[petsc-users] Detecting steady-state with TS

[Salazar De Troya, Miguel]

Thanks, can you elaborate on computing the time derived? TSMonitor only gives me the information at the current time step. I guess I could store a copy of the solution in the context so I can use it in the next call to compute the difference. On the other hand, I could also store the norm of the RHS function (since this is equal to the time derivative \frac{\partial \phi}{\partial t}).

Miguel

From: Mark Adams <mfadams at lbl.gov>
Date: Friday, April 30, 2021 at 3:56 PM
To: "Salazar De Troya, Miguel" <salazardetro1 at llnl.gov>
Cc: "Zhang, Hong via petsc-users" <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Detecting steady-state with TS

You could add a https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSMonitorSet.html<https://urldefense.us/v3/__https:/www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSMonitorSet.html__;!!G2kpM7uM-TzIFchu!hG6eR--4AkxoFHnPn3N8DJF2pPoVkaJT0f6vy9E2qTLMZ0TiqDR_kr5wbAbwapvuLtnSGw$> method, compute the time derived and decide how to declare converged.

Then set converged (https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetConvergedReason.html<https://urldefense.us/v3/__https:/www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetConvergedReason.html__;!!G2kpM7uM-TzIFchu!hG6eR--4AkxoFHnPn3N8DJF2pPoVkaJT0f6vy9E2qTLMZ0TiqDR_kr5wbAbwaptYI8kTFA$>) with TS_CONVERGED_USER

That should cause TS to wrap up the solve and exit cleanly.

Mark


On Thu, Apr 29, 2021 at 3:27 PM Salazar De Troya, Miguel via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
I am solving the signed distance equation

\frac{\partial \phi}{\partial t} + sign (\phi_{0})(|\nabla \phi| - 1) = 0

using a Local Discontinuous Galerkin (LDG) method as described in https://www.sciencedirect.com/science/article/pii/S0021999110005255<https://urldefense.us/v3/__https:/www.sciencedirect.com/science/article/pii/S0021999110005255__;!!G2kpM7uM-TzIFchu!hG6eR--4AkxoFHnPn3N8DJF2pPoVkaJT0f6vy9E2qTLMZ0TiqDR_kr5wbAbwapsr29KQOw$>

I am interested in solving it close to steady state. I was hoping I could measure how close to steady state the solution is by using the TSSetEventHandler infrastructure, but the handler does not have information on the time derivative. I looked at TSPSEUDO, but it forces me to use an implicit method, which I cannot provide because how the LDG method works (it calculates the fluxes solving additional equations). This makes me wonder if the LDG method is the best choice, so I am open to suggestions.

Given my current progress with the LDG approach, I am wondering if there is a way to solve to steady state using explicit algorithms such as Runge-Kutta.

Thanks
Miguel

Miguel A. Salazar de Troya
Postdoctoral Researcher, Lawrence Livermore National Laboratory
B141
Rm: 1085-5
Ph: 1(925) 422-6411
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