A Fully Algebraic Multigrid Software Package for Automated Solution of Unstructured Sparse Linear Systems on High Performance Computers

本课题是在高性能计算机上设计鲁棒且高效的求解大型稀疏非结构化线性系统的计算内核软件。如此大规模的问题只能通过迭代技术来解决。我们考虑的迭代技术包括多层预处理技术和代数多重网格方法。我们的目标是把这两组方法统一起来，扬长避短。我们将研究、设计和测试提供多网格技术的可扩展性、领域分解方法的并行性和不完全LIU预条件的鲁棒性的代数预条件。我们还将使用因子稀疏近似逆技术来取代代数多重网格方法中的标准迭代方案。这种方法可以增加我们的方法的鲁棒性并提高它们的并行性。子矩阵的图划分将用于平衡处理器之间的负载。所提出的研究将产生一个软件包，可被研究人员和工程师用作大规模数值模拟和计算的核心软件。本研究项目开发的通用高性能迭代求解器有望在应用科学计算领域产生重大影响。研究结果将对代数多重网格方法和多级不完全LU预处理方法的相对优缺点作出清晰的判断。这项研究在航空航天、半导体、水库模拟、燃烧、海洋/气候建模和污染跟踪等领域都有应用

This project is to design robust and efficient computational kernel software for solving large sparse unstructured linear systems on high performance computers. Such large scale problems can only be solved by iteritive techniques. The iterative techniques under our consideration include multilevel preconditioning techniques and algebraic multigrid methods. Our goal is to unify these two groups of methods and to take advantage of both and avoid the disadvantages of either.We will investigate, design, and test algebraic preconditioners that offer the scalability of multigrid techniques, the parallelism of domain decomposition methods, and the robustness of incomplete LIU preconditioners.We will also use a factored sparse approximate inverse technique to replace standard iterative schemes in algebraic multigrid methods. Such an approach may increase the robustness of our methods and improve their parallelism. Graph partitioning of submatrices is to be used to balance loads among processors. The proposed research will result in a software package that may be used by researchers and engineers as kernel software in large scale numerical simulations andcomputations.The general purpose high performance iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. The results of the research will make a clear judgment concerning the relative advantages and disadvantages of algebraic multigrid methods and multilevel incomplete LU preconditioning methods. The research has applications in aerospace, semiconductor, reservoir simulation, combustion, ocean/climate modeling, and pollution tracking