Efficient Formulation and Solution of Equations of of Motion for Optimal Parallel Computing

7 # 9 9 $ $ $ $ $ 2 D D D D D D X X X D 6 * ' $ 6 * 6 '。本研究的主要目标是提高复杂多体系统动态行为的有效建模和仿真的技术水平。这将通过运动方程的公式来完成，该方程与并行计算机系统的节点拓扑/节点间通信体系结构高度耦合，并行计算机系统将在其上运行。这项工作最初将针对允许使用显式时间数值积分方案的系统。一旦完成，注意力将转向将这项工作的有益计算方面应用于导致刚性方程组的应用，因此仅限于使用隐式时间积分程序。努力将是利用O(N)和其他低阶动态方程的表述过程（例如，使用递归关系来减少操作）的方面，以及高度并行化的描述符表述。预期的结果是开发一个多体程序/代码，该程序/代码可以自动生成特定复杂多体系统的运动方程和相关仿真代码，该系统是低运算次数和并发方程形式的最佳组合（在最大吞吐量的意义上），用于在规定的并行计算系统上实现。这将产生最大可能的聚合吞吐量，从而在可用的并发处理系统上实现系统模拟的最大总体速度。*** u推进了复杂多体系统的动态行为的有效建模和仿真的艺术状态。这将通过方程9的公式来实现@ 5 9!!!9 9 9 p 9 ！9:~ H H (F G) H H (d ' @ = / R B H -:LaserWriter Times E E E P。安德森。艾丽西亚·哈里斯

7 # 9 9 $ $ $ $ $ 2 D D D D N X X $ | x D 6 * ` $ 6 * 6 6 ` . 6 6 6 6 6 6 9409782 Anderson The prime objective of this research is to advance the state of the art for the efficient modeling and simulation of the dynamic behavior of complex multibody systems. This will be accomplished through a formulation of the equations of motion which is highly coupled with the node topology/internode communication architecture of the parallel computer system on which it will be run. This work will be initially directed towards systems which allow for the use of explicit temporal numerical integration schemes. Once accomplished, attention will be turned towards applying beneficial computational aspects of this work to applications which result in stiff systems of equations, and thus are confined to the use of implicit temporal integration procedures. The effort will be to take advantage of aspects of O(N) and other low order dynamic equations formulation procedures (e.g. use of recursive relationships to reduce operations), as well as descriptor formulations which are highly parallelizable. The intended result is the development of a multibody procedure/code which automatically produces equations of motion and associated simulation code for a specific complex multibody system which is the optimal ( in the sense of maximizing throughput) combination of low operations count and concurrent equations form for implementation on prescribed parallel computing system. This will result in the maximum possible aggregate thoughput, and consequently, maximum overall speed for the simulation of the system on the available concurrent processing system. *** u to advance the state of the art for the efficient modeling and simulation of the dynamic behavior of complex multibody systems. This will be accomplished through a formulation o f the equations of 9 @ 5 9 ! ! ! 9 9 9P 9 ! 9 :~ H H ( F G ( H H ( d ' @ = / R B H -:LaserWriter Times E e E P . Anderson.abs Alicia Harris Alicia Harris