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

Tue Nov 3 09:24:52 CST 2015

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.

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.

  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
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