VPW: Waveform Relaxation Method

VPW：波形弛豫法

• 批准号: 9550154
• 负责人: Hong Zhang
• 金额: $ 10.77万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-15 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9550154&HistoricalAwards=false
• 关键词: VPW; Waveform; Relaxation; Method

The advent of new generation of massively parallel computers has caused previously efficient numerical algorithms to be reexamined. Massively parallel computers are comprised of many hundreds, sometimes thousands of processors. For a numerical algorithm to fully exploit the power of such machines it must be able to be 'decomposed' into largely independent pieces which can be distributed across the available computer processors. The waveform relaxation method is such a method for solving systems of ordinary differential equations and time-dependent partial differential equations. In addition to its advantages in parallel processing, it also allows different integration step sizes to be used for different subsystems, resulting in substantial savings in computation for some applications. The theoretical and experimental studies suggest that the waveform relaxation method has a great potential for developing reliable, scalable efficient parallel algorithms for solving a wide range of differential equations. The objective of this research is to further investigate the nature of the waveform relaxation method, and develop fast scalable parallel algorithms for solving certain type of ordinary differential equations and time-dependent partial differential equations. The long term goal of this research is to make the developed algorithms applicable to real-world computational problems, such as the real time integration of torpedo or missile trajectories, modeling of earthquake effects on buildings, and simulation of fluid-structure interaction. This work will involve the algorithm design, theoretical analysis with a possible focus on the search of optimal convergence rate, and numerical testing on sequential and parallel computers. Interactive activities include: teaching a course at the graduate level on numerical linear algebra, numerical partial differential equation, or on parallel numerical computation; and leading an interdisciplinary research seminar seri es on scientific computation and applications to which both local and national researchers will be invited to participate.

新一代大规模并行计算机的出现，使以前有效的数值算法被重新审视。 大规模并行计算机由数百个，有时数千个处理器组成。 对于一个数值算法，充分利用这种机器的力量，它必须能够被“分解”成很大程度上独立的部分，可以分布在可用的计算机处理器。 波形松弛法是一种求解常微分方程组和时间相关偏微分方程组的方法。 除了在并行处理方面的优势外，它还允许不同的子系统使用不同的积分步长，从而在某些应用中节省大量的计算。 理论和实验研究表明，波形松弛方法具有很大的潜力，发展可靠的，可扩展的高效并行算法求解范围广泛的微分方程。 本研究的目的是进一步研究波形松弛法的本质，并发展快速可扩展的并行算法来求解某些类型的常微分方程和时间依赖的偏微分方程。 本研究的长期目标是使所开发的算法适用于现实世界的计算问题，如鱼雷或导弹轨迹的真实的时间积分，地震对建筑物的影响建模，以及流体-结构相互作用的模拟。 这项工作将涉及算法设计，理论分析，可能侧重于搜索的最佳收敛速度，并在串行和并行计算机上进行数值测试。 互动活动包括：教授数值线性代数、数值偏微分方程或并行数值计算的研究生课程;并主持一个邀请本地和国家研究人员参加的科学计算和应用的跨学科研究研讨会系列。