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

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.

沈9623020研究者为椭圆问题开发快速算法和强大的软件，并构建，分析和实现快速准确的非定常不可压缩流动数值模拟方案。不可压缩流动的数值模拟在当前许多科学和工业应用中起着重要作用，对数值分析人员和计算动力学家来说都是一项具有挑战性的任务。所提出的快速算法基于空间变量的频谱离散化和时间变量的高阶投影格式。与传统的低阶方法相比，所提出的算法能够精确地模拟不可压缩流动，且计算量显著减少。快速准确的偏微分方程数值解在许多科学和工程领域具有重要意义，其中包括高性能计算、湍流建模和数值天气预报。该项目的主要目标是为一大类椭圆方程开发具有最佳计算复杂度的快速算法，并在通过匿名ftp和万维网向公众提供的高性能软件包中实现它们。预计所提出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。