US-France Cooperative Research: Numerical Simulation by Spectral Element Method

美法合作研究：谱元法数值模拟

• 批准号: 8914984
• 负责人: Anthony Patera
• 金额: $ 1.39万
• 依托单位: Massachusetts Institute of Technology
• 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: 1990-04-01 至 1992-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8914984&HistoricalAwards=false
• 关键词: US; France; Cooperative; Research; Numerical

This award will support collaborative research in computational fluid dynamics and numerical analysis between Dr. Anthony Patera, Massachusetts Institute of Technology and Dr. Yvon Maday, Laboratory for Numerical Analysis, University of Pierre and Marie Curie, Paris, France. The objective of the proposed project is a rigorous analysis of certain aspects of spectral methods as applied to equations governing fluid flow. The numerical simulation of phenomena governed by partial differential equations is currently of major interest. This has become even more true as computers have become more powerful and able to solve problems that used to be intractable on previous machines. In order to be able to provide a numerical solution with sufficient accuracy, the numerical methods have to become more precise and the standard methods often fail to give a satisfactory accuracy. The research of new high order methods is thus of fundamental importance. Spectral methods are amongst the most accurate numerical methods currently available for the numerical simulation of physical phenomena. In this project, the investigators propose to continue the development of the Spectral Element method, along with a rigorous mathematical theory. The project will benefit from the complementary expertise of the two investigators. Professor Maday is a leading mathematician and has made many contributions to the rigorous development of spectral and finite element methods. The Spectral Element Method was introduced by Patera and is an important contribution to the development of spectral methods.

该奖项将支持计算领域的合作研究 流体动力学和数值分析之间的安东尼帕特拉博士， 马萨诸塞州理工学院和Yvon Maday博士，实验室 皮埃尔和玛丽居里大学， 法国，巴黎。 拟议项目的目标是 严格分析光谱方法的某些方面， 应用于控制流体流动的方程。 对局部扰动现象进行了数值模拟 微分方程是当前的主要兴趣。 这 随着计算机变得越来越强大， 能够解决以前难以解决的问题， 机械. 为了能够提供一个数值解 如果有足够的精度，数值方法必须成为 更精确，标准方法往往无法给出 令人满意的准确度。 新的高阶方法的研究是 因此具有根本的重要性。 光谱方法是其中的 最精确的数值方法，目前可用于 物理现象的数值模拟。 本工程 研究人员建议继续开发光谱 单元法，沿着着严密的数学理论。 的 项目将受益于两个互补的专业知识 investigators. 马代教授是一位著名的数学家， 为光谱学的严格发展做出了许多贡献 和有限元方法。 谱元法是 它是由Patera介绍的，是对 光谱方法的发展。