Remove `ElementShapeFunctions.h/cpp`

[Psirus]

I think this ElementShapeFunctions.h/cpp file is way to big, and collects all shape functions for no good reason. And it shows in names like DerivativeShapeFunctionsTriangleOrder1, which could just be named DerivativeShapeFunctions at the appropriate interpolation class. So I think moving that there is the nicer approach. In 23b8c23a I have tried that for TriangleLinear. Does anyone see a problem with continuing that?

[TTitscher]

I am not sure about this one:

• Ok, this class is definitely to big.
• But it is one of the few files that survived the PDE transition.
• It defines N,B, nodal vales as fixed size Eigen matrices. This avoids dynamic allocation(!) and provides slightly faster algorithms (up to a certain size). So they can be reused if you try to write own as-fast-as-possible components. To match the InterpolationSimple interface, these will be dynamic.

What if, for now, we provide them as static functions in the corresponding classes like:

// class InterpolaitonTriangleLinear
static Eigen::Fix ShapeFunctions(ip){...}

Eigen::Dynamic GetShapeFunctions(ip) const override
{
return ShapeFunctions(ip);
}

The big file is gone, the change is also mainly copy-paste and we keep the option on fixed size calculations. edit: Plus, we would have them available as static functions, which can be handy, e.g. in tests

[Psirus]

It adds a bit of extra code, since everything is now there twice (see InterpolationTriangleLinear.h and InterpolationTriangleLinear.cpp), but I think its fine.

[joergfunger]

Why can't these methods that return shape functions and derivatives be always static?

[TTitscher]

They have to implement the InterpolationInterface. And virtual methods cannot be static.

[pmueller2]

The files are deleted in #250. Most content moved to the respective interpolation classes.

• shape functions for BoundaryElements were not used and have been removed.
• iga bezier extraction code was not used and was removed (I talked to Peter about this)