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Weak form boundary - details

Posted 2011年1月7日 GMT-5 07:40 Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 3.5a 4 Replies

Sullivann Craig
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Hi all,

I come back here because I have some question about Weak form
Boundary.

I have a boundary integral equation int_{boundary)u(s)=-u(s).
I use the Weak form boundary to find the unknown u(s) definined at
the surface of the geometry.

Brievely, how does comsol do to solve it by using FEM.
I think that comsol just expand the solution u in a shape functions set
then solve the equation system obtained for each node of the mesh.
I am right ? How does play the test function ?
Someone can explain to me the different steps
used by comsol to solve a problem using
Weak form boundary ?

Thank you very much !

Sullivan
4 Replies Last Post 2011年2月4日 GMT-5 09:18
Kai Herbrig
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Posted: 1 decade ago 2011年1月7日 GMT-5 08:29
That's a kind of question with a book-sized answer ... you should check the doc: "understanding FEM". There are many facts explained very well of how COMSOL works in detail.

A few remarks (thats how I understand FEM):

Using the weak form is the way of FEM.

COMSOL does not "expand" the solution to shape functions - shape functions are part of the approximations.

COMSOL solves the linear / linearized (Jacobian-)matrix.

Last but not least, the solution produced by FEM (and therefore by COMSOL) is the not the solution "for each node" - it is the "integration-averaged" (-> weak form) solution over the whole element(s).

Best regards.
That's a kind of question with a book-sized answer ... you should check the doc: "understanding FEM". There are many facts explained very well of how COMSOL works in detail. A few remarks (thats how I understand FEM): Using the weak form is the way of FEM. COMSOL does not "expand" the solution to shape functions - shape functions are part of the approximations. COMSOL solves the linear / linearized (Jacobian-)matrix. Last but not least, the solution produced by FEM (and therefore by COMSOL) is the not the solution "for each node" - it is the "integration-averaged" (-> weak form) solution over the whole element(s). Best regards.
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7日 GMT-5 09:13
Hi

there are a few interesting books, see:

www.comsol.eu/support/books/

In particular that of Zimmermann (older FEMLAB AND COMSOL 3.4) and the book of Edberg

but also
i.e. the three (to be 4 once) books of Francois Axisa (check by Amazon), on "Modelling of Mechanical Systems"

--
Good luck
Ivar
Hi there are a few interesting books, see: http://www.comsol.eu/support/books/ In particular that of Zimmermann (older FEMLAB AND COMSOL 3.4) and the book of Edberg but also i.e. the three (to be 4 once) books of Francois Axisa (check by Amazon), on "Modelling of Mechanical Systems" -- Good luck Ivar
René Christensen
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Posted: 1 decade ago 2011年1月11日 GMT-5 05:27
Where can this document 'Understanding fem' be found?
Where can this document 'Understanding fem' be found?
Kai Herbrig
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Posted: 1 decade ago 2011年2月4日 GMT-5 09:18
It's delivered with your comsol distribution :)

Check the "reference guide" chapter 3 p. 483. (V3.5a)

It's delivered with your comsol distribution :) Check the "reference guide" chapter 3 p. 483. (V3.5a)

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