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COMSOL pour des méthématiques appliquées ?

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Bonjour à tous,

Je suis étudiant en mathématiques et je souhaiterais acheter COMSOL pour mon travail de thèse. Mon travail consiste en une étude des équations intégrales par la méthode des éléments finis. Je ne connais pas du tout ce logiciel ni ses capacités de calculs. Les responsables de COMSOL ont refusé de me répondre par téléphone car je ne possède pas encore de licence. Ils n'ont pas voulu non plus m'envoyer le guide de COMSOL.
Afin d'en apprendre plus sur ce logiciel et voir si il me permettra vraiment d'avancer dans mon travail, j'aurai quelques questions à vous poser :

Je souhaiterais utiliser COMSOL pour résoudre une équation intégrale par la méthode des éléments finis (une équation vraiment simple pour commencer) :

1) COMSOL résout t-il les équations intégrales comme pour une EDP ? je veux dire le logiciel multiplie t-il mon équation intégrale par une fonction test "v" ?

2) Quelles méthodes sont utilisées par COMSOL pour le choix des fonctions tests et des fonctions de base Est-ce une méthode de Galerkin ? par collocation ? Avons-nous le choix de la méthode et peut-on passer de l'une à l'autre ?

3) Quels types de fonction de base sont utilisées ? polynômes ? polynômes d'Hermite ? Pouvons-nous changer le type de fonction de base ?

Je signale encore une fois, que je souhaiterais acheter COMSOL seulement si 1-3 sont possibles avec ce logiciel...
Les seules équations que je souhaite résoudre sont des équations intégrales ! Ce ne sont donc pas des EDP et je me demande si COMSOL résout ces équations intégrales comme si il devait résoudre une EDP (multiplication par une fonction test puis fonctions test = fonctions de base ? méthode de Galerkin ?)

Merci pour votre aide

Allan Kortes


1 Reply Last Post 5 ott 2010, 02:07 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 5 ott 2010, 02:07 GMT-4
Hi Allan

I'll answer you (partly) in English because we are all asked to keep one language to make it more general to all out here, and English is not even the natural language of the COMSOL founders, but our local Scandinavian languages is not very largely understood anyhow.

So in generla, COMSOL is, for me, first of all an general PDE solver, but a numerical one (not like Maple or Matematica, even if I suspect they have some analytical solving support under the hood). Thereafter COMSOl has been tailored and completed to trat PDEs of teh type found in physiscs problems, and all the toolboxes/modules are really just ready cooked boundary condition set-ups and more or less complete equations introduced into the PDE coefficients.

The methods used are not all described in detial (and I have not really concentrated on this as I'm first of all an engineer using the tool for physics and not for PDE mathematics). But COMSOl does distinguis the elements and their shape functions that can be higher order polynomials, at will (selectable).

What I would suggest is that you get onto one of the workshops, and ask your local COMSOL rep for a demo version to test it. But as the tool is still complex and based on one way to represent physics I can only insist on taking the workshop opportunity (or a one day introduction course) as thisallows you to ask many questions to the people presenting the tool, these are scientist/engineers, before salesmenn so they know how to answer even complex math/physics questions.

--
Have fun Comsoling
Ivar
Hi Allan I'll answer you (partly) in English because we are all asked to keep one language to make it more general to all out here, and English is not even the natural language of the COMSOL founders, but our local Scandinavian languages is not very largely understood anyhow. So in generla, COMSOL is, for me, first of all an general PDE solver, but a numerical one (not like Maple or Matematica, even if I suspect they have some analytical solving support under the hood). Thereafter COMSOl has been tailored and completed to trat PDEs of teh type found in physiscs problems, and all the toolboxes/modules are really just ready cooked boundary condition set-ups and more or less complete equations introduced into the PDE coefficients. The methods used are not all described in detial (and I have not really concentrated on this as I'm first of all an engineer using the tool for physics and not for PDE mathematics). But COMSOl does distinguis the elements and their shape functions that can be higher order polynomials, at will (selectable). What I would suggest is that you get onto one of the workshops, and ask your local COMSOL rep for a demo version to test it. But as the tool is still complex and based on one way to represent physics I can only insist on taking the workshop opportunity (or a one day introduction course) as thisallows you to ask many questions to the people presenting the tool, these are scientist/engineers, before salesmenn so they know how to answer even complex math/physics questions. -- Have fun Comsoling Ivar

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