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.

在本项目中，研究高阶数值方法的算法设计和分析，包括用于双曲线和其他对流主导的偏微分的有限差分和有限体积加权本质上非振荡（WENO）格式、不连续伽辽金有限元方法和粒子方法将进行方程，特别是在自适应、多尺度和不确定环境中的方程。 还将讨论这些方法的并行实施和应用。 该活动的智力优势在于其全面覆盖算法开发、分析、实现和应用。 应用中的问题激发了新算法的设计或现有算法的新功能；数学工具用于分析这些算法，为它们的适用性和局限性提供指导；解决了包括并行实现问题在内的实际考虑因素，以使算法在大规模计算中具有竞争力；与工程师和其他应用科学家的合作使得这些新算法或现有算法中的新功能能够得到有效应用。所提出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时，将有助于解决多样化应用中的许多问题，例如例如用于飞机设计的空气动力学和气动声学、用于通信的电磁波仿真以及用于计算机行业的半导体器件仿真。该提案的主旨是使用强大的数学工具来指导算法的设计，使它们更高效、更可靠。可靠，并且在应用中更强大。