This patch contains only whitespace changes.

Previously, some code was in Dune::GFE, some was in Dune::,
and a lot of it was in the global namespace.

I wrote them years ago mainly because I thought they should exist.
But they were never actually used them for anything, and I don't
really know were they could be used either.  Supposedly they
could be useful for implementing problems without a minimization
formulation, but that's not currently planned, and I don't know
what the precise requirements would be, either.

Since the code is short and almost trivial, and easily resurrected,
this commit removes the two files.  For newcomers this will mean
two less files to wonder about.

Lisa Julia Nebel authored 1 year ago and Sander, Oliver committed 8 months ago

The LocalIntegralStiffness assembles a tangent matrix by
suitably combining derivatives of the energy density with
derivatives of the geometric FE interpolation.  See the
detailed description in dune-gfe-manual.pdf.

This patch also includes a new test in localintegralstiffnesstest.cc.
It checks if the assembled matrix is the same as the one computed
by LocalGeodesicFEADOLCStiffness.

For a 3d Cosserat material I get a speedup of about 3x.

I am not too happy about this method, because for the scalar finite
element is an implementation detail.  But for the time being I need
this method for the upcoming LocalIntegralStiffness.

It is used by the upcoming LocalIntegralStiffness.

Previously they were returned by value, but I do not remember any
actual reason for that.  Return by const reference leads to a
measurable speed increase when computing the derivatives of
projection-based FE onto the sphere.  It also fixed some
undefined behavior in that code, which took const-references
of the returned temporaries.

Returning the coefficients by const reference is more difficult
for product manifolds, because previously the interpolation rules
stored the coefficients separately for each factor space.
With this patch, these rules now store the coefficients twice:
once in the old separate format, and once as needed for returning
them by reference.  Interpolation rules are not meant to exist
in large numbers, and therefore I do not think that this
extra space consumption matters.

This broke recently (or never worked), because nonconforming
discretizations were not tested anywhere.  This patch therefore
also generalizes harmonicmaptest to also test with a
nonconforming discretization.

As part of the fix, the interpolation rules get a new method
`evaluateValueAndDerivative`, because the previous way to get
the value and the derivative in a single call (the `evaluateDerivative`
method that takes a value as an argument) only worked for the
conforming case.

The ProductManifold class generalizes RigidBodyMotion, and can do
everything that the RigidBodyMotion class can.  Therefore there is
no point in keeping RigidBodyMotion any longer.  Having two
implementations for the same thing will just confuse people.

The multiplication by operator* between a ScaledIdentityMatrix
and a FieldMatrix only got introduced in Dune 2.9.  Therefore,
avoid it if we are building with earlier versions of Dune.

Move the polar decomposition to a separate file and add the algorithm by Higham and Noferini (from Robin Fraenzel)

In the test for the Higham and Noferini algorithm, we see:
Unfortunately, for matrices that are close to an orthogonal matrix, this algorithm is
about 2x slower. One can benefit from the Higham and Noferini algorithm only if the
matrix is quite far away from an orthogonal one.

Before, the calculation was terminated after exactly three iterations, now the
stopping criterion is fulfilled if the change in the norm of the polar factor is
small enough.

So far, the Cosserat rod energy implementation hat a first-order
finite element space hardcoded.  This patch removes that restriction.
As for the other models in this Dune module, the finite element basis
is now a template parameter of the model energy, and can be set to
any reasonable basis.

The dune-common 2.7 release finally adds all those standard
binary addition, multiplication, etc operators for FieldVector
and FieldMatrix.  Hence we do not have to have our own
implementation anymore.  We still keep it for backward-
compatibility with dune-common 2.6, but guard it behind
cpp conditionals.

Previously, the actual projection happened by calling the constructor
of one of the classes that implements points on a manifold.  This patch
introduces an new method projectOnto, which makes the projection more
explicit.

Makes it faster, but only by 1 or 2 percent.

The method using the SVD works in principle.  However, it does not play nicely
with automatic differentiation, because singular values are not always differentiable.

The method proposed by Higham to compute the polar factor, on the other hand,
is a Newton method at heart.  Therefore, it can be used together with AD without
problems.

[[Imported from SVN: r10076]]

[[Imported from SVN: r10070]]

[[Imported from SVN: r10069]]

As of yet completely untested

[[Imported from SVN: r9898]]

[[Imported from SVN: r9682]]