High Order Numerical Methods for Wave Phenomena in Adaptive, Multiscale and Uncertain Environments

自适应、多尺度和不确定环境中波动现象的高阶数值方法

基本信息

批准号：
0510345
负责人：
Chi-Wang Shu
金额：
$ 35.84万
依托单位：
Brown University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2005
资助国家：
美国
起止时间：
2005-08-01 至 2009-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0510345&HistoricalAwards=false
关键词：
Order Numerical Methods Wave Phenomena

项目摘要

Many physical, biological, and engineering problems involve linear or nonlinear wave phenomena in adaptive, multiscale, and uncertain environments. The focus of this proposal is to design, analyze and apply high-order accurate and highly efficient numerical algorithms, including high-order weighted essentially non-oscillatory methods, high-order discontinuous Galerkin finite element methods, and spectral methods, for effective simulations of such wave phenomena using computers. Mathematical tools will be used to guide the design of such algorithms so that they will be able to produce reliable and accurate results for such complicated wave phenomena with a high speed and hence a fast turnaround time. This will in turn allow a deeper understanding of the physical and biological phenomena and also to help in many engineering designs, such as the design of aircrafts and semiconductor devices. In this project, problems in applications will motivate the design of new algorithms or new features in existing algorithms; mathematical tools will be used to analyze these algorithms to give guidelines for their applicability and limitations; practical considerations including parallel implementation issues for the computation on massively parallel computers will be addressed to make the algorithms competitive in large scale calculations; and collaborations with engineers and other applied scientists will enable the efficient application of these new algorithms or new features in existing algorithms. The training of young researchers in this area will also be an important component of this project.

许多物理，生物学和工程问题涉及自适应，多尺度和不确定环境中的线性或非线性波现象。该提案的重点是设计，分析和应用高阶准确且高效的数值算法，包括高阶加权基本上是非振荡方法，高阶不连续的不连续的Galerkin有限元方法和光谱方法，以进行有效的模拟这种波浪现象使用计算机。数学工具将用于指导此类算法的设计，以便它们能够以高速的方式为如此复杂的波浪现象产生可靠，准确的结果，从而快速转移时间。反过来，这将使人们对物理和生物学现象有了更深入的了解，也可以帮助许多工程设计，例如飞机和半导体设备的设计。在该项目中，应用程序中的问题将激发新算法的设计或现有算法中的新功能；数学工具将用于分析这些算法，以提供有关其适用性和局限性的准则；实际的考虑因素包括在大规模计算中进行大规模计算的计算计算的平行实施问题，以大规模计算竞争；与工程师和其他应用科学家的合作将使这些新算法或现有算法中的新功能有效地应用。该领域的年轻研究人员的培训也将是该项目的重要组成部分。