Numerical Methods for Molecular Dynamics

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Proposal: DMS-0204442PI: Robert D. SkeelInstitution: University of Illinois at Urbana-ChampaignTitle: Numerical Methods for Molecular Dynamics ABSTRACTThe primary goal of the research is to create more efficient propagators for atomistic computer simulations that reliably achieve acceptable levels of accuracy and thus to make possible more ambitious scientific calculations. A second goal is to explore innovative techniques that simulate long-time molecular motions without sequentially stepping through billions of intermediate states, as would be necessary with standard approaches. New algorithms for both dynamics and sampling are to be constructed using such techniques as modified energy functions that compensate for finite steps, stochastic stabilization, and optimization of method parameters, together with physical insight. Promising algorithms are tested and compared using mathematical analyses and computer experiments. Tools for mathematical analysis include the concept of effective accuracy, the method of modified equations, linear analysis, and KAM theory. Computer experiments are performed on model problems chosen to reveal unambiguously the properties of interest. Faster algorithms are to be implemented in molecular simulation software developed and distributed for public use in a project at the University of Illinois Beckman Institute. Many of the techniques will apply not only to molecular simulations but also to simulations in astrophysics, structural mechanics, and fluids.Computer simulations of atomic detail are heavily employed in physics, chemistry, materials science, and structural biology. These calculations require the generation of sequences of atomic configurations either for the purpose of modeling actual motion or for the purpose of calculating averaged values and structures from a wide range of representative samples. The computing time ranges from hours to months, so it can benefit tremendously from faster algorithms. It is the objective of this research project to do this: to create much more efficient propagators for dynamics and sampling that reliably achieve acceptable levels of accuracy. The construction of such algorithms employs ideas from mathematics and computer science together with physical insight. Promising algorithms are tested and compared using mathematical analyses and computer experiments. The successful ones are implemented in molecular modeling software being developed for widespread use in a project at the University of Illinois Beckman Institute. These advances in methodology are also to be disseminated in articles targeted to practitioners. Many of the techniques will apply not only to molecular simulations but also to simulations in astrophysics, structural mechanics, and fluids. Potentially, the availability of accelerated propagation algorithms will lead to a variety of scientific results that otherwise would not be obtained. The performance of the research will be a valuable interdisciplinary experience for a graduate student.