[[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]]

[[Imported from SVN: r9572]]

[[Imported from SVN: r9571]]

[[Imported from SVN: r9563]]

The old implementation used quaternion multiplication to transport
the argument to the Lie algebra, and use the standard formula there.
However, one may as well use the formula for the unit sphere in R^4,
which is much simpler, and also faster.  I fact, this patch gives
a few percent of speedup for the overall code.

[[Imported from SVN: r9562]]

There is one copy which takes FieldVector<T,4> as its second argument.
Since EmbeddedTangentVector ( = Quaternion<T>) derives from FieldVector<T,4>,
that second implementation should work in all cases.

[[Imported from SVN: r9560]]

The methods 

Rotation<T,3> exp(const Rotation<T,3>& p, const EmbeddedTangentVector& v) 

and

otation<T,3> exp(const Rotation<T,3>& p, const Dune::FieldVector<T,4>& v)

do literally the same.  So they should be next to each other in the code.

[[Imported from SVN: r9559]]