[Dune] Feature request

[Adrian Burri]

Hi everyone,

Andreas and I have encountered a problem while implementing a 
discontinuous Galerkin method and came up with a possible solution. I've 
added a detailed description below. We would be glad if you could tell 
us your view on the topic, especially if a) the proposed solution is 
acceptable to everyone and b) if anyone sees an alternative way to 
tackle the described problem.

Cheers

Adi

Feature request
===========
Request:
---------
Addition of a "twist" method to IntersectionIterator. The twist 
indicates the
orientation of the neighboring face with respect to the face of the element,
where the IntersectionIterator was started.

- Signature: int IntersectionIterator::twist() const
- Affected classes: IntersectionIterator
- Default implementation possible: yes

Motivation:
-----------
In discontinuous Galerkin methods, there are higher order face integrals 
which
necessitate the evaluation of the adjacent elements' base functions at a 
given
(quadrature) point on the face. These (quadrature) points are given in 
the local
coordinates of one face's reference element. To determine the corresponding
reference element coordinates in the other element, one now needs to map the
reference element coordinates in the physical space (using 
Geometry::global) and
back again into the other reference element (using Geometry::local), 
which is
too costly considering the non-linearity of the mapping for hexahedra.
The introduction of the twist information not only allows to directly 
map the
reference element coordinates of the adjactent faces onto each other, 
but also
to identify corresponding quadrature points on these faces, so that an
additional speedup can be achieved by caching the base function evaluations
locally.


Open questions:
---------------
- Treatment of non-conforming grids (the definition of the twist is
straightforward, but the twist alone is not sufficient to define the 
mapping)
- Alternative approach: in an alternative approach, the identification 
of quadrature points on the adjacent faces must be possible and efficient