Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets |
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Authors: | Oleg V Vasilyev |
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Institution: | Department of Mechanical Engineering , University of Colorado , 427 UCB, Boulder, CO, 80309-0427, USA |
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Abstract: | A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems. |
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Keywords: | Wavelets Lifting Scheme Second Generation Wavelets Partial Differential Equations Adaptive Grid Numerical Method |
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