[Dune] Trace-Meshes like ALBERTA "Sub-Meshes" (which are trace meshes, i.e. codim 1)

[Sacconi, Andrea]

Hi Claus-Justus,

AFAIK, there is no direct implementation in DUNE of what you are enquiring about. That's why me and another PhD student in my department have implemented ourselves what is needed to extract a "trace-mesh" from a given mesh.
So far, only for 2D/1D though.

Cheers,
Andrea
__________________________________________________________

Andrea Sacconi
PhD student, Applied Mathematics
AMMP Section, Department of Mathematics, Imperial College London,
London SW7 2AZ, UK
a.sacconi11 at imperial.ac.uk

________________________________________
From: dune-bounces+a.sacconi11=imperial.ac.uk at dune-project.org [dune-bounces+a.sacconi11=imperial.ac.uk at dune-project.org] on behalf of Claus-Justus Heine [Claus-Justus.Heine at ians.uni-stuttgart.de]
Sent: 18 March 2014 22:22
To: dune at dune-project.org
Subject: [Dune] Trace-Meshes like ALBERTA "Sub-Meshes" (which are trace meshes, i.e. codim 1)

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Hi there,

recently I have been asked whether there is some Dune facility, add on,
project, grid stuff which has a functionality comparable to Alberta's
"Sub-Meshes" (would better have been labeled: trace-meshes).

Ok, for Alberta (1d, 2d, 3d simplex meshes with recursive bisection)
this is "easy": there is some theoretical overhead which ensures that
any trace-mesh (e.g. the 2d boundary mesh of a 3d triangulation) is
auto-"magically" an admissible 2d mesh, trivially this holds also for
the 1d trace-meshes derived from 2d surface meshes. Also, the affine
closures generated by either refining the trace mesh are somehow
compatible to the affine closures generated by a mere bisection of the
trace mesh. Additionally, one can then define the respective traces of
finite element spaces and it shows that all this works out quite nicely.

Is there some Dune equivalent/something for this?

Please do not point me to the dune-subgrid module, as this would be
completely off-topic. Despite of the somewhat matching names
dune-subgrid deals with complete other stuff. ALBERTA's sub-meshes
define traces, whereas the subgrid module of Dune treats a selection of
bulk-elements as a new mesh in its own right. (no offend meant, and also
I suspect that consistent trace-meshes + trace spaces in the context of
standard, i.e. continuous finite elements, are probably a specialty of
certain simplicial meshes, taking the refinement algorithm into account
as well)

Asking just out of curiosity.

Kind regards,

Claus


- --
Dr. Claus-Justus Heine
Institut für Angewandte Analysis und Simulation
* Numerische Mathematik für Höchstleistungsrechner
Universität Stuttgart

Fon: +49 (0) 711 - 685 65558
Fax: +49 (0) 711 - 685 65507
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