小波插值Galerkin法解二维静电场中的边值问题

提出了一种偏微分方程的数值解法，即小波插值Ｇａｌｅｒｋｉｎ法，它是利用具有紧支撑 　的 Ｄａｕｂｅｃｈｉｅｓ小波函数的自相关函数得到解空间的一组具有插值特性的 Ｒｉｅｓｚ基．讨论了 系数矩阵的预处理技术和多介质问题的处理方法；在混合边界条件的处理中使用了外小波， 既简化了边界条件的处理，又提高了近似解的精度．并将小波插值 Ｇａｌｅｒｋｉｎ法应用在二维 静电场边值问题的数值计算中，得到了较好的结果，与此同时给出了有限元法的计算结果．

A Wavelet Interpolation Galerkin Method for the Solution of Boundary Value Problems in 2D Electrostatic Field

This paper presents a new method for the numerical solution to partial difference equations named a wavelet interpolation Galerkin method, in which autocorrelation functions of Daubechies's compactly supported wavelets are taken as the Riesz's basis with interpolation properties for the solution space. It is discussed to precondition the coefficient matrix and to treat the domain with several media. Then external wavelets are used to deal with mixed boundary conditions, which simplifies the disposal of boundary conditions and improves the accuracy of approximate solutions. Applied for the numerical computation of boundary value problems in 2D electrostatic field, some results show its validity. And results from finite element method are also given.