5.5.6 IUL-factorization with reduced pattern

In the 3D case or in the 2D case with bilinear/quadratic/... elements, the requirements on the matrix (a) and (b) from Sec. 4.3.1 cannot be fulfilled. We have to factor in these cases instead of the original matrix  ${\ensuremath{\color{red}\mathfrak{K}}}$ a (spectrally equivalent) matrix  $\widetilde{{\ensuremath{\color{red}\mathfrak{K}}}}$ with the proper reduced pattern. This matrix  $\widetilde{{\ensuremath{\color{red}\mathfrak{K}}}}$ can be achieved by deleting all entries not included in the reduced pattern or by lumping these entries. We have to change the internal storage of the pattern of  $\widetilde{{\ensuremath{\color{red}\mathfrak{K}}}}$ (usually stored in some index arrays) in any case, i.e., only setting the not admissible entries to zero causes errors in the factorization of  $\widetilde{{\ensuremath{\color{red}\mathfrak{K}}}}$.