Acceleration of Primitive Variable Hydrocodes by the Non- Linear Generalized Minimum Residual Method

非线性广义最小残差法对原始变量水编码的加速

• 批准号: 8707109
• 负责人: David Keyes
• 金额: $ 5.99万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8707109&HistoricalAwards=false
• 关键词: Acceleration; Primitive; Variable; Hydrocodes; Non

Computational modeling has become an essential tool in the analysis and design of engineering systems. Often such models involve the reduction of continuous system of governing partial differential equations to a set of discrete nonlinear algebraic equations. The accurate and efficient solution of the large set of nonlinear algebraic system poses a great challenge to the numerical analysts. Existing algorithms for the discrete nonlinear system convergence thus slowly limits the size of the problem that can be effectively handled. The dollar value of increasing the execution.time efficiency of these codes over their life.cycle is staggering. Yet many innovations from computational mathematics which can yield comparable results in less time are only slowly being incorporated into production codes. This is due to the high cost of retrofitting existing applications codes with new algorithmic kernels and of developing new codes which inherit all of the application.specific features of existing codes. An adaptive nonlinear generalized minimum residual (NLGMR) algorithm which would accelerate convergence where possible and pass the iterates through unmodified, otherwise, is the goal of this Engineering Initiation project. The NLGMR lgorithm treats an existing iteration scheme as a "black box" and computes improved iterates on the basis of iteration history alone. Thus, it can be used to retrofit existing codes. However, the memory requirements of an NLGMR.enhanced algorithm are more substantial than those of the original code, but with the availability of supercomputer resources limitations on memory storage, this should not be a problem. The institutional support is adequate and the P.I. is well qualified to carry out the research. I strongly recommend support.

计算建模已成为工程系统分析和设计的重要工具。 通常，此类模型涉及将控制偏微分方程的连续系统简化为一组离散非线性代数方程。 大型非线性代数系统的准确高效求解对数值分析人员提出了巨大的挑战。 因此，现有的离散非线性系统收敛算法慢慢地限制了可以有效处理的问题的规模。 提高这些代码在其生命周期内的执行时间效率的美元价值是惊人的。 然而，计算数学的许多创新可以在更短的时间内产生可比较的结果，但它们只是慢慢地被纳入生产代码中。 这是由于使用新算法内核改造现有应用程序代码以及开发继承现有代码的所有应用程序特定功能的新代码的成本很高。 该工程启动项目的目标是一种自适应非线性广义最小残差（NLGMR）算法，该算法将在可能的情况下加速收敛，并在其他情况下不加修改地进行迭代。 NLGMR 算法将现有的迭代方案视为“黑匣子”，并仅根据迭代历史记录来计算改进的迭代。 因此，它可以用来改造现有的代码。 然而，NLGMR.enhanced 算法的内存需求比原始代码的内存需求更大，但由于超级计算机资源对内存存储的限制，这应该不是问题。 机构支持充足，P.I.完全有资格进行这项研究。 我强烈建议支持。