Non-fastdg: Permutation of the input happens before the sum factorization
kernel when we setup the input. This is done by a method of the corresponding
interface class.

Fastdg: In this case the input will always be ordered according to x,y,... This
means the permutation needs to happen in the sumfact kernel. Since we want to
vectorize sumfact kernels with different input permutation in an upper/lower
way we need to do this permutation in the corresponding interface class. This
is done in the realize_direct method and in the vectorized case the
corresponding methods of the scalar sumfact kernels are called.

Note: They are not yet used but in the long term the permutation should be
handled here since it is about input/output setup.

Note: Not yet working for gmsh files

Calculate the evaluation and jacobians of geometry mappings of cells
using sum factorization. By avoiding all geometry mapping of intersections
we can avoid the face-twist problem and just make the grid consistens (not
yet done).

TODO:
- Make grid consistent
- Vectorization
- 3D

Not yet implemented:

- Vectorization of quadrature loop
- Anisotropic amount of quadrature points per direction

René Heß authored 6 years ago and Dominic Kempf committed 6 years ago

Rename the function and remove the backend switch. Reasoning:

- This function was only called once without the backend switching
  mechanism.
- The function takes different arguments than the pdelab
  pymbolic_quadrature_position.
- It returns only one component of the quadrature point.

Rename the function and remove the backend switch. Reasoning:

- This function was only called once without the backend switching
  mechanism.
- The function takes different arguments than the pdelab
  pymbolic_quadrature_position.
- It returns only one component of the quadrature point.

I was tired of the amount of ifs that changed behaviour
depending on stage 1 or 3. This is a cleaner approach.

Instationary stuff not fixed so far.

This time only for sumfact, as we need direction dependency.

When doing jacobians of nonlinear systems, the inames used for
a given sum factorization kernel output depend on the accumulation
context.