Numerical Methods for Molecular Dynamics

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The primary goal of the research is to create more efficientpropagators for atomistic computer simulationsand thus to make possible more ambitious scientific calculations.New deterministic and stochastic algorithms for both dynamics and samplingare to be constructed using such techniques as operator splitting, modifiedenergy functions that compensate for finite steps,and optimization of method parameters, together with physical insight.Promising algorithms are tested and compared using mathematical analysesand computer experiments. Tools for mathematical analysis include theconcept of effective accuracy, the method of modified equations, linearanalysis, and KAM theory. Computer experiments are performed on modelproblems chosen to reveal unambiguously the properties of interest.Faster algorithms are to be implemented in molecular modeling softwarebeing developed for widespread use in a couple of projects at theUniversity of Illinois Beckman Institute. Most of the work issufficiently general that is transfers to other types of problems suchas occur in astrophysics, wave phenomena, and mechanical engineering.And many of the techniques can be abstracted and applied to generic problems.Computer simulations of atomic detail are heavily employed in physics,chemistry, materials science, and structural biology.These calculations require the generation of sequences of atomicconfigurations either for the purpose of modeling actual motion or for thepurpose of calculating averaged values and structuresfrom a wide range of representative samples. The computing time rangesfrom 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 dynamicsand sampling that reliably achieve acceptable levels of accuracy.The construction of such algorithms employs ideas from mathematicsand computer science together with physical insight.Promising algorithms are tested and compared usingmathematical analyses and computer experiments.The successful ones are implemented in molecular modeling softwarebeing developed for widespread use in a couple of projects at the Universityof Illinois Beckman Institute. These advances in methodology are also to bedisseminated in articles targeted to practitioners.Many of the techniques will apply not only to molecular simulationsbut also to simulations in astrophysics, structural mechanics, and fluids.Potentially, the availability of accelerated propagation algorithmswill lead to a variety of scientific results that otherwise would not beobtained. The performance of the research will bea valuable interdisciplinary experience for a graduate student.