The Linked Cell Method for Short-Range Potentials

Abstract

In Chapter 1 we introduced the particle model, first potential functions and the basic algorithm. Further potentials were presented in Section 2.2.4. So far, we left open how to evaluate the potentials or forces efficiently and how to choose a suitable time integration method. The following chapters will cover these issues. Note that the different methods and algorithms for the evaluation of the forces depend strongly on the kind of the potential used in the model. We will start in this chapter with the derivation of an algorithm for short-range interactions. This approach exploits the fast decay of a short-range potential function and the associated forces. Thus, short-range interactions can be approximated well if only the geometrically closest neighbors of each particle are considered. Note that the algorithm presented here also forms the basis for the methods discussed in the subsequent Chapters 7 and 8 for problems with long-range interactions.