[Gmsh] Characteristic length

[Christophe Geuzaine]

On 20 Aug 2012, at 17:50, Andres Gonzalez Estrada <agestrada at gmail.com> wrote:

> Does anyone have a clue about how gmsh interpret the characteristic lenght?. The problem has been described before in several post with no successful reply, e.g.:
> 

Hi Jo - it's the length of mesh edges.

Christophe


> 
> Jö Fahlke
>  
>     
> jorrit at jorrit.de
> 
> 
>     
> Mon Feb 14 16:31:08 CET 2011
> 
> 
> I can think of several meanings for "characteristic length" (or "elements
> size" for that matter):
> 
>  * The length of the mesh elements' edges,
>  * the cubic root of the mesh elements' volume,
>  * the diameter of the circumscribed sphere of the mesh elements, or
>  * the radius of the circumscribed sphere of the mesh elements.
> 
> There are probably more possibilities.  What I want to know is whether gmsh
> follows a one consistent meaning for the characteristic length, and if yes,
> which one.
> 
> (More accurately, I want to limit the edge sizes in the grid, an I suspect the
> characteristic length can be used for that, but I can't figure out how
> exactly.  The obvious approach of "max characteristic length" == "max edge
> size" did not work, see my first mail.)
> 
> Am Mon, 14. Feb 2011, 15:49:58 +0100 schrieb David Colignon:
> >
>  do a search with the keyword "characteristic" on this page: https://geuz.org/gmsh/doc/texinfo/gmsh.html
> >
>  
> 
> > and/or see http://geuz.org/gmsh/doc/texinfo/gmsh.html#Specifying-mesh-element-sizes
> 
> I did, but I could not find an answer to the above question.  The closest to
> an explanation of the meaning of the characteristic length was
> 
> |
>  Every meshing step is constrained by a “size field” (sometimes called
> 
> |
>  “characteristic length field”), which prescribes the desired size of the
> 
> |
>  elements in the mesh.
> 
> 
> (from section 1.2 "Mesh: finite element mesh generation"), which links the
> characteristic length to the mesh element size, but does not explain how the
> mesh element size is measured or how exactly it is linked to the
> characteristic length.
> 
> Thanks,
> Jö.
> 
> -- 
> --
> Octavio Andrés González Estrada
> Research Associate
> Institute of Mechanics and Advanced Materials
> Cardiff School of Engineering
> Cardiff University 
> The Parade
> Cardiff CF24 3AA, Wales, UK
> 
> Email: 
> agestrada at gmail.com
> 
>        
> estradaoag at cardiff.ac.uk
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-- 
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science 
http://www.montefiore.ulg.ac.be/~geuzaine