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首页> 外文期刊>Journal of Computational Physics >An adaptive wavelet collocation method for the solution of partial differential equations on the sphere
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An adaptive wavelet collocation method for the solution of partial differential equations on the sphere

机译：球面偏微分方程解的自适应小波配置方法

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A dynamic adaptive numerical method for solving partial differential equations on the sphere is developed. The method is based on second generation spherical wavelets on almost uniform nested spherical triangular grids, and is an extension of the adaptive wavelet collocation method to curved manifolds. Wavelet decomposition is used for grid adaption and interpolation. An O(N) hierarchical finite difference scheme based on the wavelet multilevel decomposition is used to approximate Laplace-Beltrami, Jacobian and flux-divergence operators. The accuracy and efficiency of the method is demonstrated using linear and nonlinear examples relevant to geophysical flows. Although the present paper considers only the sphere, the strength of this new method is that it can be extended easily to other curved manifolds by considering appropriate coarse approximations to the desired manifold (here we used the icosahedral approximation to the sphere at the coarsest level). (c) 2008 Elsevier Inc. All rights reserved.
机译：提出了一种求解球面上偏微分方程的动态自适应数值方法。该方法基于几乎均匀嵌套的球形三角网格上的第二代球形小波，是自适应小波配置方法对弯曲流形的扩展。小波分解用于网格自适应和插值。基于小波多级分解的O（N）层次有限差分方案用于逼近Laplace-Beltrami，Jacobian和通量发散算子。使用与地球物理流有关的线性和非线性示例证明了该方法的准确性和效率。尽管本文只考​​虑了球体，但这种新方法的优势在于可以通过考虑所需流形的适当粗略近似，轻松地将其扩展到其他弯曲流形（此处，我们在最粗糙的水平上使用二十面体近似于球面） 。 （c）2008 Elsevier Inc.保留所有权利。

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