J-P,

I should not have given Mesquite such short shrift in my reply yesterday. 
 With regard to the MappingQEulerian approach, I would imagine Mesquite 
would take the mapped points as the mesh points (basically, what my figures 
show as the mesh), then smooth those out a bit, and return new vertex 
locations.  Then I would need to update the euler_vector to reflect the new 
vertex positions - this seems to me like a difficult step since the 
euler_vector describes displacements of degrees of freedom rather than 
vertices.  My difficulty comes from not truly understanding how to think 
about degrees of freedom in that euler_vector in relation to my naive view 
of the descriptors of a mesh - i.e. vertices. 

This of course begs the question of how the hell am I going to fix my mesh 
if I don't understand the relation between dofs and the vertices I am not 
happy with!  I'll be working on this at my desk, any further discussion 
would be appreciated! 

Also, thank you again for offering help with adding Mesquite to dealii.  My 
reluctance to immediately take you up on this offer is that I am afraid of 
going down a rabbit hole, although I acknowledge that the solution to my 
mesh problems most likely lies deep in a tunnel somewhere.

Tom

On Tuesday, November 15, 2016 at 1:27:52 AM UTC-5, Jean-Paul Pelteret wrote:
>
> Hi Thomas,
>
> Trilinos' Mesquite <https://trilinos.org/packages/mesquite/> package 
> provide mesh optimisation tools. I'd be happy to see this integrated into 
> deal.II, so if you decide that this would help you solve your problem then 
> I'd be willing to help you to do so. The challenge here would be the fact 
> that its a co-dim 1 problem, so you of course need to adjust the position 
> of vertices without changing the final topology (too much). I'm not 
> immediately sure how one could manage this without some underlying 
> parametric description of the surface, but perhaps its possible.
>
> Regards,
> J-P
>

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