Numerical Methods for Molecular Dynamics

提案：DMS-0204442 PI：Robert D. SkeelInstitution：伊利诺伊大学厄巴纳-香槟分校标题：分子动力学的数值方法摘要这项研究的主要目标是为原子计算机模拟创造更有效的传播器，可靠地达到可接受的精度水平，从而使更雄心勃勃的科学计算成为可能。 第二个目标是探索创新技术，模拟长时间的分子运动，而不需要像标准方法那样连续地通过数十亿个中间状态。 动态和采样的新算法将使用诸如补偿有限步骤的修改能量函数、随机稳定和方法参数优化以及物理洞察等技术来构建。 使用数学分析和计算机实验对有前途的算法进行测试和比较。 数学分析的工具包括有效精度的概念，修正方程的方法，线性分析和KAM理论。 计算机实验上选择的模型问题，以明确地揭示感兴趣的属性。 更快的算法将在伊利诺伊大学贝克曼研究所的一个项目中开发和分发供公众使用的分子模拟软件中实现。 许多技术不仅适用于分子模拟，也适用于天体物理学、结构力学和流体模拟。原子细节的计算机模拟在物理学、化学、材料科学和结构生物学中得到大量应用。 这些计算需要生成原子构型的序列，用于对实际运动建模的目的或者用于从广泛的代表性样品计算平均值和结构的目的。 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受益匪浅。 本研究项目的目标是：为动态和采样创建更有效的传播器，以可靠地达到可接受的精度水平。 这种算法的构建采用了数学和计算机科学的思想以及物理洞察力。 有前途的算法进行了测试和比较，使用数学分析和计算机实验。 这些成功的实验都在伊利诺伊大学贝克曼研究所的一个项目中广泛使用的分子建模软件中实现。 这些方法上的进展也将在针对从业人员的文章中传播。 许多技术不仅适用于分子模拟，而且适用于天体物理学、结构力学和流体模拟。 潜在地，加速传播算法的可用性将导致各种科学结果，否则将无法获得。 研究的表现将是一个宝贵的跨学科的经验，为研究生。

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.