谱方法数值计算研究进展

为了推动谱方法在科学计算中的广泛应用,给出了谱方法的基本原理和计算框架;总结了谱方法椭圆问题与双曲问题中的研究进展;论述了球面坐标和极坐标下的谱方法;分析了球谐谱方法在计算中的特点和存在问题;讨论了基于区域分解思想的谱方法,并对谱方法在实际计算中几个相关问题进行了分析.其中基于区域分解的谱方法可分为多域拟谱方法和谱元素方法,目前对二者的研究都非常活跃.

The Development of Numerical Computing by Spectral Method

We discuss the principles and computational framework of spectral method. The development of spectral method on elliptical and hyperbolic problems is summarized, and spectral method under sphere coordinates and polar coordinates is touched too. As a result, we analyze the characteristics of the spherical harmonics spectral method. In addition, the spectral method based on domain decomposition and some involved problems in real computation are analyzed. We point out that the spectral method based on domain decomposition can be classified into two methods named multi domain pseudospectral and spectral element. Above both methods are very active research directions. We hope that the discussion about the development and future of thd spectral method will promote the research and application of the powerful method in the field of scientific compution.