ALGORITHMS: Parallel Large-Scale Sparse Linear System Solvers: New Methods and Paradigms

调查人员 开发了一套 并行代数多级技术解决分布式稀疏线性方程组，导致“并行代数递归多级求解器”（pARMS），一个便携式和通用的图书馆解决稀疏线性系统的并行计算机。其目标之一是开始解决“特殊用途”和“一般用途”方法之间的“效率差距”。 在可用的求解器的频谱的一个极端，谎言稀疏直接方法是强大的，通用的，但昂贵的。 在另一个极端，是特殊用途的方法，如多重网格，它利用有关底层的信息， 问题，以量身定制设计某些解决方案的程序。 这种方法可以是最优的，但它们的目的是解决原始的物理问题，而不是得到的线性系统。 在这两个极端之间的是预处理Krylov方法，其性能是可变的。这项研究的特点是一个不同的视觉库的并行迭代求解器应该提供什么。研究人员坚信，需要一种新的范式，其中求解器不再是包括一组预处理器的单片框，而是允许用户输入特定信息，甚至是求解算法的部分，以定制多级求解过程。 pARMS的模块化设计使这种方法成为可能，与工业中使用的标准方法完全一致。 在这项研究中设想的新的范式和方法也将包括在一个典型的解决过程中出现的其他一些关键问题。 因此，在求解非线性方程组时，利用潜在的上下文是很重要的。 同样重要的是确保pARMS代码为迭代求解器失败的情况提供有效稀疏直接求解器的回退选项。研究人员还计划探索随着计算网格的出现而开始出现的新问题。最后，他们将牢记解决方案算法的体系结构和问题相关的调整。 这两位研究人员都与重要应用领域的研究人员有着重要的互动。 pARMS-X代码也可能对研究生教育产生影响，就像过去的SPARSKIT一样。

The investigators have developed a set of parallel algebraic multilevel techniques for solving distributed sparse linear systems of equations, leading to the ``parallel Algebraic Recursive Multilevel Solver'' (pARMS), a portable and general purpose library for solving sparse linear systems on parallel computers. One of their goals is to begin to address the `efficiency gap' between `special purpose' and `general purpose' methods. On one extreme of the spectrum of solvers available, lie sparse direct methods which are robust, general-purpose, but expensive. On the other extreme, are special purpose methods, such as multigrid, which utilize information about the underlying problem to tailor-design certain solution procedures. Such methods can be optimal but they aim at solving the original physical problem instead of the resulting linear system. In between these extremes are the preconditioned Krylov methods whose performance is variable.This research is characterized by a different vision of what a library of parallel iterative solvers should offer. The investigators strongly believe that a new paradigm is required where a solver is no longer a monolithic box comprising a set of preconditioners, but allows the user to input specific information, indeed even parts of the solution algorithm, in order to tailor the multilevel solution procedure. This approach, which is enabled by the modular design of pARMS, is in perfect agreement with the standard approach used in industry. The new paradigms and methods envisioned in this research will alsoinclude a number of other key issues which arise in a typical solution process. Thus, it is important to exploit the underlying context when solving nonlinear systems of equations. It is also important to ensure that the pARMS code provides a fall-back option to an efficient sparse direct solver for situations where the iterative solver fails. The investigators also plan to explore new questions which are starting to emerge with the advent of the Computational Grid. Finally, they will keep in mind architecture- and problem-dependent tuning of solution algorithms.The software developed by the investigators will continue to be made publicly available. Both investigators have major interactions with researchers in important applications areas. The pARMS-X code is also likely to have an impact on graduate education, as was the case with SPARSKIT in the past.