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

该奖项将支持麻省理工学院Anthony Patera博士和法国巴黎皮埃尔和玛丽居里大学数值分析实验室Yvon Maday博士在计算流体动力学和数值分析方面的合作研究。拟议项目的目标是对应用于流体流动方程的谱方法的某些方面进行严格分析。偏微分方程控制现象的数值模拟是目前的主要研究方向。随着计算机变得越来越强大，能够解决以前的机器难以解决的问题，这一点变得更加真实。为了能够提供具有足够精度的数值解，数值方法必须变得更加精确，而标准方法往往不能给出令人满意的精度。因此，研究新的高阶方法具有根本性的意义。谱方法是目前物理现象数值模拟中最精确的数值方法之一。在这个项目中，研究人员建议继续发展谱元方法，以及严格的数学理论。该项目将受益于两位研究人员的互补专业知识。Maday教授是一位领先的数学家，对谱和有限元方法的严格发展做出了许多贡献。谱元法是由Patera提出的，是对光谱方法发展的重要贡献。

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.