Fast algorithms for the simulation of polygonal particles

Three algorithms to speed up discrete-element simulations for granular matter are presented in this paper. The first algorithm allows to determine neighborhood relations in polydisperse mixtures of particles of arbitrary shape, either discs, ellipses, or polygons. The second algorithm allows to calculate the distance of two polygons in constant time, independently of the complexity of the shape of the polygons. This makes fast simulations of polygonal assemblies possible. The third method is a special type of parallelization technique which is optimized for workstations with shared memory.