The Tersoff many-body potential: Sustainable performance through vectorization

We extend the LAMMPS molecular dynamics program with a new, vectorized implementation of the Tersoff potential [7]. Given the well-established and well-studied mechanisms for parallelism in molecular dynamics programs [1], our efforts focus on vectorization as a further step to fully utilize available hardware. This contribution describes how our implementation achieves sustainable performance across a number of architectures, most notably the Xeon Phi coprocessor, using vectorization. On current architectures, vectorization contributes greatly to the system’s peak performance; this is true for CPUs with the SSE or AVX instruction set extensions, and especially for machines with wide vectors, such as the Xeon Phi. Many successful open-source molecular dynamics packages—e.g. Gromacs, NAMD, LAMMPS and ls1 mardyn [6, 9, 8]—take advantage of vectorization. Implementation methods vary between hand-written assembly, intrinsics (compiler-provided functions that closely map to machine instructions), and annotations that guide the compiler’s optimization [10]. Typically, only the parts of the calculation that consume a large fraction of the total runtime are optimized; among them, the neighbor list construction and the force calculation. For most simulations, the forces are derived from pair potentials, such as the Coulomb or Lennard-Jones potentials. Indeed, vectorized implementations of the force calculation due to pair potentials are found in many molecular dynamics programs. However, some applications, especially in materials science, require many-body potential formulations. With these, the force between two atoms does not depend solely on the distance between them, but also on the relative position of the surrounding atoms. For many-body potentials, the force calculation is not vectorized in the available molecular dynamics programs. There has been previous work on implementing many-body potentials on the GPU [3, 4, 5], but not on more conventional architectures with vectorization support.