We will present both underlying ideas and concepts, and first results and experiencesgained within an ongoing project to implement a highly memory efficient version of thegrid generator amatos [BRH+05]. Our focus will be on algorithmic and implemen-tational approaches to realize multigrid algorithms on recursively structured adaptivetriangular grids. The key concept is to use a cell-oriented processing of the grids andspace-filling-curve techniques to get rid of the need to store neighbourship relations onadaptive grids.