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.

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.

The introduction of FunctionView turned out to be a major problem
with more complicated forms. The original idea was to preserver the
structure of the finite element in a way, that loops over components
of a mixed element are realized by actual loops (treating them with
free indices and such). However, this causes quite some nightmares and
was never implemented as generically as needed (I even doubt that is
possible).

However, there is another option, which is to unroll any such loops
on a symbolic level. While this may sound like a bad idea at first
there is some really positive aspects about it:
* ListTensor and ComponentTensor nodes collapse completely (and would
  otherwise have a big nightmare potential)
* Symbolic zeroes do not generate code - important in hyperbolic problems
  where the system matrices are quite sparse or for axiparallel grids,
  where geometric quantities have many zeroes.
* The compiler would unroll these small loops anyway.
* TSFC (and I guess also FFC) do it the same way.

Implementing this required me to redo the form splitting algorithm.
I rethought it and integrated it into the main ufl->loopy visitor.

... not going to the cell first.