An adaptive multilevel wavelet collocation method for elliptic problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:206

Article

Vasilyev, OV ; Kevlahan, NKR

关键词: wavelets;    lifting scheme;    second generation wavelets;    partial differential equations;    elliptic problem;    adaptive grid;    numerical method;    multilevel method;    multigrid method;   

DOI  :  10.1016/j.jcp.2004.12.013

来源: Elsevier

【 摘 要 】

An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is described. The method is based on multi-dimensional second generation wavelets, and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems [Int. J, Comp. Fluid Dyn. 17 (2003) 151]. Wavelet decomposition is used for grid adaptation and interpolation. while it hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The multilevel structure of the wavelet approximation provides a natural way to obtain the Solution Oil a near optimal grid. In order to accelerate the convergence of the solver. an iterative procedure analogous to the multigrid algorithm is developed. The overall computational complexity of the solver is O(N). where. I is the number of adapted grid points. The accuracy and computational efficiency of the method are demonstrated for the solution of two- and three-dimensional elliptic test problems. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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