Postdoc: Portable Parallel Preconditioning

本项目将研究迭代方法用于求解一般稀疏线性方程组的并行预条件。新的预处理算法将基于完全矩阵的不完全分解(IFCM；例如，ILU)和不完全矩阵的完全分解(CFIm)。后一种方法是相当新的。PI计划将并行直接方法中发展的组合算法扩展到并行预条件的构造中。通过利用原始矩阵的结构和代数特征，他们将设计并行线性求解器，使用从纯迭代到纯直接方法的连续谱上的混合技术。新的预处理子与问题域无关，适合于通用库软件的使用。除了基础算法研究，PI还将为计算科学家和工程师提供广泛使用的并行库和工具。该预处理软件将以现有最好的并行直接法软件和工具为基础并加以扩充，其中一些正在PIS论文工作中开发。新的算法和库将在几个应用中得到检验，如非对称稀疏特征值计算、地下水修复模拟和胶体悬浮物的斯托克斯动力学模型。

This project will study parallel preconditioners used by iterative methods to solve general sparse linear systems of equations. The new preconditioning algorithms will be based on Incomplete Factorization of Complete Matrices (IFCM; for example, ILU) and Complete Factorization of Incomplete Matrices (CFIM). The latter approach is rather new. The PI plans to extend the combinatorial algorithms developed in the parallel direct methods to the construction of parallel preconditioners. By exploiting both structural and algebraic features of the original matrix, they will design parallel linear solvers with a blend of techniques along the continuous spectrum from pure iterative to pure direct methods. The new preconditioners are independent of problem domain, and hence are suitable to be used in general-purpose library software. Besides fundamental algorithms research, the PI will produce widely usable parallel libraries and tools for computational scientists and engineers. The preconditioning software will be based on and augment the best available parallel direct-method software and tools, some of which is being developed in the PIs thesis work. The new algorithms and libraries will be bench marked in several applications, such as unsymmetric sparse eigenvalue computation, groundwater remediation modeling, and Stokesian dynamics models of colloidal suspensions.