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absolute tolerance for thermal stress problem

Posted Dec 10, 2011, 3:42 p.m. EST Version 4.1, Version 4.2, Version 4.2a 3 Replies

Alexander Warning
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So I am modeling the 2D transient freezing of a cylinder of tissue with 80% water (my model is a 2D wedge as Im assuming L >> D). I am using a quasi-static viscoelastic model with time dependent temperature equation in the thermal stress module. Therefore I expect a 7% increase in total volume (under the assumption volumetric expansion of water is 9%). My initial radius is 0.01m and so I expect a final radius 0f 0.0103 which tells me I expect a final displacement of 3.5*10^-4 m.

Now my question is, what do I set the relative and absolute tolerance? I know you should set the absolute tolerance one order of magnitude less than the displacement in order to get any accuracy. But which displacement do I consider? DO I use the displacement at each time step or the displacement from the initial and final states? During each time step the displacement is ~10^-8 m.

Currently, I am using relative tolerance = 0.0001 and absolute tolerance = 10^-6 to 10^-8. Any suggestions? I have been looking at the effects of varying tolerances and increasing elements. I see that as I decrease my absolute tolerance, the convergence plot osscilates more and more.

Thanks
Alex
3 Replies Last Post Dec 20, 2011, 10:09 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Dec 11, 2011, 5:17 a.m. EST
Hi

I assume your oscillations come from numerical instabilities, do not forget that the binary number representation has a limited resolution (check the variable "eps", and consider sqrt(eps) as the best of the best, I would rather use 100 to 1000 times sqrt(eps) as a reasonable relative limit). And this is not COMSOL limitation it's a number theory limitation of binary numbers applicable to any software.

My way to check convergence is to compare the results when I increase the resolution, does the result vary or converge ? Mostly FEM is for a few % precision, not to extract 18 decimals. But that depends on your model and it's finesse, are all hypothesis for the physics model correct and within limit, are ALL physics presented, ...

--
Good luck
Ivar
Hi I assume your oscillations come from numerical instabilities, do not forget that the binary number representation has a limited resolution (check the variable "eps", and consider sqrt(eps) as the best of the best, I would rather use 100 to 1000 times sqrt(eps) as a reasonable relative limit). And this is not COMSOL limitation it's a number theory limitation of binary numbers applicable to any software. My way to check convergence is to compare the results when I increase the resolution, does the result vary or converge ? Mostly FEM is for a few % precision, not to extract 18 decimals. But that depends on your model and it's finesse, are all hypothesis for the physics model correct and within limit, are ALL physics presented, ... -- Good luck Ivar
Alexander Warning
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Posted: 1 decade ago Dec 13, 2011, 1:00 p.m. EST
The 100-1000 times eps^.5 turned out to be in my original estimate for absolute tolerance of 10^-6. When I had decreased tolerance to 10^-7 to 10^-9 there was almost no improvement. Thank you so much for the explanation.

-Alex
The 100-1000 times eps^.5 turned out to be in my original estimate for absolute tolerance of 10^-6. When I had decreased tolerance to 10^-7 to 10^-9 there was almost no improvement. Thank you so much for the explanation. -Alex
Mohammad Hossein Babaei
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Posted: 1 decade ago Dec 20, 2011, 10:09 a.m. EST
Hi, How can I check the numerical value of "eps"?

Thanks
Hossein
Hi, How can I check the numerical value of "eps"? Thanks Hossein

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