Collaborative Research: Hierarchically Parallel Algorithms for Portable and Scalable Performance

本研究的目标是开发并行稀疏 对称不定和非对称线性系统解算器 诸如那些出现在计算流体动力学中的系统， 开发解决时间相关问题的并行技术，以及 建立一个快速原型开发环境， 实验稀疏矩阵计算中的算法， 和分布式存储器多处理器。 特别是下列 将审查： 类Stokes线性问题的O并行求解方案 在CFD和其他增广拉格朗日问题中出现， 线性规划的内点法， 不完全牛顿方法与Krylov或行投影迭代 内部迭代的求解器， o使用高阶并行解决时间相关问题 方法及时， o定义和开发类似于 用于密集计算的高效BLAS-3，以及 o实施稀疏分解和求解方案。 目标是可移植的效率和可扩展性， 多层次的并行性。 这反过来又会使工作 在现有和未来的计算机中广泛使用 架构，而不仅仅是一台特定的机器。

The goal of this research proposed is to develop parallel sparse system solvers for symmetric indefinite and non-symmetric linear systems such as those occurring in computational fluid dynamics, develop parallel techniques for solving time-dependent problems, and construct a rapid prototyping environment for developing and experimenting with algorithms in sparse matrix computations on shared and distributed memory multiprocessors. In particular, the following will be examined: o parallel solution schemes for solving Stokes-like linear problems arising in CFD and other augmented Lagrangian problems such as interior point methods of linear programming, o incomplete Newton methods with Krylov or row projection iterative solvers for the inner iteration, o solution of time-dependent problems using high-order parallel methods in time, o defining and developing sparse matrix primitives analogous to the highly effective BLAS-3's for dense computations, and o implementing sparse factorization and solution schemes. The goal is portable efficiency and scalability, by exploiting parallelism on multiple levels. This in turn will allow the work to be used across a wide spectrum of existing and future computer architectures, instead of simply a particular machine.