<div dir="ltr">Barry, thanks for the discussion and help.<div><br></div><div>Ling</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Nov 3, 2015 at 11:55 AM, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="HOEnZb"><div class="h5"><br>
> On Nov 3, 2015, at 9:38 AM, Zou (Non-US), Ling <<a href="mailto:ling.zou@inl.gov">ling.zou@inl.gov</a>> wrote:<br>
><br>
><br>
><br>
> On Tue, Nov 3, 2015 at 8:24 AM, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br>
> On Tue, Nov 3, 2015 at 9:12 AM, Zou (Non-US), Ling <<a href="mailto:ling.zou@inl.gov">ling.zou@inl.gov</a>> wrote:<br>
> Matt, thanks for the reply.<br>
> The simulation is a transient simulation, which eventually converges to a steady-state solution, given enough simulation time.<br>
> My code runs fine and I could tell the simulation reaches steady state by looking at the residual monitored by SNES monitor function.<br>
><br>
> See an example screen output<br>
><br>
> Solving time step 90, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 8.85.<br>
> NL step = 0, SNES Function norm = 1.47538E-02<br>
> NL step = 1, SNES Function norm = 8.06971E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 91, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 8.95.<br>
> NL step = 0, SNES Function norm = 1.10861E-02<br>
> NL step = 1, SNES Function norm = 6.26584E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 92, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.05.<br>
> NL step = 0, SNES Function norm = 7.21253E-03<br>
> NL step = 1, SNES Function norm = 9.93402E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 93, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.15.<br>
> NL step = 0, SNES Function norm = 5.40260E-03<br>
> NL step = 1, SNES Function norm = 6.21162E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 94, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.25.<br>
> NL step = 0, SNES Function norm = 3.40214E-03<br>
> NL step = 1, SNES Function norm = 6.16805E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 95, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.35.<br>
> NL step = 0, SNES Function norm = 2.29656E-03<br>
> NL step = 1, SNES Function norm = 6.19337E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 96, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.45.<br>
> NL step = 0, SNES Function norm = 1.53218E-03<br>
> NL step = 1, SNES Function norm = 5.94845E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 97, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.55.<br>
> NL step = 0, SNES Function norm = 1.32136E-03<br>
> NL step = 1, SNES Function norm = 6.19933E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 98, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.65.<br>
> NL step = 0, SNES Function norm = 7.09342E-04<br>
> NL step = 1, SNES Function norm = 6.18694E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 99, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.75.<br>
> NL step = 0, SNES Function norm = 5.49192E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 100, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.85.<br>
> NL step = 0, SNES Function norm = 5.49192E-04<br>
> total_FunctionCall_number: 0<br>
> converged, time step increased = 0.1<br>
> Solving time step 101, using BDF1, dt = 0.1.<br>
> Current time (the starting time of this time step) = 9.95.<br>
> NL step = 0, SNES Function norm = 5.49192E-04<br>
> total_FunctionCall_number: 0<br>
><br>
> I observed that after time step 99, the residual never changed, so I believe the transient simulation converges at time step 99.<br>
> 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.<br>
><br>
> Put it another way, what's the common way people would implement a scheme to detect a transient simulation reaches steady state.<br>
><br>
> I don't think so. The above makes no sense to me. You are signaling SNES convergence with a relative<br>
> residual norm of 5e-4? That does not sound precise enough to me.<br>
><br>
> I would argue that number (5.e-4) depends on the problem you are solving (actually I am solving).<br>
> The initial residual of the problem starts at ~1e8.<br>
> But you might be right, and I have to think about this issue more carefully.<br>
><br>
> As I said, I think the believable way to find steady states is to look for solutions to the algebraic equations,<br>
> perhaps by using timestepping as a preconditioner.<br>
><br>
> 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)__".<br>
<br>
</div></div> 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.<br>
<span class="HOEnZb"><font color="#888888"><br>
Barry<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
><br>
> Thanks,<br>
><br>
> Ling<br>
><br>
><br>
> Thanks,<br>
><br>
> Matt<br>
><br>
> Thanks,<br>
><br>
> Ling<br>
><br>
><br>
> On Tue, Nov 3, 2015 at 5:25 AM, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br>
> On Mon, Nov 2, 2015 at 7:29 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>> wrote:<br>
><br>
> > On Oct 30, 2015, at 12:23 PM, Zou (Non-US), Ling <<a href="mailto:ling.zou@inl.gov">ling.zou@inl.gov</a>> wrote:<br>
> ><br>
> > Hi All,<br>
> ><br>
> > From physics point of view, I know my simulation converges if nothing changes any more.<br>
> ><br>
> > I wonder how normally you do to detect if your simulation reaches steady state from numerical point of view.<br>
> > Is it a good practice to use SNES convergence as a criterion, i.e.,<br>
> > SNES converges and it takes 0 iteration(s)<br>
><br>
> 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.<br>
><br>
> There are two different situations here:<br>
><br>
> 1) Solving for a mathematical steady state. You remove the time derivative and solve the algebraic system with SNES. Then<br>
> the SNES tolerance is a good measure.<br>
><br>
> 2) Use timestepping to advance until nothing looks like it is changing. This is a "physical" steady state.<br>
><br>
> You can use 1) with a timestepping preconditioner TSPSEUDO, which is what I would recommend if you<br>
> want a true steady state.<br>
><br>
> Thanks,<br>
><br>
> Matt<br>
><br>
> ><br>
> > Thanks,<br>
> ><br>
> > Ling<br>
><br>
><br>
><br>
><br>
> --<br>
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
> -- Norbert Wiener<br>
><br>
><br>
><br>
><br>
> --<br>
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
> -- Norbert Wiener<br>
><br>
<br>
</div></div></blockquote></div><br></div>