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

计算建模已成为工程系统分析和设计的重要工具。通常这种模型涉及将连续的控制偏微分方程系统简化为一组离散的非线性代数方程。大型非线性代数系统的精确、高效解对数值分析人员提出了很大的挑战。因此，现有的离散非线性系统收敛算法限制了问题的规模，不能得到有效的处理。增加执行的美元价值。这些代码在其生命周期中的时间效率。周期是惊人的。然而，计算数学的许多创新可以在更短的时间内产生类似的结果，但它们只是慢慢地被纳入生产代码。这是由于用新的算法内核改造现有应用程序代码和开发继承所有应用程序的新代码的成本很高。现有代码的特定功能。一种自适应非线性广义最小残差（NLGMR）算法，在可能的情况下加速收敛，并在不修改的情况下通过迭代，是本工程启动项目的目标。NLGMR算法将现有的迭代方案视为一个“黑盒”，仅根据迭代历史计算改进的迭代。因此，它可以用来改进现有的代码。然而，NLGMR的内存需求。增强后的算法比原始代码更实质性，但由于超级计算机资源的可用性对内存存储的限制，这应该不是问题。机构支持充足，私家侦探有资格开展研究。我强烈建议支持。

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.