Numerical Methods for Molecular Dynamics

这项研究的主要目标是为原子计算机模拟创建更高效的传播子，从而使更雄心勃勃的科学计算成为可能。新的确定性和随机算法将被构建用于动力学和采样的新的确定性和随机算法，使用诸如算子分裂、修正的能量函数补偿有限步、方法参数的优化以及物理洞察等技术。使用数学分析和计算机实验来测试和比较概率算法。数学分析工具包括有效精度概念、修正方程法、线性分析和KAM理论。计算机实验是在选定的模型问题上进行的，以明确地揭示兴趣的性质。更快的算法将在伊利诺伊大学贝克曼研究所的几个项目中广泛使用的分子建模软件中实现。大多数工作都是一般性的，即转移到其他类型的问题上，如天体物理、波动现象和机械工程中发生的问题。许多技术可以抽象并应用于一般问题。原子细节的计算机模拟在物理、化学、材料科学和结构生物学中被广泛使用。这些计算需要生成原子构型序列，目的要么是为了模拟实际运动，要么是为了从广泛的代表性样本中计算平均值和结构。计算时间从几个小时到几个月不等，因此它可以从更快的算法中获得巨大的好处。这项研究项目的目标是：为动态和采样创建更高效的传播器，可靠地达到可接受的精度水平。这种算法的构建结合了数学和计算机科学的思想以及物理见解。授权算法通过数学分析和计算机实验进行测试和比较。成功的算法在伊利诺伊大学贝克曼研究所的几个项目中开发的广泛使用的分子建模软件中实现。方法论上的这些进展也将以实践者为目标的文章进行传播。许多技术不仅将应用于分子模拟，而且还将应用于天体物理、结构力学和流体的模拟。潜在地，加速传播算法的可用性将导致各种否则不会获得的科学结果。对于研究生来说，这项研究的表现将是一次宝贵的跨学科经历。

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.