Collaborative Research: Simulation of Multibody Dynamics. Leveraging New Numerical Methods and Multiprocessor Capabilities

该项目利用新的数值积分方法和多处理器技术（软件和中档硬件）的最新突破，提供理论和计算基础，使机械系统仿真的范式转变成为可能。 最近的数值积分方法开发的机械系统模拟的大型工业问题（如车辆，飞机，航天器，齿轮，链条/轨道，接触/冲击等）。已经证明了将模拟时间减少二到三倍的能力。 拟议的工作借鉴这些结果（a）调查和扩展使用的Hilber-Hughes-Taylor（HHT）型积分器在机械系统仿真，和（B）调查和扩展新的专门分区添加剂龙格库塔方法，具有良好的稳定性，可调数值阻尼，和广泛的收敛阶数。 这一努力也将导致精确的积分公式与可调数值阻尼的一阶微分方程的解决方案。 这些公式将使机电系统（混合多体动力学和控制问题）的模拟在一个统一的框架。 研究的第二个方向将调查机械系统仿真技术，利用软件和中档硬件支持并行计算的最新进展。 多体动力学特定的负载平衡和进程间通信管理，考虑到机械系统的拓扑结构，沿着异步雅可比评估策略，将使可扩展的方程制定和多处理器平台上的数值解。这项研究的两个重点新的数值积分技术和相关的并行计算支持对于大型工业类型的机械系统，将在仿真时间上产生一到两个数量级的减少。 在经济方面，这项工作有利于设计工程师依靠基于仿真的工程，提高他们的生产力。 在教育方面，这项工作提供了材料和实例，用于计算动力学和数值分析的实践课程，以及旨在通过一系列研讨会和讲习班向高中学生和教师介绍代表性不足的群体到计算科学领域的长期倡议的基础。

This project capitalizes on new numerical integration methods and recent breakthroughs in multi-processor technologies (software and midrange hardware) to provide the theoretical and computational foundation that will enable a paradigm shift in mechanical system simulation. Recent numerical integration methods developed for mechanical system simulation of large industrial problems (e.g. vehicles, aircraft, spacecraft, gears, chains/track, contact/impact, etc.) have demonstrated the ability to reduce simulation times by a factor of two to three. The proposed work draws on these results to (a) investigate and extend the use of Hilber-Hughes-Taylor (HHT)-type integrators in mechanical system simulation, and (b) investigate and extend new specialized partitioned additive Runge-Kutta methods that have excellent stability properties, adjustable numerical damping, and a wide range of convergence orders. This effort will also lead to accurate integration formulas with adjustable numerical damping for the solution of first order differential equations. These formulas will enable the simulation of mechatronic systems (mixed multibody dynamics and controls problems) in a unified framework. A second direction of research will investigate mechanical system simulation techniques that leverage recent advances in software and midrange hardware support for parallel computation. Multibody dynamics specific load balancing and inter-process communication management that account for the topology of the mechanical system, along with an asynchronous Jacobian evaluation strategy, will enable scalable equation formulation and numerical solution on multiprocessor platforms.Together, the two thrusts of this research (new numerical integration techniques and the associated parallel computation support) will yield one to two orders of magnitude reduction in simulation times for large industrial-type mechanical systems. In economic terms, this work benefits design engineers relying on simulation-based engineering by enhancing their productivity. In educational terms, this work provides material and examples for hands-on classes in Computational Dynamics and Numerical Analysis, as well as the foundation for a longer term initiative aimed at introducing under-represented groups to the field of Computational Science through a series of seminars and workshops offered to High School students and teachers.