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flat values - not interpolated

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Bonjour à tous,

J'ai passé ma soirée à lire et à relire les guides d'utilisateur de COMSOL mais je n'ai encore pas trouvé de réponse à ma question...

Il y a quelques années, j'utilisais le logiciel d'éléments finis CATIA. La résolution des EDP se faisait de la manière suivante :

1) Les deux membres de l'EDPà résoudre sont multipliés par une fonction test w puis la forme faible équivalente de l'EDP est obtenue en utilisant le théorème de Green;
2) La géométrie du problème est discrétisée et sur chaque élément de la discrétisation, l'inconnu u ainsi que la fonction test w sont développées dans une base commune de polynômes (dont on peut choisir le degré). L'équation finale est alors un système d'équations dont les inconnus sont maintenant la valeur de u aux différents noeuds de la discrétisation.

Sur chaque élément, la fonction peut ainsi être interpolée par un polynôme (dans l'approximation nodale) de sorte que sur CHAQUE élément, la valeur de u n'est pas constante : u(élément 1)(x,y,z) = u_1*phi_1(x,y,z)+u_2*phi_2(x,y,z)+...

Comment se fait t-il qu'à la visualisation, avec COMSOL la valeur de mon inconnu soit constante sur chaque éléments ? Je m'attendais à observer une valeur différentes de ma solution en chacun des points de mon élément...

Que fait exactement COMSOL pour afficher la solution sur un élément de la discrétisation ? Fait-il une moyenne des valeurs correspondantes aux nœuds de cet élément ? Comment alors visualiser les valeurs interpolées et pas seulement une moyenne ?

Il y a vraiment très peu d'information sur ces détails dans les guides fournis avec le logiciel.
Je n'ai pas envie "d'appuyer sur le bouton" sans comprendre ce que fait le logiciel :)

Merci pour vos idées !

D. Smouthie

5 Replies Last Post 2011年1月13日 GMT-5 06:09
Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 2011年1月12日 GMT-5 16:45
English, please.
English, please.

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Posted: 1 decade ago 2011年1月13日 GMT-5 03:13
Hi all

I have just a question about Comsol :
So far, I used the software CATIA to solve my PDE.
The different steps are very easy :
- first : the PDE is multiplied by a test function w. A weak form Is obtained
by using Green's theorem,
- the geometry is discretized then in each element of the mesh, the unknown u and w
are developped in a polynoms set.
-We obtain an equations system where the
unknowns are now the value of u in each nodes
of the mesh,
- this system thus solved.

In this way, the solution u is interpoled in each element of the mesh
and this solution is not a constant in this element.

Why in COMSOL, in the visualization step, we obtain
always a constant solution in each element ?
Does COMSOL do an average of u of the value at the nodes of the element to show
the result ? How can I obtain the interpoled solution in each element ? The previous polynom are used ?

The COMSOL's books do not explain this
procedure...

Thank you for your ideas

D. S





Hi all I have just a question about Comsol : So far, I used the software CATIA to solve my PDE. The different steps are very easy : - first : the PDE is multiplied by a test function w. A weak form Is obtained by using Green's theorem, - the geometry is discretized then in each element of the mesh, the unknown u and w are developped in a polynoms set. -We obtain an equations system where the unknowns are now the value of u in each nodes of the mesh, - this system thus solved. In this way, the solution u is interpoled in each element of the mesh and this solution is not a constant in this element. Why in COMSOL, in the visualization step, we obtain always a constant solution in each element ? Does COMSOL do an average of u of the value at the nodes of the element to show the result ? How can I obtain the interpoled solution in each element ? The previous polynom are used ? The COMSOL's books do not explain this procedure... Thank you for your ideas D. S

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2011年1月13日 GMT-5 04:24
Hi

I agree not everything is written out, but already now, with 4-5 modules there is enough to read. for some time.

My way to understand is to make simple models and test it out. Why not try it out in 2D a square with 2-4 elements and then see the different options, particularly when plotting the default is with higher order polynomials too, so there the changes of the shape function for the calculations, and then the polynomials for the display mixes.

I normally check my models with flat mesh grid, no interpolation, then I look at the nicer smoothened results

--
Good luck
Ivar
Hi I agree not everything is written out, but already now, with 4-5 modules there is enough to read. for some time. My way to understand is to make simple models and test it out. Why not try it out in 2D a square with 2-4 elements and then see the different options, particularly when plotting the default is with higher order polynomials too, so there the changes of the shape function for the calculations, and then the polynomials for the display mixes. I normally check my models with flat mesh grid, no interpolation, then I look at the nicer smoothened results -- Good luck Ivar

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Posted: 1 decade ago 2011年1月13日 GMT-5 05:47
Hi Ivar,

I already made a simple model 2D (solution of Poisson's equation in a square 1X1 by using squared element and linear shape functions)...I remarked that in each elements, the value of the solution u given is the average of the solution at the different nodes (there 4 nodes by elements) of the squared-element...why ? why the given solution in each element is not interpoled ? Every other softwares make like this !

D. S
Hi Ivar, I already made a simple model 2D (solution of Poisson's equation in a square 1X1 by using squared element and linear shape functions)...I remarked that in each elements, the value of the solution u given is the average of the solution at the different nodes (there 4 nodes by elements) of the squared-element...why ? why the given solution in each element is not interpoled ? Every other softwares make like this ! D. S

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2011年1月13日 GMT-5 06:09
Hi

have you checked the Plot Group - Surface - Quality
with i.e no refinement, or normal refinement, smoothing off and compared that to the true mesh (not the smoothened display mesh) ?

For me COMSOL is doing even more than any other FEM, in addition you have the shape elements, try solving the same simple case with linear or higher order shape elements, and without/with smoothing

--
Good luck
Ivar
Hi have you checked the Plot Group - Surface - Quality with i.e no refinement, or normal refinement, smoothing off and compared that to the true mesh (not the smoothened display mesh) ? For me COMSOL is doing even more than any other FEM, in addition you have the shape elements, try solving the same simple case with linear or higher order shape elements, and without/with smoothing -- Good luck Ivar

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