求解任意多边形区域二维偏微分方程的小波精细积分法  

Wavelet precise integration method for 2D partial differential equations in polygon domain

作　　者：德淑敏[1] 黄成[2] 梅树立[1] 

机构地区：[1]中国农业大学信息与电气工程学院,北京100083 [2]上海师范大学基建规划处,上海201418

出　　处：《中国农业大学学报》2007年第3期81-84,共4页Journal of China Agricultural University

基　　金：国家自然科学基金资助项目(10372036);中国农业大学科研启动基金(2005037)

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。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.

关 键 词：小波 精细积分 虚拟区域 偏微分方程 

分 类 号：TN911.73[电子电信—通信与信息系统] O351.2[电子电信—信息与通信工程]