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Scaled variables
Posted 2011年11月28日 GMT-5 10:36 Studies & Solvers Version 4.2a 3 Replies
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I don't fully understand the meaning of "scaled variables", especially in relation to the solver settings. For example Comsol manual says:
"The absolute-tolerance parameters are used for time-dependent studies are very problem specific. By default, the absolute tolerance is applied to scaled variables, with the default value being 0.001 for all solution components.
The default scaling for the displacement components is based on the size of the geometry in the model, and certain reasonable scales are used for the pressure and contact force variables, if any. You are encouraged to change these scales as soon as better values are known or can be guessed or estimated from the applied forces, yield stress, reaction forces, maximum von Mises stress. The same suggestion applies to the displacement scale, which can be estimated easily if the problem is displacement controlled. This approach can significantly improve the robustness of the solution. The scales need to be entered using the main unit system within the model."
Can anyone give me a brief explanation of the above lines? I can't fully understand how the scaling works.
Best,
J
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When solving the dependent variables, any numerical system must be scaled such that the matrix values are reasonnably close to 1, because if you want to mix i.e. 1E9 [Pa] sized items with 1E-6 [m] sizes you might easily get numerical overflows/underflows. therefore COMSOL scales all variables (check the solver log) before starting to mix the matrixes and to invert them.
But, COMSOL does not alway s choose a "correct" scale value , so sometimes it's worth to manually scale your variables.
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Good luck
Ivar
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Thank for your explanation.
Can you give me more information ? For instant, your example has 1e9 [Pa] and 1e-6[m] size, what are the appropriate scale for them ?
Best
Duc
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Normally Comsol has a good internal algorithm to estimate the scaling values so 99% of the time I do not bother to use manual scaling.
Manual scaling is some times required for solid contact physics or user defined equations and dependent variables. The idea is that the scaling brings the variable to roughly 1 unit
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Good luck
Ivar