[petsc-users] DMPlex higher order elements

[Mark Lohry]

On 08/24/2016 11:27 AM, Andrew Ho wrote:
> Good geometric accuracy is very import for achieving appropriate 
> convergence rates in complex geometry, not just using higher order 
> polynomials on flat elements.
>
> If you look at Hesthaven's book Nodal Discontinuous Galerkin Methods, 
> Table 9.1 shows that without support for curved elements, higher order 
> DG element on flat elements converges at sub optimal rates due to 
> inaccuracies produced by the boundary conditions.
>
> There's no way to re-construct this curved information correctly after 
> the fact; it must be generated by the meshing software.
>

I don't *entirely* agree with the suggestion the mesh generator has to 
provide that information. Some people reconstruct splines through the 
nodes to create higher order meshes after the fact (which also requires 
some detection or specification of sharp corners to break the spline). I 
personally take the given mesh from the generator in addition to an 
IGES/NURBS type CAD file for complex geometries, and then do a kind of 
projection for sub-cell curved boundary faces.


> On Wed, Aug 24, 2016 at 10:12 AM, Jed Brown <jed at jedbrown.org 
> <mailto:jed at jedbrown.org>> wrote:
>
>     Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> writes:
>     >> Yes, I do not support that since I think its a crazy way to
>     talk about
>     >> things. All the topological information is in the Tri3 mesh, and
>     >> Cubit has no business telling me about the function space.
>     >>
>     >>
>     >> Do you support / plan to support curved elements?
>     >>
>     >
>     > I had "support" in there, but there were bugs. Toby and Mark
>     discovered
>     > these, and Toby has fixed them. I think
>     > all of the fixes are in master now.
>
>     The context is clearly that the mesh generator needs to express the
>     curved elements.  DMPlex doesn't have a geometric model available,
>     so it
>     doesn't know how to make the Tri3 elements curve to conform more
>     accurately to the boundary.  The mesh generator has no business
>     telling
>     you what function space to use for your solution, but it'd be a
>     shame to
>     prevent it from expressing element geometry.
>
>
>
>
> -- 
> Andrew Ho


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