Sparsify data transfer for mass-conserving basis functions

[freifrauvonbleifrei]

Currently, the basis transforms for the biorthogonal and full weighting functions exchange all of the data along one pole at once:

DisCoTec/src/hierarchization/DistributedHierarchization.hpp

Line 406 in d1a8586

static void exchangeAllData1d(const DistributedFullGrid<FG_ELEMENT>& dfg, DimType dim,

This is not optimal, in particular if hierarchization is performed only to some minimal level > 0.

This thesis describes some conditions:

• the hat dehierarchization needs the data defined by the "Kegel-Bedingung" (cone condition) / KegelFill algorithm . this optimization is already implemented for the hat functions. (for hierarchization, the hat function only needs its direct parents.)
• the biorthogonal and full weighting bases need variants of the LiftingFill algorithm for both transforms. In particular, the data dependency is symmetric for our purposes: if a finer-level point needs the data from a coarser-level point, then the reverse will also be true, as scaling function coefficients need to be updated.

Thus, it is worth considering to hierarchize in multiple "rounds" and communicate updated data for each level of hierarchization only.