This project is concerned with efficient numerical solution of the dynamics of large groups of particles or bodies interacting under the forces of nature. Many-body and many-particle systems are encountered, for example, in studies of the dynamics of biological macromolecules, in drug design, in the simulation of plasmas, in vehicle and space-structure simulation, and in cosmology. Related problems arise through spatial semidiscretization of time-dependent partial differential equations. By looking beyond the application-specific features of the various codes and numerical techniques, this project will seek new, broadly applicable mathematical and computational tools for dynamical simulations. The focus of the mathematical study will be on preserving and exploiting Hamiltonian structure in the equations of motion, e.g. by using new symplectic discretization schemes. The project will broaden the current research dialogue among numerical analysts by considering constrained Hamiltonian systems and nearly Hamiltonian systems. Methods suited to implementation on parallel computers will be sought. At all stages, computational efficiency and practicality will be emphasized over mere mathematical novelty, and an experimental approach consistent with the tradition of the physical sciences will be adopted.
