Parallel Multilevel Elliptic Preconditioners

并行多级椭圆预处理器

• 批准号: 9003002
• 负责人: Tony Chan
• 金额: $ 20.89万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003002&HistoricalAwards=false
• 关键词: Parallel; Multilevel; Elliptic; Preconditioners

In the last few years, there has been an increased interest in the study of multilevel preconditioners for solving elliptic problems in conjunction with the conjugate gradient method. Part of the motivation is that these methods are highly parallelizable, in addition to usually possessing good convergence properties, a combination that most of the classical preconditioners (e.g. SSOR, incomplete factorizations and polynomial preconditioners) lack. The authors' previous work in this area has convinced them that this is a very promising approach for constructing efficient and robust iterative methods for solving large elliptic difference equations on massively parallel computers. Continued research in this area, will include a careful study of implementation issues for massively parallel computers such as the CM.2, a theoretical study of the relationships among different multilevel preconditioners and the class of domain decomposition methods, hybrid multilevel methods which retain the nice properties of incomplete factorization methods with respect to non.smooth coefficients, and extensions beyond self-adjoint second order elliptic operators (e.g.indefinite, convection-diffusion and biharmonic operators.)

在过去的几年里，人们对 解椭圆型方程的多级预条件子研究 结合共轭梯度法的问题。 部分 的动机是，这些方法是高度 可并行化，除了通常具有良好的 收敛性，一个组合，大多数经典的 预条件（例如SSOR，不完全因子分解和 多项式预条件子）缺乏。 作者以前的工作 这个地区使他们相信这是一个非常有前途的 一种构造高效鲁棒迭代方法的方法 求解大型椭圆型差分方程 并行计算机 在这方面的研究，将 包括认真研究大规模 并行计算机，如CM.2，理论研究， 不同多级预处理器之间的关系以及 一类区域分解方法，混合多层方法 它保留了不完全因式分解的优良性质 关于非光滑系数的方法及其推广 超自伴二阶椭圆算子 （例如不定、对流扩散和双调和算子。）