Using Mixed Discrete-Continuum Representations to Characterize the Dynamics of Large Many-Body Dynamics Problems

使用混合离散连续体表示来表征大型多体动力学问题的动力学

• 批准号: 1635004
• 负责人: Dan Negrut
• 金额: $ 40万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1635004&HistoricalAwards=false
• 关键词: Using; Mixed; Discrete; Continuum; Representations; Using; Mixed; Discrete; Continuum; Representations

The goal of this project is to understand how computer simulation can be used to predict the motion of large systems of bodies interacting with each other through friction and contact. Studying these so-called "many-body dynamics problems" has theoretical and practical relevance in several disciplines (physics, chemistry, astronomy, geomechanics), industries (pharmaceuticals, food processing, farming, manufacturing, construction, mining), and engineering applications (additive manufacturing, nanoparticle self-assembly, robotics, ground vehicle mobility). In terms of educational and outreach impact, initiatives undertaken as part of this project will (i) promote the discipline of Computational Science at middle and high-school levels via a "The Science Behind Video Gaming" short course and a residential summer program, respectively; (ii) update and expand curricula in two graduate courses on high performance computing and advanced computational dynamics; (iii) expand a biannual advanced computing forum that facilitates transfer of technology; and, (iv) provide training via a Master of Engineering distance learning program for practitioners who need to analyze, process, and solve problems using information generated by the growing use of data collection in engineering design and industrial operations.The research effort will focus on investigating techniques that facilitate a discrete-continuum dual representation in the simulation of many-body dynamics problems. The fundamental question answered is how should one handle parts of a many-body dynamics problem using a continuum formalism so that the new mixed discrete-continuum representation manages to preserve the dynamics of the original problem? Also, how should a continuum representation be fine-grained into a discrete one, and conversely, what techniques should be used to coarse-grain a discrete representation into a continuous one? Mechanical engineering expertise (dynamics of many-body systems, solid mechanics, plasticity), applied math techniques (meshless methods for solving partial differential equations, optimization methods), and computer science components (machine learning, software engineering) will combine in a coordinated effort to solve the stated problem. In this context, the goal of this project is to (a) establish a systematic methodology for producing rheologies that, when embedded in a continuum mechanics model, produce a solution that is close to that of a large discrete many-body dynamics problem; and (b) use this methodology to understand whether there are rheologies that have a universal attribute; i.e., that are applicable to all, or a large spectrum of, many-body dynamics problems. In this context, a rheology is regarded as a methodology that ties at microscale the dynamics/flow of a continuum to the forces acting on it. The research plan is built around the idea of augmenting physical insights with a machine learning process that uses large amounts of data generated by fully-resolved, many-body dynamics solutions to produce rheology candidates.

该项目的目的是了解如何使用计算机模拟来预测通过摩擦和接触相互交互的大型物体的运动。研究这些所谓的“多体动态问题”在多个学科（物理，化学，天文学，地质力学），行业（制药，食品加工，农业，农业，制造，建筑，矿业）和工程应用（nanoparticle Indivate，Nananoparticle自动化自动化，Robot，Robost，Roberics，Mosportions）中具有理论和实际相关性。在教育和外展影响方面，作为该项目的一部分进行的倡议将（i）通过“视频游戏背后的科学”简短课程和住宅夏季计划来促进中和高中级别的计算科学学科； （ii）在两个研究生课程中更新和扩展有关高性能计算和高级计算动力学的课程； （iii）扩展了一个每半年高级计算论坛，该论坛促进了技术的转移； （iv）通过工程远程学习计划提供培训，为需要分析，处理和解决问题的从业人员使用越来越多地收集数据收集在工程设计和工业运营中的信息。研究工作将集中于研究促进离散型互联性双重表示的技术。回答的基本问题是，如何使用连续性形式主义处理多体动态问题的一部分，以便新的混合离散式代表代表能够保留原始问题的动力学？另外，如何将连续表示形式细化为离散的表示，相反，应使用哪些技术将离散表示形式用于连续形式？机械工程专业知识（多体系统的动态，固体力学，可塑性），应用数学技术（用于求解偏微分方程的无网格方法，优化方法）和计算机科学组件（机器学习，软件工程）将结合起来，以共同努力解决所述问题。在这种情况下，该项目的目的是（a）建立一种系统的方法论，用于产生流变学，当嵌入连续力学模型中时，会产生与大型离散多体动力学问题相关的解决方案； （b）使用这种方法来了解是否存在具有普遍属性的流变。即，适用于所有人或大量多体动态问题。在这种情况下，流变学被认为是一种在微观上将连续性与作用在其上作用的力的动力学/流动的方法。该研究计划围绕着通过机器学习过程来增强物理见解的想法，该过程使用了大量由完整的，多体动力学解决方案生成的数据来生产候选流变学的候选者。