Hi John,<br><br>Just out of curiosity:<br>Don't you need to "smooth" the elements close to the "snapped" boundary nodes?<br>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?<br>
Finally, isn't this algorithm like a morphing algorithm?<br><br>I actually sent a mail to the mailing list to know what are GMSH' capabilities regarding morphing, but there were not much answer. <br><br>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.<br>
You would then have all the nodes positioned accordingly their distance from the originally "snapped" nodes.<br><br>Regards,<br><br>Pierre<br><br><br><br><div class="gmail_quote">2009/7/29 John Blackburn <span dir="ltr"><<a href="mailto:John.Blackburn@npl.co.uk">John.Blackburn@npl.co.uk</a>></span><br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div>
<div><font face="Arial" size="2"><span>Dear
Sir,</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>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. </span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>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:</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>* 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?</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>* 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.</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>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.</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>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.</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>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.</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>Best
Regards,</span></font></div>
<div><font face="Arial" size="2"><span></span></font> </div>
<div><font face="Arial" size="2"><span>John
Blackburn</span></font></div>
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