Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets
Wang Ping (汪萍), Dai Xin-Gang (戴新刚)
Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, START Regional Center for Temperate East Asia, Beijing 100029, China
Abstract The numerical solution of the Helmholtz equation for barotropic atmosphere is estimated by use of the wavelet-Galerkin method. The solution involves the decomposition of a circulant matrix consisting up of 2-term connection coefficients of wavelet scaling functions. Three matrix decompositions, i.e. fast Fourier transformation (FFT), Jacobian and QR decomposition methods, are tested numerically. The Jacobian method has the smallest matrix-reconstruction error with the best orthogonality while the FFT method causes the biggest errors. Numerical result reveals that the numerical solution of the equation is very sensitive to the decomposition methods, and the QR and Jacobian decomposition methods, whose errors are of the order of $10^{-3}$, much smaller than that with the FFT method, are more suitable to the numerical solution of the equation. With the two methods the solutions are also proved to have much higher accuracy than the iteration solution with the finite difference approximation. In addition, the wavelet numerical method is very useful for the solution of a climate model in low resolution. The solution accuracy of the equation may significantly increase with the order of Daubechies wavelet.
Received: 18 February 2004
Revised: 20 May 2004
Accepted manuscript online:
(Properties and dynamics of the atmosphere; meteorology)
Fund: Project supported by the National Key Planning Development for Basic Research (Grant No 1999043403) and the National Natural Science Foundation of China (Grant No 49875024).
Cite this article:
Wang Ping (汪萍), Dai Xin-Gang (戴新刚) Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets 2004 Chinese Physics 13 1770
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
