CAREER: Advanced Computational Multi-Body Dynamics for Next Generation Simulation-Based Engineering

随着计算机微处理器行业支持一种强调大规模并行架构的新设计范式，今天？计算多体动力学方法逐渐变得过时，无法应对基于仿真的工程带来的日益增长的挑战。该职业建议的动机是有机会通过新的仿真方法重塑现有的计算多体动力学领域。具体来说，开发的方法将从新的算法角度解决复杂的动态应用，这些算法将利用可负担得起的高性能并行计算硬件。从原子运动到颗粒材料（砂、砾石等）的流动，再到预测/理解/优化重型机械（如1500吨电动挖掘机）的动力学，目前限制基于仿真的工程潜力的三个效率障碍如下：(i)数值解方法植根于顺序算法，（ii）数值方法不能扩展到有效地处理非常大的系统，（iii）数值积分方法仅限于非常小的积分步长。在这项研究中，利用新兴的大规模并行商用计算机硬件的先进数值方法将被识别、研究和证明，以有效地克服这些效率障碍。具体而言，(a)依赖于显式数值积分，将研究迭代求解框架的并行模拟潜力，(b)利用微分变分不等式方法，将研究可扩展互补方法，因为它们有可能使用数万个并行计算线程来解决具有摩擦接触的数十亿个物体动力学问题，(c)依赖于隐式数值公式。辛方法在分子动力学模拟中具有更大积分步长的潜力。如果它是一个领域分解技术，一个多重网格方法，或者一个新的变分隐式积分器，在这个项目下研究的方法最终利用应用数学和利用计算机科学的新兴趋势来推进/加速工程中的发现。在具体的经济方面，这项研究工作将：(1)由于与几个联邦政府和行业合作伙伴的现有技术转让安排，将转化为基于仿真的工程的直接生产力提高；(2)协助NASA研究人员设计下一代月球和火星探测器所需的仿真技术。在教育/推广方面，这项努力将(3)通过正在进行的年度夏季科学、技术、工程和数学（STEM）项目，增加威斯康星大学工程学院的少数民族入学率，该项目有明确的目标和成功指标；(4)促进威斯康星大学研究生/本科生机械工程教育，强调应用数学和计算机科学是新工程师技术形成的基本组成部分；(5)提高公众对计算多体动力学主题的认识，特别是应用数学和计算机科学学科的潜力。

As the computer microprocessor industry rallies behind a new design paradigm that emphasizes massively parallel architectures, today?s Computational Multi-Body Dynamics methods are gradually becoming obsolete and ill-positioned to answer the ever growing challenges posed by Simulation-Based Engineering. This Career proposal is motivated by the opportunity to reshape the existing Computational Multi-Body Dynamics landscape through new simulation methods. Specifically, the developed methods will tackle complex dynamics applications from new algorithmic perspectives that draw on affordable high performance parallel computing hardware.From the motion of atoms to the flow of granular material (sand, gravel, etc.) and on to predicting/understanding/optimizing the dynamics of heavy duty machinery such as a 1,500 ton electric excavator, three efficiency barriers that currently limit the potential of Simulation-Based Engineering are identified as follows: (i) numerical solution methods are rooted in sequential algorithms, (ii) numerical methods do not scale to handle very large systems efficiently, and (iii) numerical integration methods are limited to very small integration step-sizes. Under this research, advanced numerical methods leveraging emerging massively parallel commodity computer hardware will be identified, investigated, and demonstrated to effectively overcome these efficiency barriers. Specifically, (a) relying on explicit numerical integration, an iterative solution framework will be investigated for its potential for parallel simulation, (b) drawing on a differential variational inequality approach, scalable complementarity methods will be investigated for their potential to use tens of thousands of parallel computational threads to solve billion body dynamics problems with frictional contact, and (c) relying on implicit numerical formulas, symplectic methods will be investigated for their potential for larger integration step-sizes in Molecular Dynamics simulation.If it is a domain decomposition technique, a multigrid methodology, or a new variational implicit integrator, the approaches investigated under this project ultimately draw on Applied Mathematics and leverage emerging trends in Computer Science to advance/accelerate discovery in Engineering. In specific economic terms, this research effort will (1) translate into immediate productivity gains in Simulation-Based Engineering as a result of existing technology transfer arrangements with several federal government and industry partners, and (2) assist NASA researchers with simulation technology required to design the next generation of Lunar and Mars rovers. In educational/outreach terms, this effort will (3) increase minority enrollment in the College of Engineering at the University of Wisconsin through an ongoing annual summer Science, Technology, Engineering, and Mathematics (STEM) program with clearly stated goals and success metrics, (4) promote a graduate/undergraduate Mechanical Engineering educational track at Wisconsin that emphasizes Applied Mathematics and Computer Science as fundamental building blocks in the technical formation of new Engineers, and (5) increase public awareness of the Computational Multi-Body Dynamics topic in particular and the potential of Applied Mathematics and Computer Science disciplines in general.