Mathematical Sciences: Topics in Spectral Methods

数学科学：谱方法主题

• 批准号: 8810150
• 负责人: David Gottlieb
• 金额: $ 16.44万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8810150&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Spectral; Methods

This research will consider three topics in high order and spectral methods for the numerical solution of partial differential equations. Domain decomposition for spectral methods will be considered. Results of this portion of the work will make it easier to deal with complex gemetries. Techniques for using spectral methods for shock wave calculations will be developed. The total variation bounded spectral method will be reconstructed so as to retain spectral accuracy away from the shock. Finally, pointwise order ENO schemes will be generalized to two dimensional problems. Results of this work should find immediate application in high-speed aerodynamics and other related physical areas.

这项研究将在高阶和光谱方法中考虑三个主题，用于偏微分方程的数值解。 将考虑光谱方法的域分解。 这部分工作的结果将使处理复杂的宝石更容易。 将开发用于使用光谱方法进行冲击波计算的技术。 总变化有限光谱法将被重建，以使光谱精度远离冲击。 最后，点阶的命令ENO方案将被推广到二维问题。 这项工作的结果应立即在高速空气动力学和其他相关物理领域中应用。