Hard Disk Molecular Dynamics (HDMD) techniques often exhibit significant loss in calculation speed when applied to the simulation of highly polydisperse particle systems. The collision rate of the reported algorithms may be lower by as much as two orders of magnitude if compared to the collision rate of a monodisperse system of the same number of particles. This is mainly due to the fact that the rectangular cells in the simulation domain used in HDMD methods must meet a certain size criterion. In this paper, we introduce a cell technique that removes the requirement on the cell size enabling simulation of particles with sizes much larger than the cell size. This approach improves the collision rates in the simulation of tested polydisperse systems by factors ranging from 5.5 to 57 depending on the size distribution of the particle population simulated. This may enable the simulation of grand canonical systems in which the size and the number of particles can change throughout the simulation. The technique is compatible with the simulation of disk-like as well as irregularly shaped particles and can be extended to three dimensions.