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

[Sacconi, Andrea]

Hi,

to complete my previous answer, we are dealing with 2D conforming meshes, from which 1D conforming meshes originate.
You traverse the intersections and select the ones on the portion of the interface you need; the coupling between the two grids (if you need boundary integrals where functions from both grids are involved) reduces to a vector where you store the correspondence between the global indices of corners in the 2D and 1D grids, respectively.

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 Andreas Dedner [a.s.dedner at warwick.ac.uk]
Sent: 18 March 2014 21:28
To: dune at dune-project.org
Subject: Re: [Dune] Trace-Meshes like ALBERTA "Sub-Meshes" (which are trace meshes, i.e. codim 1)

Hi.
Actually I would love to have that as well. But I do not think there yet
is a "metagrid" is this type available. But perhaps somebody is working on
this?

I do not think the conformity etc. is the problem - the trace mesh would be a
dune grid in any case. The metagrid would simply only be conforming if the underlying
grid has some special property. But in principal there is no issue. I guess implementing
the intersections on the tracegrid would be the main work which would have
to done.

Andreas

On 18.03.2014 22:22, Claus-Justus Heine wrote:
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


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