  In this work, a cell agglomeration strategy for the cut cells arising in the
extended discontinuous Galerkin (XDG) method is presented. Cut cells are a
fundamental aspect of unfitted mesh approaches where complex geometries or
interfaces separating sub-domains are embedded into Cartesian background grids
to facilitate the mesh generation process. In such methods, arbitrary small
cells occur due to the intersections of background cells with embedded
geometries and lead to discretization difficulties due to their diminutive
sizes. Furthermore, temporal evolutions of these geometries may lead to
topological changes across different time steps. Both of these issues, i.e.,
small-cut cells and topological changes, can be addressed with a cell
agglomeration technique. In this work, a comprehensive strategy for the typical
issues associated with cell agglomeration in three-dimensional and
multiprocessor simulations is provided. The proposed strategy is implemented
into the open-source software package BoSSS and tested with 2- and
3-dimensional simulations of immersed boundary flows.
