Mathematical Sciences: Fast Spectral-Galerkin Algorithms for Elliptic Problems and Efficient Solution Techniques for Unsteady Navier-Stokes Equations

数学科学：椭圆问题的快速谱伽辽金算法和非定常纳维-斯托克斯方程的高效求解技术

• 批准号: 9623020
• 负责人: Jie Shen
• 金额: $ 5.8万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623020&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Fast; Spectral; Galerkin; Mathematical; Sciences; Fast; Spectral; Galerkin

Shen 9623020 The investigator develops fast algorithms and robust software for elliptic problems and constructs, analyzes, and implements fast and accurate schemes for numerical simulation of unsteady incompressible flows. The numerical simulation of incompressible flows, which plays an important role in numerous scientific and industrial applications of current interest, is a challenging task for both numerical analysts and computational dynamicists. The proposed fast algorithms are based on the spectral discretization for the space variables and high-order projection schemes for the time variable. The proposed algorithms allow accurate numerical simulation of incompressible flows with significantly less computational effort than the traditional lower-order methods. Fast and accurate numerical solution of partial differential equations is of major importance in many fields of science and engineering, including among others high performance computing, turbulence modeling and numerical weather prediction. A main objective of this project is to develop fast algorithms with optimal computational complexity for a large class of elliptic equations, and to implement them in a high performance software package that is made available to the public through anonymous ftp and World Wide Web. It is expected that the proposed fast algorithms and software will become an important tool for many scientists and engineers.

Shen 9623020研究者开发了快速算法和可靠的软件，用于椭圆问题，构造，分析和实施快速，准确的方案，以进行数值模拟不稳定的不可压缩流。 不可压缩流的数值模拟在当前兴趣的许多科学和工业应用中都起着重要作用，这对于数值分析师和计算动力学家来说都是一项艰巨的任务。 提出的快速算法基于空间变量的光谱离散化和时间变量的高阶投影方案。 所提出的算法允许对不可压缩流的准确数值模拟，而计算工作的数值明显少于传统的低阶方法。 在科学和工程的许多领域，包括高性能计算，湍流建模和数值天气预测，包括偏微分方程的快速准确的数值解决方案至关重要。 该项目的一个主要目的是为大型椭圆方程式开发具有最佳计算复杂性的快速算法，并将它们通过匿名FTP和万维网提供给公众提供的高性能软件包。 预计提议的快速算法和软件将成为许多科学家和工程师的重要工具。