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Degrees of Freedom v. number of Mesh Elements
Posted 16.08.2011, 15:10 GMT-4 Low-Frequency Electromagnetics, Mesh, Studies & Solvers Version 4.2 4 Replies
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Hello All~
I am trying to understand how COMSOL solves for some of the fields. My research currently involves 1-5um thick layers separated by the same distance in a somewhat large (respectively) volume. We want to understand what is going on with eddy currents and hysteresis in magnetic materials near the boundaries of these layers (sub micron), and so our meshes need to be small. But I need to know just how far I can push these limits. My mesh elements are generally around 150k but the degrees of freedom solved for are are often in the 1-2 million. What is the difference between these two? Thanks for any help you can provide.
~Brock
I am trying to understand how COMSOL solves for some of the fields. My research currently involves 1-5um thick layers separated by the same distance in a somewhat large (respectively) volume. We want to understand what is going on with eddy currents and hysteresis in magnetic materials near the boundaries of these layers (sub micron), and so our meshes need to be small. But I need to know just how far I can push these limits. My mesh elements are generally around 150k but the degrees of freedom solved for are are often in the 1-2 million. What is the difference between these two? Thanks for any help you can provide.
~Brock
4 Replies Last Post 25.08.2011, 12:35 GMT-4
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Posted:
1 decade ago
Hi
check the knowledge base of COMSOL here is a specific entry for this. the number of DoF depends on the meshing type but more on the shape functions selected and the number of dependent variables from the different physics, the
--
Good luck
Ivar
check the knowledge base of COMSOL here is a specific entry for this. the number of DoF depends on the meshing type but more on the shape functions selected and the number of dependent variables from the different physics, the
--
Good luck
Ivar
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Posted:
1 decade ago
Ivar, thank you for the help. I checked out article www.comsol.com/support/knowledgebase/875/ of the knowledge base that described the elements, nodes, and degrees of freedom DoF very well. I do have a followup question though.
When the model is solved for, I look at the results and see a solution that is not extremely blocky. I can see the individual mesh elements in the image since I know where they are, but there is definitely some kind of shooting going on.
If I understand it correctly, COMSOL solves for the dependent variables of the model (4 or 5 for mef), once for each element and then smoothes the results across its boundaries? Thank you again for the help.
~Brock
When the model is solved for, I look at the results and see a solution that is not extremely blocky. I can see the individual mesh elements in the image since I know where they are, but there is definitely some kind of shooting going on.
If I understand it correctly, COMSOL solves for the dependent variables of the model (4 or 5 for mef), once for each element and then smoothes the results across its boundaries? Thank you again for the help.
~Brock
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Posted:
1 decade ago
Hi
it's a bit more complex, first of all COMSOL uses mostly by default 2nd order shape functions ontop of a "normal" mesh (which is more or less equivalent to other FEM programmes "higher order mesh elements"), in COMSOL really the meshing is mostly in simple form: "tri/quad" or "theth/cube" and the shape functions of first, 2nd, third type ... which increases the interpolation level (hence also the total number of DOF per element)
Then you have also 1st, 2nd or higher order interpolation on the results again, on top.
All this might give you some ringing on large gradient / transition regions, see the doc on smoothing/damping, but mostly it gives you smoother results.
And also, you the user have full control of the shape function order, just as for the postprocessing interpolation functions in the respective nodes (under some of the by-default-hidden sub-tabs).
I usually leave the defaults, except if I'm working on contact issues, then I mostly use 1st order shape elements (and comsol uses by default 1st order elements locally if the mesh shape is poor and it detects chances for inverted mesh elements when using the default higher order shape functions, you see the warning time to time in the solver logs)
And if I need 2nd or 3rd derivatives of the dependent variables, then I add 1 or 2 levels to the shape function order, hoping that my RAM is sufficient to handle all the new DoF's.
Finally in the postprocessing, I check my results, particularly when using coarse meshing by turning off the postprocessing interpolation, and looking directly on the 1st order wire-frame results.
My experience is that if you "see" the underlying mesh structure on default settings with COMSOL, you have a somewhat coarse meshing, but note this does not necessarily mean that the results are wrong, but perhaps the gradients are somewhat spiky
--
Good luck
Ivar
it's a bit more complex, first of all COMSOL uses mostly by default 2nd order shape functions ontop of a "normal" mesh (which is more or less equivalent to other FEM programmes "higher order mesh elements"), in COMSOL really the meshing is mostly in simple form: "tri/quad" or "theth/cube" and the shape functions of first, 2nd, third type ... which increases the interpolation level (hence also the total number of DOF per element)
Then you have also 1st, 2nd or higher order interpolation on the results again, on top.
All this might give you some ringing on large gradient / transition regions, see the doc on smoothing/damping, but mostly it gives you smoother results.
And also, you the user have full control of the shape function order, just as for the postprocessing interpolation functions in the respective nodes (under some of the by-default-hidden sub-tabs).
I usually leave the defaults, except if I'm working on contact issues, then I mostly use 1st order shape elements (and comsol uses by default 1st order elements locally if the mesh shape is poor and it detects chances for inverted mesh elements when using the default higher order shape functions, you see the warning time to time in the solver logs)
And if I need 2nd or 3rd derivatives of the dependent variables, then I add 1 or 2 levels to the shape function order, hoping that my RAM is sufficient to handle all the new DoF's.
Finally in the postprocessing, I check my results, particularly when using coarse meshing by turning off the postprocessing interpolation, and looking directly on the 1st order wire-frame results.
My experience is that if you "see" the underlying mesh structure on default settings with COMSOL, you have a somewhat coarse meshing, but note this does not necessarily mean that the results are wrong, but perhaps the gradients are somewhat spiky
--
Good luck
Ivar
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Posted:
1 decade ago
That was perfect, thank you.