Collaborative Research: Hierarchically Parallel Algorithms for Portable and Scalable Performance

本研究的目的是开发并行 对称不定和非对称系统求解器 系统，如那些发生在计算流体中的系统， 动力学，发展并行技术，解决时间依赖 问题，并构建了一个快速原型环境，用于开发和试验稀疏矩阵计算中的算法 在共享和分布式内存多处理器上。 特别是 研究了：（1）求解Stokes类线性方程组的并行求解方法 在CFD和其他增广拉格朗日问题中出现， 线性规划内点法，（2）Krylov投影或行投影不完全牛顿法 内迭代求解器;（3）高阶非线性时变问题的求解 方法，（4）定义和开发稀疏矩阵基元 类似于用于密集计算的高效BLAS-3，以及（5）实现稀疏因子分解和求解方案。 目标是可移植的效率和可扩展性， 多层次的并行性。 这反过来又使工作 广泛应用于现有和未来的 架构，而不仅仅是一台特定的机器。

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.