This proposal centers on the creation, analysis, and implementation of methods of broad applicability and unsurpassed effectiveness for calculating pairwise interactions arising in time-consuming simulations in chemistry, particularly molecular dynamics.

Molecular simulations of scientific interest require vast amounts of computer time, and the bulk of this time is typically spent on calculating pairwise interactions between particles. It is currently not feasible to do simulations of the duration or scale needed for many scientific investigations. Additionally, current models are often compromised based on the features and strengths of existing N-body solvers. In particular, the lack of an efficient solver for nonperiodic boundaries discourages the use of solvent boundary potentials as well as the use of implicit solvent models based on the Poisson equation. These shortcomings of current N-body technology will be addressed by the developments described below.

Typically, the calculation of pairwise interactions is done either directly or with standard tools like the fast Fourier transform (or the fast multipole method). For many of these problems there exists a less well known O(N) algorithm, namely the multilevel summation method, which is fast, general, and scalable to large numbers of processors. A recently completed study for molecular dynamics demonstrates a remarkable performance advantage of the multilevel summation method over implementations of the fast multipole method and of the particle-mesh Ewald method. Although these results indicate the potential of the approach, there are many unexplored and promising possibilities involving mathematical techniques and capabilities of emerging hardware and software. It is the objective of the proposal to explore these further, to analyze them theoretically and experimentally, and to implement and disseminate the results.

  Last updated 2014-6-22