[petsc-users] How do I know it is steady state?

Zou (Non-US), Ling ling.zou at inl.gov
Tue Nov 3 13:05:09 CST 2015 

Barry, thanks for the discussion and help.

Ling

On Tue, Nov 3, 2015 at 11:55 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> > On Nov 3, 2015, at 9:38 AM, Zou (Non-US), Ling <ling.zou at inl.gov> wrote:
> >
> >
> >
> > On Tue, Nov 3, 2015 at 8:24 AM, Matthew Knepley <knepley at gmail.com>
> wrote:
> > On Tue, Nov 3, 2015 at 9:12 AM, Zou (Non-US), Ling <ling.zou at inl.gov>
> wrote:
> > Matt, thanks for the reply.
> > The simulation is a transient simulation, which eventually converges to
> a steady-state solution, given enough simulation time.
> > My code runs fine and I could tell the simulation reaches steady state
> by looking at the residual monitored by SNES monitor function.
> >
> > See an example screen output
> >
> > Solving time step 90, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 8.85.
> >         NL step =  0, SNES Function norm =  1.47538E-02
> >         NL step =  1, SNES Function norm =  8.06971E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 91, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 8.95.
> >         NL step =  0, SNES Function norm =  1.10861E-02
> >         NL step =  1, SNES Function norm =  6.26584E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 92, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.05.
> >         NL step =  0, SNES Function norm =  7.21253E-03
> >         NL step =  1, SNES Function norm =  9.93402E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 93, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.15.
> >         NL step =  0, SNES Function norm =  5.40260E-03
> >         NL step =  1, SNES Function norm =  6.21162E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 94, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.25.
> >         NL step =  0, SNES Function norm =  3.40214E-03
> >         NL step =  1, SNES Function norm =  6.16805E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 95, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.35.
> >         NL step =  0, SNES Function norm =  2.29656E-03
> >         NL step =  1, SNES Function norm =  6.19337E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 96, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.45.
> >         NL step =  0, SNES Function norm =  1.53218E-03
> >         NL step =  1, SNES Function norm =  5.94845E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 97, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.55.
> >         NL step =  0, SNES Function norm =  1.32136E-03
> >         NL step =  1, SNES Function norm =  6.19933E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 98, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.65.
> >         NL step =  0, SNES Function norm =  7.09342E-04
> >         NL step =  1, SNES Function norm =  6.18694E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 99, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.75.
> >         NL step =  0, SNES Function norm =  5.49192E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 100, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.85.
> >         NL step =  0, SNES Function norm =  5.49192E-04
> >         total_FunctionCall_number: 0
> > converged, time step increased = 0.1
> > Solving time step 101, using BDF1, dt = 0.1.
> > Current time (the starting time of this time step) = 9.95.
> >         NL step =  0, SNES Function norm =  5.49192E-04
> >         total_FunctionCall_number: 0
> >
> > I observed that after time step 99, the residual never changed, so I
> believe the transient simulation converges at time step 99.
> > I wonder can I use the criterion "SNES converges and it takes 0
> iteration" to say the simulation reaches a steady state. Such that I don't
> have to look at the screen and the code knows it converges and should stop.
> >
> > Put it another way, what's the common way people would implement a
> scheme to detect a transient simulation reaches steady state.
> >
> > I don't think so. The above makes no sense to me. You are signaling SNES
> convergence with a relative
> > residual norm of 5e-4? That does not sound precise enough to me.
> >
> > I would argue that number (5.e-4) depends on the problem you are solving
> (actually I am solving).
> > The initial residual of the problem starts at ~1e8.
> > But you might be right, and I have to think about this issue more
> carefully.
> >
> > As I said, I think the believable way to find steady states is to look
> for solutions to the algebraic equations,
> > perhaps by using timestepping as a preconditioner.
> >
> > You still need a numerical criterion to let the code understand it
> converges, right? For example, "a set of solutions have already been found
> to satisfy the algebraic equations because ___residuals drops below (a
> number here)__".
>
>   After each SNESSolve you could call SNESGetConvergedReason() and if the
> number of iterations was 0 and the reason was snorm then declare it steady
> state.
>
>    Barry
>
> >
> > Thanks,
> >
> > Ling
> >
> >
> >   Thanks,
> >
> >      Matt
> >
> > Thanks,
> >
> > Ling
> >
> >
> > On Tue, Nov 3, 2015 at 5:25 AM, Matthew Knepley <knepley at gmail.com>
> wrote:
> > On Mon, Nov 2, 2015 at 7:29 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> > > On Oct 30, 2015, at 12:23 PM, Zou (Non-US), Ling <ling.zou at inl.gov>
> wrote:
> > >
> > > Hi All,
> > >
> > > From physics point of view, I know my simulation converges if nothing
> changes any more.
> > >
> > > I wonder how normally you do to detect if your simulation reaches
> steady state from numerical point of view.
> > > Is it a good practice to use SNES convergence as a criterion, i.e.,
> > > SNES converges and it takes 0 iteration(s)
> >
> >    Depends on the time integrator and SNES tolerance you are using. If
> you use a -snes_rtol 1.e-5 it will always try to squeeze 5 MORE digits out
> of the residual so won't take 0 iterations even if there is only a small
> change in the solution.
> >
> > There are two different situations here:
> >
> >   1) Solving for a mathematical steady state. You remove the time
> derivative and solve the algebraic system with SNES. Then
> >       the SNES tolerance is a good measure.
> >
> >   2) Use timestepping to advance until nothing looks like it is
> changing. This is a "physical" steady state.
> >
> > You can use 1) with a timestepping preconditioner TSPSEUDO, which is
> what I would recommend if you
> > want a true steady state.
> >
> >   Thanks,
> >
> >      Matt
> >
> > >
> > > Thanks,
> > >
> > > Ling
> >
> >
> >
> >
> > --
> > 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
> >
> >
> >
> >
> > --
> > 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
> >
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20151103/911845a9/attachment-0001.html>

More information about the petsc-users mailing list