Mathematical Sciences: Algorithms and Numerical Analysis forPartial Differential Equations

数学科学：偏微分方程的算法和数值分析

• 批准号: 9007185
• 负责人: James Bramble
• 金额: $ 42万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007185&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algorithms; Numerical; Analysis

This award will support the efforts of the principal investigators to continue their studies of finite element methods for the numerical solution of partial differential equations. In particular, the researchers will construct preconditioners that will enable them to solve the resulting systems of algebraic equations more efficiently. The theoretical insights gained from their studies should lead to the development of improved software for use on parallel computers, which in turn will lead to improved solutions of a host of problems in two and three space dimensions. The computer has changed forever the way we go about finding solutions of partial differential equations that arise in science and technology. Unfortunately the ability of even the most powerful supercomputer to solve complicated systems is limited very often by the sheer size of the algebraic equations that result from discretizing the differential equations. In order to overcome this "size" limitation numerical analysts have devised ways to "precondition" these algebraic equations so as to make them more digestible to the computer. The principal investigators on this grant will seek better ways to achieve this preconditioning.

这个奖项将支持校长的努力 研究人员继续他们的研究有限元方法 偏微分方程的数值解法。 特别是，研究人员将构建预条件子 这将使他们能够解决由此产生的代数系统， 更高效的方程式 从以下方面获得的理论见解 他们的研究应该导致改进软件的开发 在并行计算机上使用，这反过来又会导致 一系列二、三空间问题的改进解法 尺寸.计算机永远地改变了我们的生活方式 求偏微分方程的解 科学技术 不幸的是， 解决复杂系统的最强大的超级计算机是 往往受限于代数方程组的庞大规模 这是微分方程离散化的结果。 在 为了克服这种“规模”限制，数值分析人员 设计了一些方法来“预处理”这些代数方程， 让它们更容易被电脑理解 校长 研究人员将寻求更好的方法来实现这一目标 预处理