静电磁场不规则区域问题的小波插值Galerkin算法  

A Wavelet Interpolation Galerkin Algorithm for Static Electromagnetic Field Analysis in Irregular Regions

作　　者：侯霞[1] 范植华[1] 顾永耕[2] 杨鸿波[3] 

机构地区：[1]中科院软件所通用软件实验室,北京100080 [2]湖南师范大学数学与计算机科学学院,湖南长沙410081 [3]中科院电子所,北京100080

出　　处：《计算物理》2005年第6期539-548,共10页Chinese Journal of Computational Physics

摘　　要：讨论了用小波插值Galerkin方法(WIGM)求解椭圆型偏微分方程,特别是求解区域不规则时的问题.在归纳出WIGM一般形式的基础上,推导出该方法在Sobolev空间范数下的误差界限为C2-m.提出了一种解决不规则区域中静电磁场场分析问题的数值算法,其中选用对称插值尺度函数为基函数,它的对称性及其与平均插值尺度函数的关系可以在一定程度上降低数值求解的计算量.最后通过计算实例说明该算法的有效性.A Wavelet Interpolating Galerkin Method（WIGM） for elliptic partial differential equations, especially in irregular regions, is considered. It is proved that the WIGM produces an approximation with an error no more than C2^- m in the Sobolev space norm. A numerical WIGM algorithm for static electromagnetic field analysis in irregular regions is presented. A symmetric interpolating scaling function is selected as the base function. Its symmetry and relation with average-interpolating scaling function are used to reduce numerical computations. Examples presented demonstrate validity of the algorithm.

关 键 词：边值问题 多分辨分析(MRA) 小波插值Galerkin法 SOBOLEV空间 外小波 

分 类 号：TM154[电气工程—电工理论与新技术]