Numerical Analysis of Quasicontinuum Methods

准连续介质方法的数值分析

• 批准号: 0811039
• 负责人: Mitchell Luskin
• 金额: $ 28.2万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0811039&HistoricalAwards=false
• 关键词: Numerical; Analysis; Quasicontinuum; Methods

Many physical processes of great importance to science and technology require numerical methods that couple modeling of the interactions of individual atoms in small regions with modeling of the interactions among larger sets of atoms (continuum models) in the remaining regions. An important example is crack growth, where practical predictive models require the accuracy of the detailed interaction of the atoms in a small region near the crack tip, along with the efficiency of continuum modeling in the larger surrounding material.Although the greatest accuracy could be achieved by a computer simulation of the interactions of all of the atoms in the material, the large number of atoms in the material makes this approach infeasible for even the fastest computers. The quasicontinuum method can make possible such simulations without sacrificing the accuracy needed for reliable prediction by coupling an atomistic model in the neighborhood of the crack tip with a continuum model in the surrounding material. The continuum model achieves the desired accuracy with a major reduction in computational work by replacing the large numbers of atoms in selected regions with representative atoms.The principal investigator proposes to develop analysis and adaptive algorithms for quasicontinuum methods that will ensure their reliability and improve their efficiency. Theory and rigorous numerical experiments will be developed to determine the most accurate and efficient atomistic-continuum coupling. The development of the quasicontinuum method has the potential to facilitate the design of new materials better able to resist failure and having other properties important for science and technology.

许多对科学和技术非常重要的物理过程都需要数值方法，使小区域中各个原子的相互作用进行建模与较大的原子集（连续模型）之间相互作用的建模。 一个重要的例子是裂纹增长，实用的预测模型需要在裂纹尖端附近的一个小区域中详细相互作用的准确性，以及在较大的周围材料中连续建模的效率。尽管可以通过计算机模拟所有原子在材料中的相互作用来实现最大的准确性，这使得材料的大量计算机都可以使材料的计算机变得非常快。 Quasicontinuum方法可以使这种模拟成为可能，而无需牺牲可靠预测所需的准确性，该准确性是通过将裂纹尖端附近的原子模型与周围材料中的连续模型耦合。 连续模型通过替换具有代表性原子的选定区域的大量原子的计算工作实现了所需的准确性。 将开发理论和严格的数值实验，以确定最准确，最有效的原子偶联耦合。 Quasicontinuum方法的开发有可能促进设计新材料的设计，能够更好地抵抗失败并使其他对科学和技术重要的特性。