In COMSOL Multiphysics, I notice that using the Generalized Alpha with strict/intermediate time steps is the best way to converge my structural based nonlinear solution. In BDF, I get lot of fluctuations in the solutions.
Using GA with small enough time steps, fluctuations in solutions can be reduced. But making very small steps (constant through out the simulation), makes the solver to take forever to complete one simulation (for example 1e-4 time step and I have to solve for total 4e3 seconds). I want to update the time step (variable time steps) based on the difference in solution between previous and current time. If it is too high then change the timestep otherwise keep the highest value (which is the time stored in output).
To achieve this, I am using "nojac operator" in the ODE and DAE module to store the previous solution and taking the difference in global variables, this way I have defined a piece-wise function to update the time step based on solution difference. I am still getting few (one or two) fluctuations.
I just want to ask, anyone have experienced this type of problem before? If have, what do you think should be the best way to solve this? Is there anyother way to get rid of the fluctuation in the solutions?
Thanks
Hello Noman,
I have also noticed what you mention, the Generalized Alpha is the best option in highly nonlinear problems.
I want to mention another thing that is quite interesting and you may also have found out, once you select
the option for strict/intermediate time steps, the solution ( I mean the graphs and their values) , depend indeed on the maximum time limit you use, ( i.e. t=tmax ). So, I propose that you manually set the time-step, for each trial. Now, back on your question, you see fluctuations on the reciprocal of step size or on the values of the output variables?
Hi E. N. Petrakakis , I am setting the time steps manually. But my time frame is quite long ~ lets say 10,000s, at start, condition 1, problem is stable, after 5,000 could be earlier or after a certain phenomena occur-call it condition 2, which is highly non-linear here I have to take very small time steps, that's also okay. Major problem is after that it goes back to condition 1, again I want to use max defined time step. I do not know when it goes back to cond 1, it depends on the rate of solution being changed. That is why I am asking if somehow I can use the previous step info to update my time step.
And yes fluctuations are in the solutions.
Noman
Dear Nomad,
I am not sure if I understand correctly your case. Why are you setting a constant time-step? Doing that is quite risky unless you have good info of the behaviour of your differential equations beforehand. Besides what you are describing looks very similar to what the adaptive time-step does in COMSOL, i.e. why not use a strict/intermediate strategy (adaptive method) to let the solver decide the time-step based on the error of the previous solution? If you need to control the time-step in some regions due some nonlinear events then you can add an event controller to your problem so the solver will restart and take small time-steps when the event happens, and then expand the time-step again according to the error of the solution.
E.g: https://www.comsol.com/blogs/implementing-a-thermostat-with-the-events-interface/
Kind regards,
Julian
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