Parallel Multiscale Iterative Methods

我们建议进行分析和发展的研究 具有良好收敛速度的迭代方法， 适用于解决线性和非线性系统所产生的3D 偏微分方程，也具有足够的 固有的并行度， 先进的并行计算机 我们专注于两个具有代表性的 类型的迭代算法，一个细粒度（多尺度 预处理器）和一个粗晶粒（区域分解）， 我们认为这是发展的基础， 高效的算法，为各自的架构。 我们 应特别注意粗糙和 不连续系数，对流扩散问题和 模型Navier-Stokes问题 此外，新类别的 并行机也出现了（例如CMX和MASPAR），我们 建议调查其中一些新的 这两类迭代方法的架构。

We propose to carry out research on the analysis and development of iterative methods that possess good convergence rates when applied to solving linear and nonlinear systems arising from 3D partial differential equations and that also possess sufficient inherent degree of parallelism for efficient implementation on advanced parallel computers. We focus on two representative types of iterative algorithms, one fine grain (multiscale preconditioners) and one coarse grain (domain decomposition), that we feel offer the best hope as a basis for developing efficient algorithms for their respective architectures. We shall pay particular attention to problems with rough and discontinuous coefficients, convection-diffusion problems and model Navier-Stokes problems. In addition, new classes of parallel machines have also emerged (e.g. CMX and MASPAR), and we propose to investigate the suitability of some of these new architectures for these two classes of iterative methods.