Skip to content

Draft: Add second order derivative to geometry class

Alexander Müller requested to merge alexander.mueller/dune-geometry:feature/secondOrderDerivatives into master

This MR aims to add second order derivative information to the Dune::Geometry interface, i.e. a Hessian functionality.

Hessian hessian ( const LocalCoordinate &local ) const;

It should be a base for the discussion about interface discussions and also about implementations.

Up to now here only MultiLinearGeometry would have a non-zero implementation. Even then, for affine transformation it is still zero.

Therefore, this boils down to implement cubes(2D,3D),prisms(3D) and pyramids(3D). An implementation that works for these case can be done, but I have a hard time understanding the current implementations. In especially, the jacobianTransposed Link function somehow only deals with pyramids and prisms and not cubes, which indicates that I don't really understand what's going on.

Furthermore, maybe a derivative transformation function is also needed, such that Hessians can be transformed but not with unnecessary computations.

@maik.porrmann we can first discuss maybe.

see also dune-grid#177

Merge request reports