# [Gmsh] suggested new meshing algorithm in Gmsh: hex gridding

Pierre JUILLARD pierre.juillard at gmail.com
Thu Jul 30 07:14:36 CEST 2009

```Hi John,

Just out of curiosity:
Don't you need to "smooth" the elements close to the "snapped" boundary
nodes?
If yes, doesn't it mean that you also need to reposition the nodes not only
close to the interfaces, but also those which are in the geometry?
Finally, isn't this algorithm like a morphing algorithm?

I actually sent a mail to the mailing list to know what are GMSH'
capabilities regarding morphing, but there were not much answer.

Regarding this smoothing function, it would make use of the GMSH finite
element solver part, and deal with the existing mesh, make it deformed
linearly with a given E modulus to make it fit a new shape.
You would then have all the nodes positioned accordingly their distance from
the originally "snapped" nodes.

Regards,

Pierre

2009/7/29 John Blackburn <John.Blackburn at npl.co.uk>

>  Dear Sir,
>
> I have recently been trying out Gmsh and am most impressed with its
> capabilities. I am writing an FE code of my own which uses hexahedrons. I've
> noticed that, while Gmsh does generate hex's this is quite a painful process
> and involves splitting the geometry into many more parts than would be the
> case for tets. Hex meshes can only be generated for transfinite volumes or
> ones which can be made from extrusions. I would like to suggest another
> method to generate (structured) hex meshes which is to have a "logical
> mesh", which is just a cubic grid of nodes, and then "snap" the nodes onto
> nearby interface points. You then end up with a mesh with the same topology
> as the original but distored to fit the required shapes.
>
> I would like to add this functionality to Gmsh as I think it would greatly
> improve the program. However, I am mainly a Fortran programmer. I can code
> in C with some difficulty but full OO C++ is beyond me! I was wondering, if
> I send you a detailed write up of the algorithm I have in mind (with all the
> maths/geometry written out explicitly), could you code it in for me? I
> suspect this simple algorithm would be easy to implement given Gmsh's
> existing capablities. Basically two things are needed:
>
> * a function to decide whether an arbitrary point (x,y,z) is inside a given
> volume (defined, as usual by plane or ruled surfaces themselves defeined by
> curves: just the way Gmsh works now). I'm sure Gmsh already has a function
> like this?
>
> * a funciton to "snap" a point to the nearest point on the volume surface.
> Note that only points at the interface between two regions are candidates
> for snapping.
>
> I've written a little program to implement this algorithm as I see (in 2-D
> for the moment but 3-D would not be much more difficult). The program
> outputs a .MSH file which I've plotted using Gmsh and attached. Notice how
> the algorithm involves INSERTING shapes into each other: the orange square
> was defined first, then the green circle, blue circle, and finally, yellow
> polygon. This is very different from Gmsh's current approach but its a very
> powerful technique.
>
> I also intend to write a final "relaxation" part to the meshing so the
> unecessarily distorted nodes in the blue circle would return to their
> original positions.
>
> What do you think about incorporating this functionality? Basically, the
> user would do everything he normally does to prepare the GEO file. Then
> there would be an extra button on the Mesh menu, "Grid" for example.
>
> Best Regards,
>
> John Blackburn
>
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