Collaborative Research: Hierarchically Parallel Algorithms for Portable and Scalable Performance

本研究的目标是为计算流体动力学中出现的对称不确定和非对称系统开发并行系统求解器，开发解决时间相关问题的并行技术，并构建一个快速原型环境，用于在共享和分布式内存多处理器上开发和实验稀疏矩阵计算算法。特别要审查的是：(1)求解CFD中的类stokes线性问题和其他增广拉格朗日问题（如线性规划的内点法）的并行求解方案；(2)用Krylov或行投影求解内迭代的不完全牛顿方法；(3)用时间上的高阶方法求解时间相关问题；(4)定义和开发类似于高效BLAS-3的稀疏矩阵原语，用于密集计算。(5)实现稀疏分解和求解方案。目标是通过在多个级别上并行实现可移植效率和可伸缩性。这反过来又允许工作在现有和未来架构的广泛范围内使用，而不仅仅是特定的机器。

The goal of this research is to develop parallel system solvers for symmetric indefinite and non-symmetric 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 are examined: (1) parallel solution schemes for solving Stokes-like linear arising in CFD and other augmented Lagrangian problems such interior point methods of linear programming, (2) incomplete Newton methods with Krylov or row projection solvers for the inner iteration, (3) solution of time-dependent problems using high-order methods in time, (4) defining and developing sparse matrix primitives analogous to the highly effective BLAS-3's for dense computations, and (5) implementing sparse factorization and solution schemes. The goal is portable efficiency and scalability, by parallelism on multiple levels. This in turn allows the work be used across a wide spectrum of existing and future architectures, instead of simply a particular machine.