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需要数值方法，将小区域中单个原子相互作用的建模与剩余区域中较大原子组之间相互作用的建模（连续介质模型）结合起来。 一个重要的例子是裂纹扩展，其中实际的预测模型需要裂纹尖端附近小区域中原子详细相互作用的准确性，以及较大周围材料中连续介质建模的效率。尽管可以实现最大的准确性通过计算机模拟材料中所有原子的相互作用，材料中的大量原子使得这种方法即使对于最快的计算机也是不可行的。 准连续介质方法可以通过将裂纹尖端附近的原子模型与周围材料中的连续介质模型耦合来实现此类模拟，而不会牺牲可靠预测所需的精度。 通过用代表性原子替换选定区域中的大量原子，连续介质模型实现了所需的精度，并大大减少了计算工作。主要研究者建议开发准连续介质方法的分析和自适应算法，以确保其可靠性并提高其效率。 将开发理论和严格的数值实验来确定最准确和最有效的原子连续介质耦合。 准连续介质方法的发展有可能促进新材料的设计，这些新材料能够更好地抵抗失效并具有对科学技术重要的其他特性。