Those do many-to-one communication with a single method call.
Previously, two subsequent calls were needed.  There is no reason
why the interface has to consist of two calls.  A single one is
much easier to use.

[[Imported from SVN: r9730]]

[[Imported from SVN: r9729]]

After much back and forth: this is the correct way.  This size cannot
be taken from the transfer operators, because these operators exist
only if there is more than one level.

[[Imported from SVN: r9728]]

[[Imported from SVN: r9727]]

[[Imported from SVN: r9726]]

That works for fe spaces of all orders.

[[Imported from SVN: r9725]]

[[Imported from SVN: r9724]]

[[Imported from SVN: r9723]]

[[Imported from SVN: r9721]]

Christian Engwer told me a trick how to get the mpiHelper instance without
known argc and argv.

[[Imported from SVN: r9720]]

That way we can handle multigrid transfer matrices as well.

[[Imported from SVN: r9719]]

The globalindex.hh and uniqueentitypartition.hh is from Benedikt Oswald.
The rest is from Benjamin Bykowski, with a few fixes from me.

The globalindex stuff should go into dune-grid eventually, but it needs
some polishing first.

[[Imported from SVN: r9718]]

[[Imported from SVN: r9710]]

[[Imported from SVN: r9708]]

This does what we want both on one and on many processors.

[[Imported from SVN: r9707]]

This has two advantages:
- The two matrices use different number types (adouble vs. double),
  but the generic multiplication in dune/istl/matrix.hh doesn't support
  that.  Hence before this change I had to patch dune-istl.
- It avoids one extra copying operation

[[Imported from SVN: r9703]]

[[Imported from SVN: r9693]]

With the better initial iterate introduced in the previous patch,
this lower number seems to be sufficient.

[[Imported from SVN: r9684]]

The new initial iterate is constructed by interpolating the values in Euclidean
space, and projecting back onto TargetSpace.  This has two advantages:
1) It's a better initial iterate, so we should converge faster than starting
   from coefficients_[0]
2) It makes it easier for ADOL-C to pick up correct second derivatives.
   Hence we are able to reduce the minimum number of iterations of the
   target space tr solver.

[[Imported from SVN: r9683]]

[[Imported from SVN: r9682]]

[[Imported from SVN: r9666]]

That way, they can at least be looked at.  You won't see the intra-element
details, but frequently they are not even all this important.  Proper
subsampling of higher-order functions is more difficult and has to wait
for another day.

[[Imported from SVN: r9665]]

[[Imported from SVN: r9663]]

This will be generalized to take any Lagrange basis, to allow some form
of visualization for higher-order functions.

[[Imported from SVN: r9662]]

This move more than halfs the size of this file, and makes it *much* easier
to understand.  If we ever need the gradient code we can still recover it
from the 2.3-2 branch.

[[Imported from SVN: r9650]]

[[Imported from SVN: r9648]]

[[Imported from SVN: r9614]]

[[Imported from SVN: r9601]]

[[Imported from SVN: r9588]]

[[Imported from SVN: r9587]]

[[Imported from SVN: r9586]]

Assuming that the AverageDistanceAssembler can provide it.

This is for the Gram-Schmidt solver only.  The old Gauss-Seidel
code will still use a full matrix.

[[Imported from SVN: r9585]]

[[Imported from SVN: r9584]]

viz.:

field_type
blocklevel
operator=(scalar)

[[Imported from SVN: r9583]]

[[Imported from SVN: r9582]]

CG seems to converge to quickly.  If too few iterations are performed,
then ADOL-C has trouble determining the correct second derivatives.
Since the Gram-Schmidt solver is a direct solver, OTOH, the derivatives
should be perfect.  It is also faster than the Gauss-Seidel solver I
was previously using.

[[Imported from SVN: r9581]]

Nice, because it works for rank-deficient matrices.

And still fast enough for the systems I am considering here.

[[Imported from SVN: r9580]]

I hoped that this would be faster.  However, it seems to deterioate the
convergence of the outer trust region algorithm.  Apparently, the steps
taken by a CG make it difficult for ADOL-C to compute the correct
derivatives.

[[Imported from SVN: r9576]]

We have the correct value in the variable 'oldEnergy' anyway.

[[Imported from SVN: r9575]]

We normalize unit vectors again in the constructor and the assignment operator.
This makes sure we never drift away from the unit sphere, and it also allows
us to init unit spheres with any value in R^n and be sure we obtain a unit
vector.  This makes the test pass again.  Leaving the projection out didn't
really make a measurable difference anyway.

[[Imported from SVN: r9574]]