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

计算建模已成为一个重要的工具， 工程系统的分析与设计。 这些模型往往 涉及到减少连续系统的管理部分 离散非线性代数微分方程组 方程 大集的精确高效求解 对非线性代数系统的研究提出了很大的挑战， 数字分析师 现有的离散算法 因此，非线性系统收敛缓慢地限制了 可以有效处理的问题。 的美元价值 提高这些代码的执行时间效率， 它们的生命周期是惊人的。 然而，许多创新， 计算数学，可以产生类似的结果， 更少的时间只是慢慢地被纳入生产 代码. 这是由于改造现有的高成本 应用程序代码与新的算法内核和开发 继承所有应用程序的新代码。特定功能 现有的代码。 一种自适应非线性广义最小残差（NLGMR） 算法将加速收敛，在可能的情况下， 不加修改地传递迭代，否则，目标是 这个工程启动项目 NLGMR出租车对待 一个现有的迭代方案作为一个“黑盒子”，并计算 改进的迭代仅基于迭代历史。 因此，在本发明中， 它可以用来改进现有的代码。 然而，记忆 NLGMR增强算法的要求更为实质 比原来的代码，但与可用性， 超级计算机资源对内存存储的限制，这 应该没问题 机构支持是充分的，P.I.得很好 有资格进行研究。 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.