Massively Parallel Preconditioners for Krylov Subspace Methods

这项研究的目的是调查 高度并行预处理技术，用于求解一般大型稀疏线性方程组。 特别感兴趣的是 非结构网格上偏微分方程离散化所产生的系统。 的 专注于高效的预处理器，当 处理器的数量非常大。 在这种情况下，标准的不完全因式分解预条件子并不令人满意。 该项目调查了一些非标准的替代品，强调近似 基于“高精度”。这些类似于具有高填充级别的ILU因式分解。 许多 并行预处理器的缺点是， 需要比标准预处理器更多的迭代次数来实现收敛。 这往往超过 更高程度的合作所带来的潜在收益 平行性 然而，最近的经验表明， 是一个很好的策略，通过减少迭代次数来实现更快的执行。 使用 还研究了多色技术。

The goal of this research is to investigate highly parallel preconditioning techniques for solving general large sparse linear systems of equations. Of particular interest are systems that arise from the discretization of partial differential equations on unstructured grids. The focuses on efficient preconditioners which scale well when number of processors is very large. In this situation, the standard incomplete factorization preconditioners are not satisfactory. The project investigates a number of non-standard alternatives which emphasize approximations based on ``high level of accuracy.'' These are similar to ILU factorizations with high level of fill-in. Many of the parallel preconditioners, suffer from the disadvantage that entail a larger number of iterations than standard preconditioners to achieve convergence. This often outweighs potential gains arising from the higher degree of parallelism. However, recent experience suggests that increasing the of the preconditioner is a good strategy for achieving faster execution by reducing the number of iterations. The use of multi-coloring techniques is also investigated.