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.

本研究将考虑三个主题在偏微分方程数值解的高阶和谱方法。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几何图形变得更容易。将发展使用谱法计算激波的技术。对全变分有界谱法进行重构，使谱精度不受冲击影响。最后，将点阶ENO格式推广到二维问题。这项工作的结果将立即应用于高速空气动力学和其他相关的物理领域。