ALGORITHMS: New Concept and Parallel Algorithms for Robust Preconditioning in Large Scale Parallel Matrix Computation

在各种计算机模拟和建模中产生的大型稀疏非结构矩阵通常采用预条件迭代法求解。本研究项目将基于一类多步连续稀疏近似逆预处理技术，研究和设计大型稀疏线性系统并行解的鲁棒高性能预处理器。我们将发展多步连续预处理的新概念和并行算法，以增强标准稀疏近似逆预处理技术的鲁棒性，并将这一概念推广到其他预处理技术的背景下。本文将进一步研究该方法在提高预处理精度和分解稳定性方面的优势。我们将构建便携式软件包来实现新的预处理策略，以解决高性能并行计算机上的非结构化一般稀疏线性系统。本研究项目的通用高性能预条件迭代求解器有望在应用科学计算领域产生重大影响。我们的经验和现有实力将确保该项目完全按照建议进行。随着美国工业越来越依赖计算机辅助设计和制造，大规模的计算机仿真和建模将成为新产品研发的重要组成部分。这项研究的结果将通过为大规模计算机模拟提供更高效的内核软件，使美国工业和科学研究界受益。

Large sparse unstructured matrices arising from various computer simulation and modeling are commonly solved by preconditioned iterative methods. This research project will study and design robust high performance preconditioners for parallel solution of large sparse linear systems, based on a class of multistep successive sparse approximate inverse preconditioning techniques.We will develop new concept and parallel algorithms of multistep successive preconditioning for enhancing the robustness of standard sparse approximate inverse preconditioning techniques, and generalize this concept to the context of other preconditioning techniques. Study will be conducted to show the advantages of such approach to enhance both preconditioning accuracy and factorization stability. We will build portable software packages to implement new preconditioning strategies for solving unstructured general sparse linear systems on high performance parallel computers.The general purpose high performance preconditioned iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. Our experience and existing strength will ensure that theproject be carried out fully as proposed. As U.S. industry is more and more relying on computer aided design and manufacturing, large scale computer simulation and modeling will be a vital component in new products research and development. The outcome of this research will benefit U.S. industry as well as scientific research community by providing more efficient kernel software forlarge scale computer simulations.