dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

Hello, all.  I've been thinking about this higher order mesh stuff, and I 
need to be more clear about what I want to do.   I'm not sure it would be 
good to make an ultra-general higher order mesh format.  It seems to be 
more trouble than it is worth (right now).

What I would like to have is a format for higher order meshes based on 
polynomial mappings (ONLY!).  Currently, everything in FENICS assumes that 
a P1 map is used for each element in the mesh.  Of course, this only 
requires knowledge of the vertex coordinates of the element.  If a higher 
order polynomial map is used, all you need are the positions of the extra 
control points.  And this would extend the P1 map quite naturally.  For 
the .xml format, I think the data for the control points should contain 
the usual vertex coordinates also (not just the extra control points). 
This would be redundant, but a little simpler to read in from the XML 
file.  Note that storing the coordinates for each element separately would 
not be good, because even the edge mid-point positions would be used by 2 
(or more) elements, so you need to keep this connectivity information.

One advantage of using a polynomial map (besides for free boundary 
problems) is that the element tensor can be computed exactly in some cases 
(but not for a stiffness matrix).  This isn't bad.

Anyway, I know this is probably boring some of you.  And I know this is 
not a high priority, but I am willing to put in time implementing this 
(mostly because it would be useful to me).  I will repost another format 
for the mesh.xml file and see what people think.

- Shawn