Granular materials composed of particles with complex shapes are challenging to simulate due to the high number of collisions between the particles. In this context, star shapes are promising: they cover a wide range of geometries from convex to concave and have interesting geometric properties. We propose an efficient method to simulate a large number of identical star-shaped particles. Our method relies on an effective approximation of the contacts between particles that can handle complex shapes, including highly non-convex ones. We demonstrate our method by implementing it in a 2D simulation using the Discrete Element Method, both on the CPU and GPU.