ffc team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

ok, but I have a couple other questions/comments?

1. Has there been a decision on what kinds of curved meshes will be 
allowed?  And what would the mesh format be?  This seems to be the first 
decision.  It would seem natural to only allow polynomial based maps 
(for now), i.e. a quadratic triangle would require a 2nd order polynomial 
mapping (instead of a 1st order map).  You could also have higher degrees 
if you wanted.  I think the 'curved' mesh feature could be implemented 
first.  And the assembly could just IGNORE the extra curvy info for each 
triangle (for now).

2. For the assembly, I think it is still possible to compute the matrices 
exactly in SOME cases.  For example, a mass matrix could be computed 
exactly, as well as \int_{\Omega} q div(u), because the det(J) would 
cancel the 1/det(J) part of the inverse of the gradient map.  Of course, 
the stiffness matrix cannot be computed exactly.  For this, I think 
quadrature is the only way.  Or one could maybe take advantage of doing an
asymptotic expansion (taylor series) of the algebraic expression and 
compute that using enough terms based on the desired number of digits of 
accuracy.  I don't know.

3. One could add another boolean property to each triangle called:

Is_Straight

This could give a switch between computing exactly, and using quadrature. 
Most meshes will have straight interior elements; you don't really need 
them inside so much.  only the triangles with a face on the boundary 
would be curved.  So this would help prevent possible performance hit of 
doing high order quadrature.

4. How hard would it be to understand UFC~FFC for someone who knows just a 
little Python and a decent amount of C++?

If there is anything written up on how FENICS wants to do this (i.e. 
desired mesh format, etc...) please tell me.

- Shawn

On Wed, 13 Aug 2008, Anders Logg wrote:

> On Wed, Aug 13, 2008 at 11:56:11AM -0400, Shawn Walker wrote:
> > Hello.  I know this isn't very critical on the list of things to do, but
> > is there any document somewhere saying how they propose to implement
> > curved meshes with the UFC/FFC code?
> >
> > - Shawn
>
> No, I guess they have no idea how to do this. ;-)
>
> It would require an extension of UFC and it would require someone
> willing to spend the time on making it work. It's not on the top of my
> TODO list, but anyone wishing to investigate is welcome.
>
> --
> Anders