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This paper analyses a PDE solver working on adaptive Cartesian grids. While a rigorous element-wise formulation of this solver offers great flexibility concerning dynamic adaptivity, and while it comes along with very low memory requirements, the realisation's speed can not cope with codes working on patches of regular grids--in particular, if the latter deploy patches to several cores. Instead of composing a grid of regular patches, we suggest to identify regular patches throughout the recursive, element-wise grid traversal. Our code then unrolls the recursion for these regular grid blocks automatically, and it deploys their computations to several cores. It hence benefits from multicores on regular subdomains, but preserves its simple, element-wise character and its ability to handle arbitrary dynamic refinement and domain topology changes.