[Dune] [#469] interface for periodic grids (Attachment added)

[Dune]

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User who did this - Andreas Dedner (dedner) 

Attached to Project - Dune
Summary - interface for periodic grids
Task Type - Support Request
Category - Discussion
Status - New
Assigned To - 
Operating System - Unspecified / All
Severity - Low
Priority - Normal
Reported Version - SVN
Due in Version - Undecided
Due Date - Undecided
Details - In the attached files two relevant cases (CASE 1,CASE 2 in the following)
from application are described where periodic grids are used.

So far there are two suggestions for implementing periodic grids:
1) use of ghost cells and communication
2) use of periodic GridViews (periodic index sets and intersections)

The GridView can always be implemented (we think) if the communication
method is available. For CASE 1 this is the simpler approach and it would
be a good idea to additionally provide a PeriodicGridView.

As far as we can see CASE 2 can not be realized using PeriodicGridViews
but with the communication method available in DUNE it is also
not clear how to implement this setting since the transformation from
one boundary to the other is required.

Suggestion:
the method scatter should be extended:
template< class Buffer, class Entity, class Transformation >
void scatter ( Buffer &buffer,
               const Entity &entity,
               const Transformation &transformation,
               size_t n );
This transformation should map a neighborhood of
the sending boundary to the receiving boundary and
implement the jacobian (or jacobian inverse transpose)
for the transformation of vector field. In the case of a simple
periodic topology transformation=identity and could be 
implemented in a way that the compiler can remove any call to
the transformation (template argument). 
---------------------------------------------------
---------------------------------------------------
Here are a few questions which should be answered by the DUNE
documentation - some of them are but a discussion over the last
few months show that a lot is still not clear):
(1) equality of entity pointers (notation taken from periodic.eps)
   e=e_g? f=f_g?
   f'=f_g? f'=f?
(2) id/index sets (same question as in (1))
(3) intersection iterators:
    on e' should e or e_g be returned (different geometry)?
    on e' should boundary and neighbor be true or should this depend on the
    grid view used?
    If a transformed geometry is used, should e_g allow an intersection
    iterator to its neighbor (ghost or overlap behavior?)




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http://www.dune-project.org/flyspray/index.php?do=details&task_id=469

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