Refinement and coarsening is performed on the primal grid only. The corresponding dual grid is defined implicitly based on the primal grid. It is ensured that nodes of the primal grid correspond uniquely to cells in the dual grid. The construction of the adaptive dual grid is completely local. On a primal cell it depends only on the configuration of the primal cell and the adjacent cells.
Data access is based on hash tables.
The concept has already been worked out in 2D and applied to MHD simulations.