| 摘要: |
| 张量积小波数值法方法具有自适应性和较高的精度,但只适合求解定义在矩形区域的偏微分方程。将小波精细积分法与虚拟区域法相结合,构造了一种求解定义在任意多边形区域的二维偏微分方程的新小波数值方法。小波函数的紧支撑性降低了虚拟区域法的计算工作量。该方法可为求解定义在不规则区域上的工程动力学模型提供参考。 |
| 关键词: 小波 精细积分 虚拟区域 偏微分方程 |
| DOI：10.11841/j.issn.1007-4333.2007.03.068 |
| 修订日期：2006-11-24 |
| 基金项目:国家自然科学基金;中国农业大学校科研和教改项目 |
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| Wavelet precise integration method for 2D partial differential equations in polygon domain |
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| Abstract: |
| The tensor wavelet numerical method possesses the self-adaptability and higher precision.But it is suitable to the problems only restricted to partial differential equations defined in rectangle domain.A kind of new wavelet numerical method for solving 2D partial differential equations in polygon domain is proposed.Based on the combination wavelet precise integration method with the fictious domain method.In this method,the compact support property improves the calculation efficiency of the fictious domain method,which is helpful to solving the dynamic model in engineering such as the rill erosion model. |
| Key words: wavelet,precise integration method,fictious domain,partial differential equation |
