Spatial Reasoning for Generalized N - Body Physics - Discrete Element Algorithms

Discrete element simulation solves Newton's dynamic equilibrium equations for a large set of constantly moving objects. In order to simulate the interaction of these objects, it is necessary, at every timestep, to find and resolve their spatial relationships. For large simulations this process is very computationally intensive, and dominates the cost of the whole simulation. It is desirable, therefore, to develop algorithms for processing this spatial intersection query as efficiently as possible. Many methods have been developed recently, both specifically for discrete element contact detection, and for spatial queries in general. Here we develop a general statement of the Discrete element contact problem, and describe an interface to a generalized contact detection module. A range of methods is then discussed and implemented. From these reults we develop improved methods that attempt to maximize performance over a wide range of problems. Finally, the implementations are compared using the MIMES 2D discrete element simulation environment. Thesis Supervisor: Prof. John R. Williams Title: Professor of Civil and Environmental Engineering