| 静电磁场不规则区域问题的小波插值Galerkin算法 |
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| 引用本文： | 侯霞,范植华,顾永耕,杨鸿波. 静电磁场不规则区域问题的小波插值Galerkin算法[J]. 计算物理, 2005, 22(6): 539-548 |
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| 作者姓名： | 侯霞 范植华 顾永耕 杨鸿波 |
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| 作者单位： | 中科院软件所通用软件实验室,北京,100080;湖南师范大学数学与计算机科学学院,湖南,长沙,410081;中科院电子所,北京,100080 |
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| 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.
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| 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 |
| 文章编号： | 1001-246X（2005）06-0539-10 |
| 收稿时间： | 2004-07-06 |
| 修稿时间： | 2005-02-01 |
A Wavelet Interpolation Galerkin Algorithm for Static Electromagnetic Field Analysis in Irregular Regions |
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| HOU Xia,FAN Zhi-hua,GU Yong-geng,YANG Hong-bo. A Wavelet Interpolation Galerkin Algorithm for Static Electromagnetic Field Analysis in Irregular Regions[J]. Chinese Journal of Computational Physics, 2005, 22(6): 539-548 |
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| Authors: | HOU Xia FAN Zhi-hua GU Yong-geng YANG Hong-bo |
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| Affiliation: | 1. General Software Lab, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China ; 2 . College of Mathematics and Computer Science , Hunan Normal University , Changsha 410081,China; 3. Institute of Electronics, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | 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. |
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| Keywords: | boundary value problem multiresolution analysis(MRA) wavelet interpolating Galerkin method(WIGM) Sobolev space external wavelet |
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