Quadratic mesh

[akd]

Hi,

In the GID manual it says quadratic meshes (say tetrahedral) would have a middle node at the mid-point of the two vertices for each edge. Is that always true? I found some elements that were not following this criteria. I know there's an inbuilt script that can bring the centre node to the middle location but is it possible to predict beforehand if GID would create curved elements where the node doesn't necessarily lie exactly in the middle location of the edge in case of tetrahedral meshes?

Thank you

[escolano]

Where is explained in the manual that quadratic nodes have always its coordinates at the mid-point of the two vertices)? It must be changed to explain it better!!

The mid-node of quadratic elements is in general located projected on the geometry, its coordinates are not located at the mid-point of the two vertex, the edge could be curved.

In case of a tetrahedral mesh, the nodes generated from the curves are located on the curves, the nodes generated from the surfaces are located on the surfaces and the rest of nodes from the volume are in the mid-point because there is no geometry to be projected inside the volume.

As you pointed there is a macro button that force all quadratic nodes to be at the mid-point of the corner vertices (but this macro is not visible by default in the macros toolbar)

macro_align_quadratic_nodes.png (99.76 KiB) Viewed 10848 times

[akd]

Thanks for the clarification. It doesn't say always,the user manual had an example for quadrilateral quadratic mesh where it adds middle node at the mid-point so I got confused.

So, apart from the curved line, say I have a surface with a curved edge, would the element whose nodes doesn't lie on the curve can still have curved edges? I think the mesher says some elements might be distorted based on what mesher we choose.

[escolano]

If do you have a surface with with a curved edge, only the nodes lying on the curve will be projected to the curve (and could then provide a curved edge). The rest of the nodes of the surface will be projected on the surface. If the surface has planar shape, then it is expected that its edges become aligned.
if the surface is curved, e.g. half-sphere, then mid-nodes will become also curved

The distortion of the mesh based on what mesher you choose (rfast vs rsuf) is not specially related with the position of the 'quadratic nodes', but with the shape of the elements considering only the 'corner nodes'. (the 'quadratic nodes' are created in a second step of the meshing. initially in the mid-edge location and then mapped to the curve/surface if belong to them)

rfast creates a 2D mesh in a '2D space parameter of the parametric surface', and then this mesh is mapped with the surface parametrization to the final 3D location.

rsurf try to directly find the position of the nodes in the 3D surface position.

rfast is faster than rsurf (as its name suggest) but for some pathological surfaces (with very non-uniform parametrization) an element well-shaped in 2D could become distorted when mapping to 3D.

[aortizb]

I know this is an old post, but after reading it's not clear to me why the 8-node quad elements don't have their midside nodes exactly in the middle between two vertices (I checked this in GiD 16 and it always gave the mid nodes not in the middle). Do we have to click on "Align the quadratic nodes to the mid edges" every time an 8-node quad mesh is generated? Why isn't this the default?

[escolano]

The mesh approximate better the original geometry if the nodes are projected on this geometry, not simply located as mid-edge coordinates, then this is off course the default.

quadratic_nodes_projected_on_the_geometry.png (21.73 KiB) Viewed 6149 times

quadratic_nodes_aligned.png (21.36 KiB) Viewed 6149 times

Only in rare cases, where maybe the curved shape provide self-intersections or negative jacobians, seems interesting to be located in the mid-edge, then can simply use the tool you know.

Why do you really want quadratic elements for the result, but do now want quadratic approximation of the shape?

[aortizb]

Thank you very much for the reply, Enrique. From a very general point of view, it really doesn't matter to me whether the nodes are exactly in the middle or not. It is just something aesthetical when considering a very simple domain (like a square) meshed with a regular mesh. It is weird to have the nodes not in the middle in this case because it is too notorious that they are not. But it is something I can live with, and I can use the tool to correct them. Thanks again and best regards.