On 14/03/11 06:26, Mikhail Artemiev wrote:
Hello.
Dear Christophe,
is there any parameter in gmsh to handle the distribution of the second
order additional nodes?
I mean - can I change any parameter to stand these additional nodes at
the middles of the edges regadless curvilinear geometry?
Hi Mikhail,
Yes: to insert the high order nodes by linear interpolation on the
straight edges, set "Mesh.SecondOrderLinear=1;".
If you want the high order nodes to be equispaced in parameter space,
but still on the curved edges, you;ll have to slightly modify the source
code (cf. computeEquidistantParameters in Mesh/HighOrder.cpp)
Christophe
Thanks
Mikhail Artemiev
----- Original Message ----- From: "Christophe Geuzaine"
<[email protected]>
To: "Geordie McBain" <[email protected]>
Cc: "Mikhail Artemiev" <[email protected]>; <[email protected]>
Sent: Wednesday, March 09, 2011 2:37 PM
Subject: Re: [Gmsh] The volume of the second order tetrahedron
On 08/03/11 04:46, Geordie McBain wrote:
2011/3/7 Mikhail Artemiev<[email protected]>:
Hello, Geordie.
Thank you for reply.
I used "Tools - Visibility - Numeric - Mesh - Hide all elements -
Show
Element (for instance, 1365)" to draw that figure.
Oh right, O.K. It's a funny looking shape, isn't it. Perhaps that's
just how Gmsh depicts nonlinear elements?
It's a very important question!
Indeed. I don't know much about the internals of the Gmsh, but let's
see if we can't make some progress.
Please, look at 2 figures:
this is a shpere that was approximated by first order tets
http://saveimg.ru/show-image.php?id=47cdfa0e6f7a01f5dee8880c7081e151
this is a sphere that was approximated by second order tets
http://saveimg.ru/show-image.php?id=fa66051392be4e36e2262055272170e1
These 2 meshes was created by gmsh from one geo file (and with the same
characteristic lengths).
It looks as though all the nodes on the outer six-node triangular
faces of the ten-node tetrahedra lie on the geometric sphere. Is that
right? If so, that's good, and your quadratic mesh is a better
representation of the geometry than the linear one.
I will wonder if it is a feature of visualization.
Why? I don't know how the visualizer works internally but if (say)
all it can do is depict triangles, then what it's showing is a
reasonable representation of a quadratic tetrahedron, isn't it?
Hello - The visualization of high-order mesh elements can be enhanced
with the following "Mesh.NumSubEdges" option (default=2),. For example:
gmsh demos/sphere.geo -clscale 4 -order 4 -string "Mesh.NumSubEdges=10;"
Standard 10-node second order tetrahedron differs from 4-node first
order
tetrahedron by adding 6 node in the middles of the edges of
tetrahedron.
No, the additional six nodes don't have to be on the midpoints of the
edges of the tetrahedron. They can be, and probably will be if you're
only meshing a polyhedron, but in general no. There are some
restrictions, they can't be just anywhere (or the Jacobian of the
transformation from the canonical element will change sign within the
element), but they can move around a bit, and indeed this is most
desirable when meshing a curved geometry.
I think that gmsh not only adds new 6 nodes but changes the
coordinates of
these nodes too.
Perhaps to make them lie on the geometric sphere?
Therefore we have nonstandard 10-node quadratic tetrahedron and the
formulae
of the shape functions defined on the standard one don't work.
I think they will. I'm still hopeful this is a standard quadratic
tetrahedron. In terms of figure 4.3.1 on p. 228 of Ciarlet's book,
referred to earlier, I trust that these are are `isoparametric'
tetrahedra `of type (2)'; you'll also find drawings of `three
isoparametric tetrahedra of type (2)' in figure 4.4.2 on p. 251.
Am I wrong?
I'm not sure, but I'm hopeful Gmsh is correctly approximating `a
curved boundary with isoparametric finite element' as described by
Ciarlet pp. 248 ff.
I presume the same thing happens in two-dimensions, e.g. using 6-node
triangles to mesh a sector. I've tried this, as attached. It looks
good. In sector.png, I've gotten Gmsh to number the nodes, as they
appear in sector.msh, which was generated by "gmsh -2 -order 2
sector.geo". The edges of each triangle along the geometric perimeter
aren't drawn as curves (parabolas), but I think that's just economy of
depiction, and we're free to treat the elements as isoparametric
triangles of type (2), no?
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--
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine
--
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine
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