[Gmsh] Symetry : when it is become explicit ?

[Rui Maciel]

On 02/05/2013 03:51 PM, Adrien Girard wrote:
> Hello,
>
> I just finish university and I am now working as a mechanical engineer and
> I am still confused with some points of FEM theory.
>
> I have to make the complete thermal analysis of a rectangular box, I
> decided to use the symetry of the problem and thus modelise only 1/8 of the
> box. But now, I wonder when I have to add the symetry to the problem.
>
> - 1) to the mechanical model ? (before the simulation)
> - 2) at the simulation phase ?
> - 3) only for the post process, to visualise the result ?

It's the 1st one: before the simulation.

The main point of taking advantage of a model's symmetry is to cut down 
the computational costs of getting a solution to the problem it 
describes.  In your example, if you only analyze 1/8th of a thermal 
model then it will have approximately 1/8th of the degrees of freedom 
that it would otherwise require.  Considering that the computational 
complexity of the algorithms which dominate the whole computational 
process, as it tends to lie somewhere between either O(n^2) or O(n^3), 
(n) being the number of degrees of freedom, you can get an idea of how 
much more efficient the whole process becomes.

Taking advantage of a model's symmetry can also eases the computational 
requirements of the whole visualization process, but in general, when 
compared with the previous point, this detail is pretty much a 
non-issue.  There are plenty of ways to skin this proverbial cat, and 
symmetry doesn't tend to come up in the conversation.


Hope this helps,
Rui Maciel