[dune-pdelab] Element-Jacobians by Automatic Differentiation

[Christian Waluga]

Dear PDELab-Developers/Users

I have implemented a proof of concept that demonstrates the assembly of element-Jacobians
in dune-pdelab by automatic instead of numeric differentiation (using an operator-overloading
automatic differentiation approach).

So far, the code is neither tuned for performance nor feature-complete (only volume Jacobians
are implemented atm, but the rest should be more or less copy & paste-work). I managed to run
the poisson.hh test-case from pdelab and it seems to work fine. Basically to get this running,
one only needs to derive the local operators from a new AutomaticDifferentiationJacobian-class
and perhaps make some minor adjustments to the local operator (which should be compatible with
the NumericalJacobian-classes).

However, before I put more work into this, I want to ask: Is there some interest in such an
addition to PDELab in the future? If yes, is anybody interested in looking at possible performance
improvements with me? My first shot is rather slow for higher orders and 3D cases, and there
should be much room for performance tuning. I will do some tuning myself and add more features,
when I find the time. In the meantime, if you are interested in looking at the code please ask.

Best, Christian