[Dune] how to integrate curvilinear tetrahedral elements into DUNE/Alugrid ?

[Oliver Sander]

Am 23.01.2014 11:13, schrieb Benedikt Oswald:
> Hello Andreas, thanks.
> 
> Then, I shall do so!

Hi Benedikt,
great!  Such a grid is actually a very old wish.  See the bottom of http://www.dune-project.org/contributing.html

A few thoughts from me:
- The actual implementation of a polynomial geometry should be in dune-geometry.
  Let multilineargeometry.hh inspired you.  (Maybe you don't want to support all
  those element types, though).
- The GmshReader already supports reading grids with quadratic boundary elements.
  If you read such a grid file into a UGGrid object the grid uses the extra boundary
  information as a boundary parametrization, i.e., the grid remains piecewise linear,
  but you'll approach the second order boundary as you refine.  Your data import
  from gmsh will not be much different from this.
- There is actually a method in the GridFactory interface that allows to construct
  grids with element parametrizations (like boundary parametrizations, but with elements).
  You may want to consider using those for data input.

Cheers,
Oliver

> 
> However, not being an expert in Dune internals programming,
> where would I start ?
> 
> would the extension of dune / grid / geometry grid / coordfunction be the right place ?
> 
> And, more technically speaking, should copy the geometry grid directory into my
> own source tree, implement the things there and, once it works, submit back to Dune?
> 
> What about naming the new implementation ?
> 
> Greetings, Benedikt
> 
> 
> 
> 
> --------------------------------------------------------------------------------------------------------------------------------------------------------------
> Dr. sc. techn. Benedikt Oswald - first engineer - LSPR AG - phone - +41 43 366 90 74
> Technoparkstrasse 1, CH-8005 Zürich, benedikt.oswald at lspr.ch
> --------------------------------------------------------------------------------------------------------------------------------------------------------------
> 
> On Jan 23, 2014, at 10:04 AM, Andreas Dedner <a.s.dedner at warwick.ac.uk> wrote:
> 
>> Hi Benedikt.
>> You would need to extend GeometryGrid (something many of us would
>> really appreciate). Basically GeometryGrid replaces the geometries of the host grid
>> using the GenericGeometries which are only "linear". This part of GeometryGrid
>> would need to be replaced with something higher order, e.g., some curvilinear approximation.
>> Best
>> Andreas
>>
>> On 23.01.2014 08:32, Benedikt Oswald wrote:
>>> Dear Dune
>>>
>>> as it happens we are forced to consider drastic steps to increase the efficiency of our electromagnetic solvers,
>>> especially in the frequency domain.
>>>
>>> Recently, Peter Bastian suggested we use curvilinear elements in order to model our curved geometry and domain
>>> boundaries. In fact, we believe that this will help us enormously since the element count will be much reduced.
>>>
>>> Peter also suggested we use the geometry grid on top of ALUGrid in order to achieve this.
>>>
>>> Now, my concrete questions is: given an existing curvilinear mesh (e.g. from gush), how would we do this ?
>>>
>>> I read that geometry grid manages the vertices of the underlying grid, but, a curvilinear tetrahedral element has
>>> vertices not only in the corners but also on the edges, faces and inside the volume.
>>> Perhaps my question is trivial, nevertheless, I'd appreciate your suggestions.
>>>
>>> I should say that gmsh is capable of generating quite nice curvilinear tetrahedral meshes, at least up to 3rd order.
>>>
>>> Greetings and thanks in advance, Benedikt
>>>
>>>
>>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------------------
>>> Dr. sc. techn. Benedikt Oswald - first engineer - LSPR AG - phone - +41 43 366 90 74
>>> Technoparkstrasse 1, CH-8005 Zürich, benedikt.oswald at lspr.ch
>>> --------------------------------------------------------------------------------------------------------------------------------------------------------------
>>>
>>>
>>>
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>>
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