Spectral and Spectral Element Methods

谱和谱元方法

• 批准号: 9012263
• 负责人: John Boyd
• 金额: $ 6万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012263&HistoricalAwards=false
• 关键词: Spectral; Element; Methods

This project is the continuation of Boyd and Schultz's ongoing development and application of spectral methods. This effort has produced one book and thirty-three papers over the past two years, ranging form theoretical analyses of asymptotic Chebyshev coefficients to practical applications to geophysical and engineering flows. In the proposed work, we will continue to mix numerically- oriented with application-oriented studies. Spectral domain decomposition and special handling of singularities will be major themes. We will apply multi- element Legendre spectral methods to two problems: lubrication in an elliptical journal bering, and a tree-dimensional ocean general circulation model. In these engineering studies, we will compare explicit and implicit time- marching schemes, multigrid with various smoothers (notably GMRES), and different strategies for coping with corner singularities and fronts. In addition, we will perform theoretical investigations on several topics: sum-accelerated pseudospectral methods and their relationship to finite differences, comparison of pseudospectral residuals and errors, reduced basis and Delves-Freeman iterations for solving strongly nonlinear boundary value problems, and spectral methods for fronts and shocks.

该项目是博伊德和舒尔茨正在进行的光谱方法开发和应用的继续。在过去的两年里，这一努力已经产生了一本书和33篇论文，从渐近切比雪夫系数的理论分析到地球物理和地球物理的实际应用工程流程。在拟议的工作中，我们将继续将面向数值的研究与面向应用的研究相结合。谱域分解和奇点的特殊处理将是主要主题。我们将把多元勒让德谱方法应用于两个问题：椭圆轴颈白令中的润滑，和一个三维海洋环流模式。在这些工程研究中，我们将比较显式和隐式时间推进方案，多重网格和各种光滑器(特别是GMRES)，以及处理角点奇点和前角的不同策略。此外，我们还将对几个主题进行理论研究：和加速拟谱方法及其与有限差分的关系，伪谱残差和误差的比较，解强非线性边值问题的简化基和Delves-Freeman迭代，以及波面和激波的谱方法。