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Mesh Quality basics
Posted 7 sept. 2010, 16:02 UTC−4 Version 5.2 4 Replies
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Hi,
I've got some pretty basic questions about mesh quality, but I can't find any direct answers to these questions.
Why is it important? I found sources that say that it is important for fast convergence of iterative solvers, what about direct solvers? Are there other issues such as solution accuracy, stability and mesh inversion? What causes low-quality meshes to be problematic?
Is it necessary to enforce a minimum element quality? I've read you should keep it above 0.01 but it doesn't say what happens if you don't.
Do the same meshing rules apply for triangular and quadrilateral meshes?
If anyone could answer these questions it would be of great assistance. I haven't had much luck finding explanations aimed at the beginner to intermediate users of FEA.
I've got some pretty basic questions about mesh quality, but I can't find any direct answers to these questions.
Why is it important? I found sources that say that it is important for fast convergence of iterative solvers, what about direct solvers? Are there other issues such as solution accuracy, stability and mesh inversion? What causes low-quality meshes to be problematic?
Is it necessary to enforce a minimum element quality? I've read you should keep it above 0.01 but it doesn't say what happens if you don't.
Do the same meshing rules apply for triangular and quadrilateral meshes?
If anyone could answer these questions it would be of great assistance. I haven't had much luck finding explanations aimed at the beginner to intermediate users of FEA.
4 Replies Last Post 16 mai 2016, 06:24 UTC−4
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Posted:
1 decade ago
Hi
meshing is an art :) and probably one could spend a year with all specific cases.
In a few words, generally one want to have a regular mesh with nodes roughly on the surface of a shere and even length edges, such that small displacements are distributed among all sub-items in a more or less equal way, this gives best precision. Furthermore, the gradient of the variables solved for should not be too large over the element volume, such that we get a good representativity of the gradient and its changes. Think o the nyquist criteria for representation of a Sinus wave, it's very similar.
In practice you mesh become rather squeezed or "distorted", if you apply too large deformation on a node you might even "invert" the element this is a serious topology change as the sign of displacements changes and the results are wrong (at least locally).
Then the mesh elements are used to map shape functions (linear quadratic cubic ...) the higher order the more precise, if the mesh is "good", and the higher order the less the model accepts poor mesh quality. That is why COMSOl warns you when mesh quality becomes too low, it forces first order shpae functions on these elements. Or if the displacements are too large, then it tells you that elements are inverted.
These warnings are there to tell you that the quality of the prepresentativity of your model is in doubt, mostly its a local effect, but if it is there where you have a stress concetration effect and where you would expect a rupture, then you are in a bad situation, you must do something to improve the mesh quality (local higher mesh density)
Tri or quad, thet or brick, these are then the geometrical shape of the elements, often they were linked with the shape functions applied on the elements, COMSOL treats this as two different and independent items, while classical programmes have a tendency to link the shape functions to the element types.
Personally I use mostly triangles (2D) and thethahedrals (3D) and 2nd order elements (the default) and it works fine, but when you have symmetric parts (typically revolved) then quad/bricks can be made smoother and more symmetrical (typically for optics, axes and other cylindrical symmetry items etc). Enven in 2D axi, you must use quad for any element touching the symmetry axis.
normally the higher the number of nodes per elements AND the higher shape functions, AND higest mesh quality gives the most precise results, BUT it takes the longest to solve (and sometimes ou might find out that you need your entire lifetime to get there once !)
So naother rule: use symmetry to simplify your model, the less elements the faster it solves and the quicker you can check your model. Thereafter you can increase the number of mesh elements for some final tests, and check that you get a more or less constant result out, independent of the mesh density
Hope this helps on teh way
--
Good luck
Ivar
meshing is an art :) and probably one could spend a year with all specific cases.
In a few words, generally one want to have a regular mesh with nodes roughly on the surface of a shere and even length edges, such that small displacements are distributed among all sub-items in a more or less equal way, this gives best precision. Furthermore, the gradient of the variables solved for should not be too large over the element volume, such that we get a good representativity of the gradient and its changes. Think o the nyquist criteria for representation of a Sinus wave, it's very similar.
In practice you mesh become rather squeezed or "distorted", if you apply too large deformation on a node you might even "invert" the element this is a serious topology change as the sign of displacements changes and the results are wrong (at least locally).
Then the mesh elements are used to map shape functions (linear quadratic cubic ...) the higher order the more precise, if the mesh is "good", and the higher order the less the model accepts poor mesh quality. That is why COMSOl warns you when mesh quality becomes too low, it forces first order shpae functions on these elements. Or if the displacements are too large, then it tells you that elements are inverted.
These warnings are there to tell you that the quality of the prepresentativity of your model is in doubt, mostly its a local effect, but if it is there where you have a stress concetration effect and where you would expect a rupture, then you are in a bad situation, you must do something to improve the mesh quality (local higher mesh density)
Tri or quad, thet or brick, these are then the geometrical shape of the elements, often they were linked with the shape functions applied on the elements, COMSOL treats this as two different and independent items, while classical programmes have a tendency to link the shape functions to the element types.
Personally I use mostly triangles (2D) and thethahedrals (3D) and 2nd order elements (the default) and it works fine, but when you have symmetric parts (typically revolved) then quad/bricks can be made smoother and more symmetrical (typically for optics, axes and other cylindrical symmetry items etc). Enven in 2D axi, you must use quad for any element touching the symmetry axis.
normally the higher the number of nodes per elements AND the higher shape functions, AND higest mesh quality gives the most precise results, BUT it takes the longest to solve (and sometimes ou might find out that you need your entire lifetime to get there once !)
So naother rule: use symmetry to simplify your model, the less elements the faster it solves and the quicker you can check your model. Thereafter you can increase the number of mesh elements for some final tests, and check that you get a more or less constant result out, independent of the mesh density
Hope this helps on teh way
--
Good luck
Ivar
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Posted:
1 decade ago
Thx Ivar for this great delineation of meshing.
I have another question on this topic:
How does a bad element quality effect the accuracy of the results I obtain?
From university I know you should avoid meshes with low element-quality.
Using the "boundary layer" or "refine" options I notice a better resolution of the solution but with a sacrifice of mesh-quality.
Do I generate worse values then???
I have another question on this topic:
How does a bad element quality effect the accuracy of the results I obtain?
From university I know you should avoid meshes with low element-quality.
Using the "boundary layer" or "refine" options I notice a better resolution of the solution but with a sacrifice of mesh-quality.
Do I generate worse values then???
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Posted:
1 decade ago
Hi
COMSOL uses first order shape elements when the low quality or inverted flag appears, this means that these regions might be less precise, but there is not a clear 1:1 rule here.
Plot the element quality, if your min/max dimensioning values of your design comes from the same corners where the mesh quality is bad, then I would not trust the simulation, and would redo a mshing campaign
A general comment: use the latest version and not the early 4.0, you will be less frusttrated ;)
--
Good luck
Ivar
COMSOL uses first order shape elements when the low quality or inverted flag appears, this means that these regions might be less precise, but there is not a clear 1:1 rule here.
Plot the element quality, if your min/max dimensioning values of your design comes from the same corners where the mesh quality is bad, then I would not trust the simulation, and would redo a mshing campaign
A general comment: use the latest version and not the early 4.0, you will be less frusttrated ;)
--
Good luck
Ivar
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Posted:
8 years ago
Hi Ivar
I have multiple layers surrounding to each other and I set mesh size normal for external sphere and set custom for other layers and changed min. element size according to warnings. eventually, there is no warnings, but when I plot max/min volume, it gives the same coordinate as shown in attached file. It means I should not trust my simulation results?
Any helps will be appreciated. Thanks
Enver
I have multiple layers surrounding to each other and I set mesh size normal for external sphere and set custom for other layers and changed min. element size according to warnings. eventually, there is no warnings, but when I plot max/min volume, it gives the same coordinate as shown in attached file. It means I should not trust my simulation results?
Any helps will be appreciated. Thanks
Enver
Attachments: