Many problems in computational science and engineering require the numerical solution of partial differential equations and thus the solution of large, sparse linear systems of equations. Multigrid is known to be one of the most efficient methods for this purpose, and therefore many software packages exist that are also able to run on large HPC clusters. However, the concrete multigrid algorithm and its implementation highly depends on the underlying problem and hardware. Therefore, changes in the code or many different variants are necessary to cover all relevant cases. We try to generalize the data structures and multigrid components required to solve elliptic PDEs on Hierarchical Hybrid Grids (HHG) that are a compromise between structured and unstructured grids. Out goal is the automatic generation of the HHG data structures for arbitrary primitives. As a first step, we implemented a generic 2D prototype including a multigrid solver for the two-dimensional Poisson problem. We show that the multigrid algorithm is highly scalable up to more than 450,000 cores.