Mathematical Sciences: Topics in Spectral Methods

这项研究将考虑三个主题的高秩序， 谱方法数值解偏微分方程 微分方程 谱域分解 方法将被考虑。 这部分工作的结果 将使处理复杂的宝石变得更容易。 技术 使用谱方法计算冲击波， 开发 总变分有界谱方法将是 重建，以保持光谱精度远离 冲击. 最后，推广了点态ENO格式 二维问题。 这项工作的成果应立即应用于 高速空气动力学和其他相关物理领域。

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.