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

[Claus-Justus Heine]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Hi Andrea,

many thanks for your comments.

I fear, however, that the first non-trivial step happens when chaining
3d and 2d meshes. 1d meshes are just a collection of line segments, and
 as such conformity (no hanging nodes) and compatibility are somehow not
an issue.

But yes: the 2d-1d case implemented in Alberta finally boils down to
that what you describe.

Best,

Claus

On 18.03.2014 23:35, Sacconi, Andrea wrote:
> 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?
> dune at dune-project.org
> 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
>>
>>
>>
>> _______________________________________________
>> Dune mailing list
>> Dune at dune-project.org
>> http://lists.dune-project.org/mailman/listinfo/dune
>
>
>
>
> _______________________________________________
> Dune mailing list
> Dune at dune-project.org
> http://lists.dune-project.org/mailman/listinfo/dune
>


- -- 
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
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v2.0.22 (GNU/Linux)
Comment: Using GnuPG with Thunderbird - http://www.enigmail.net/

iQIcBAEBAgAGBQJTKNGYAAoJEAbZWiFWzP01LVsQAMhVxCapisiF3Hw7W1q0R8cD
IZm10TkFZwLEOfQcCX0aUCk+s39daq6XzKz2rB0/JzfFq7tZL07vTbdTokL5oUnG
z3rzwM5+yiGcrhL/DsC6e4iyFJ2oAred5KR7oec24USiUTJRPqcmPxzi/F3gmW3c
fcNxwAyyA6CyuX/LoynxE0SnbiU7QEA+b0dE63sc+jgFAU4lRBoVqxteKDxj0c9A
WNFNMaAKowkWdzdwRZZSFN3gNB8O6cAhC3TPLon1mQeW30JxcMd12Kl7RNiaOwu3
SuNnidnlftyIs5acyN0cwNPOvIPcI7CLLf7GZEVi+hZ4dUIMaa9e78TDPG0QnTVE
pmaIcoxVo8euod4qdLZzyPsVYfBZ3YfOOWfqptQAozsTogwDtVOXVWgx8dZmAeDq
8GjHj5RJ9NGGDnfPeZOlB9rzOESq+wFnsgLOAEFhAQlp4sQ9elJRb/wIncFofbZA
n8ptBmvbpNUr+XuIBR1kFIJ5OUyBrnNswAvXjXnX65fSK1QtDRZRdl80mJ+JHbb1
ONogs+GnthX758m+OiXf4pUqLusnoMHP0kJD8h2J5Mfkw48itMiMOk90lTz1cdQH
u4wCwNTkFCL3azjj92BvBHu5hkIycNY3vbiAsb28DQI13WmQReRF6LsedbLTYxpy
TNq7tICTFNvmxOJMxlMC
=JKQo
-----END PGP SIGNATURE-----