Parallel accelerated cartesian expansions for particle dynamics simulations

Rapid evaluation of potentials in large physical systems plays a crucial role in several fields and has been an intensely studied topic on parallel computers. Computational methods and associated parallel algorithms tend to vary depending on the potential being computed. Real applications often involve multiple potentials, leading to increased complexity and the need to strike a balance between competing data distribution strategies, ultimately resulting in low parallel efficiencies. In this paper, we present a parallel accelerated Cartesian expansion (PACE) method that enables rapid evaluation of multiple forms of potentials using a common Fast Multipole Method (FMM) type framework. In addition, our framework localizes potential dependent computations to one particular operator, allowing reuse of much of the computation across different potentials. We present an implicitly load balanced and communication efficient parallel algorithm and show that it can integrate multiple potentials, multiple time steps and address dynamically evolving physical systems. We demonstrate the applicability of the method by solving particle dynamics simulations using both long-range and Lennard-Jones potentials with parallel efficiencies of 97% on 512 to 1024 processors.