>
>         Matrix-free approximation:
>
>           err=1.49012e-08 (relative error in function evaluation)
>
>           Using wp compute h routine
>
>               Does not compute normU
>
> I would like to know why the residual function can not continue to
> decline, and why the program will stop before convergence.
> I do not know much about the convergence criteria and convergence rules of
> PETSc for solving nonlinear equations. I hope I can get your help.
> I'm looking forward to your reply~
>
> 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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