ffc team mailing list archive

[Jed Brown <jed@xxxxxxxx>]

On Wed 2008-08-13 17:21, Shawn Walker wrote:
> Actually, the reason I am even considering this, is that I have a project 
> that requires 2nd order polynomial mappings for triangles with a face on 
> the boundary.  It is actually critical to the stability and accuracy of 
> the method because there is an interaction between the velocity field on 
> the boundary and the computation of curvature (because of a semi-implicit 
> time discretization).  In my method, 2nd order polynomials are used for 
> the velocity field, so I NEED a 2nd order piecewise parameterization of 
> the boundary.
> 
> Furthermore, the problem is a two-phase free-boundary problem.  I.e. the 
> geometry is NOT known a priori.  So, I am not sure how one would use the 
> iso-geometric stuff; it may be overkill or problematic.  Any 
> thoughts?  Also, I have already implemented my problem in MATLAB and it 
> works quite well.  Of course, I could just not worry about it, but I was 
> trying to think ahead.  And I wouldn't mind having my problem implemented 
> in DOLFIN.  And, no, I don't want to develop another method that would 
> fit with dolfin.  I think that is the wrong attitude.  :)

So you are moving the mesh as part of the nonlinear iteration or
time-stepping scheme?  I'm curious how you ensure quality (and validity)
of the parametrically mapped mesh under deformations (and possibly
topology changes).  I've always thought this was a hard problem.

Have you considered a level set method?  It would give you a high order
representation of the interface while circumventing any mesh gymnastics.

Jed

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