RUI: Parallel methods and software for solving sparse nonlinear systems of equations in structured approaches

本项目的目标是设计、分析、实现和测试 求解稀疏非线性方程组的几组并行方法 并行计算机上的方程组。 采取方法是 将稀疏非线性方程组转化为一些特殊的 结构，以便可以将计算分解为并行 处理. 这项研究将集中在两个重要的类 自然结构系统：1）大规模块边界 系统的非线性方程，通过置换一般 非线性系统 计划开发并行的显式和 隐式方法和迭代方法求解块边界问题 非线性方程组，包括收敛性分析， 带边奇异或近似奇异块的摄动方法 系统，割线法的应用，以及 不同类型的并行计算机上的方法。 的 研究还将扩展到不同直接和迭代 块三角形非线性方程组的求解方法 方程，包括收敛性分析，拟 求解这类问题的Newton方法和异步并行方法 的问题他过得 方法设计的动机是使用并行 计算机，实施和测试将并行进行 电脑 然而，我们的目标是发现新的方法， 有效地解决稀疏非线性方程组的结构 在并行计算机上运行。

The goal of this project is to design, analyze, implement and test several groups of parallel methods for solving sparse nonlinear systems of equations on parallel computers. The approach is to transform sparse nonlinear systems of equations into some special structures so that the computations can be decomposed for parallel processing. The research will concentrate on two important classes of naturally structured systems: 1) large-scale block bordered systems of nonlinear equations, obtained by permuting general nonlinear systems. It is planned to develop parallel explicit and implicit methods and iterative methods for solving the block bordered nonlinear systems of equations, including convergence analysis, perturbation methods for singular or nearly singular block bordered systems, applications of the secant method, and the implementations of the methods on different types of parallel computers. The investigation will also be extended to different direct and iterative methods for solving the block triangular nonlinear systems of equations including the convergence analysis, applications of quasi- Newton methods and asynchronous parallel methods for solving this type of problems. The method design is motivated by the use of parallel computers, and the implementation and testing will be on parallel computers. The goal is, however, to discover new methods that efficiently solve sparse nonlinear systems of equations in structured approaches on a parallel computer.