>
>
> In the case that the mesh lives in a higher dimensional space, you also
> have to enforce -- either as part of the problem formulation, or as a
> postprocess step for the output of Mesquite -- that the new nodes still
> need to lie on the geometry as described before. In other words, nodal
> points can move *within* the surface, but not perpendicular to it.
>
> It is my understanding that this is precisely what Bonito et al's approach
enforces - at least in the setting that I will be working in. Each
solution I obtain contains a new displacement (velocity field) *and* a new
mean curvature of the surface. The approach I am referring to, called
geometric consistency, uses the identity *h* = -\laplaceBeltrami *x *to
obtain points that lie on the new surface (at least, up to supporting the
same mean curvature *h*). Since I have the mean curvature of the new
surface at each time step, I can place points x_{n+1} on the (n+1)-st
surface according to h_{n+1} = -\lapaceBeltrami x_{n+1}, where h_{n+1} is
an interpolation of h_n onto some new mesh, and the laplace beltrami
operator is discretized using a mapping that is interpolated onto the new
mesh. This is described in the paper I attached higher up in this thread.
I'm working on implementing this right now, but I'm not sure it will
redistribute mesh points in tangential directions. I think there's a
second step to this that moves vertices around.
> I have no idea whether that is possible within Mesquite, but in the
> worst case you can always project back to the previous surface.
>
One of the bullet points on the Mesquite page
<https://trilinos.org/packages/mesquite/> is: **Improve surface meshes,
adapt to surface curvature*, which at least sounds promising - I'm looking
into that this evening.
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
For more options, visit https://groups.google.com/d/optout.
