| 小波基方法在波传问题中的应用 |
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| 引用本文： | 马坚伟,杨慧珠.小波基方法在波传问题中的应用[J].应用力学学报,2002,19(4):26-30. |
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| 作者姓名： | 马坚伟 杨慧珠 |
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| 作者单位： | 清华大学,北京,100084 |
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| 基金项目： | 国家自然科学基金资助 (批准号 19872 0 3 7) |
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| 摘 要： | 基于多尺度分析理论，引入哈密顿体系和插值小波变换，分别构造了适合于求解复杂域波传问题的快速自适应方法——多尺度辛格式和插值小波配点格式，利用小波基的局部性与消失矩等特性改善计算效率，并将插值小波应用到波动方程的多尺度反演问题中。讨论了其优缺点并提出几点展望。
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| 关 键 词： | 辛格式 插值小波 波传问题 反演 |
| 文章编号： | 1000-4939(2002)04-0026-05 |
| 修稿时间： | 2001年7月10日 |
An Application of wavelet-Based Method for Wave Propagation |
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| Ma Jianwei,Yang Huizhu.An Application of wavelet-Based Method for Wave Propagation[J].Chinese Journal of Applied Mechanics,2002,19(4):26-30. |
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| Authors: | Ma Jianwei Yang Huizhu |
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| Abstract: | Two wavelet based methods, named multi resolution symplectic scheme and interpolating wavelet collocation scheme for fast adaptive solution of wave propagation with general boundary condition are presented by introducing Hamilton system and interpolating subdivision scheme. Computational effectiveness and memory requirement are improved due to the vanishing moments, localization and multi resolution analysis of the wavelet. Then, a new method of multi resolution inversion for wave equation is proposed using interpolating wavelet. Finally, the advantage and disadvantage of these methods are discussed and several prospects are put forward. Numerical results in geophysics exploration show the potential of the methods. |
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| Keywords: | Symplectic Interpolating wavelet Wave Propagation Multi resolution inversion |
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