Efficient High Order Numerical Methods for Convection Dominated Partial Differential

对流主导偏微分的高效高阶数值方法

• 批准号: 0809086
• 负责人: Chi-Wang Shu
• 金额: $ 52.7万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0809086&HistoricalAwards=false
• 关键词: Efficient; Order; Numerical; Methods; Convection

In this project, research in the algorithm design and analysisof high order numerical methods, including the finite differenceand finite volume weighted essentially non-oscillatory (WENO) schemes, discontinuous Galerkin finite element methods, and particle methods, for hyperbolic and other convection dominated partial differential equations, especially in adaptive, multiscale and uncertain environments, will be carried out. Parallel implementation and applications of these methods will also be addressed. The intellectual merit of the proposed activity lies in its comprehensive coverage of algorithm development, analysis,implementation and applications. Problems in applicationsmotivate the design of new algorithms or new features inexisting algorithms; mathematics tools are used to analyzethese algorithms to give guidelines for their applicabilityand limitations; practical considerations including parallelimplementation issues are addressed to make the algorithmscompetitive in large scale calculations; and collaborationswith engineers and other applied scientists enable theefficient application of these new algorithms or new featuresin existing algorithms.The proposed research aims at the design of efficient algorithms,which, when used on today's powerful computers, will help to solve many problems from diversified applications such asaerodynamics and aeroacoustics for aircraft design, electromagnetism wave simulation for communications, and semiconductor device simulation for the computer industry.The thrust of this proposal is to use powerful mathematicaltools to guide the design of algorithms, so that they are moreefficient, more reliable, and more robust in applications.

在该项目中，在高阶数值方法的算法设计和分析中的研究，包括有限的有限量加权本质上是非振荡（WENO）方案，不连续的Galerkin有限元方法和粒子方法，用于双重差异和其他对流的部分差分差分差异，将执行方程，尤其是在自适应，多尺度和不确定的环境中。 这些方法的并行实现和应用也将被解决。 拟议活动的智力优点在于其对算法开发，分析，实施和应用的全面覆盖范围。 应用程序中的问题可以使新算法的设计或新功能没有算法；数学工具用于分析算法，以提供有关其适用性和限制的准则；解决了包括平行实现问题在内的实际考虑因素，以使大规模计算中的算法竞争；与工程师和其他应用科学家合作以及现有算法中的这些新算法或新功能的效率应用。拟议的研究旨在设计有效的算法，当在当今强大的计算机上使用，该算法将有助于解决多元化应用程序中的许多问题。用于飞机设计的Asaerodynanic和空气声学，通信电磁波波和计算机行业的半导体设备模拟。该提案的目的是使用强大的数学工具来指导算法的设计，以使它们更效率更高，更可靠，更可靠，并且更可靠，并且更可靠，并且更可靠，和更高在应用中强大。