| 用正则化方法求解声波散射反问题 |
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| 引用本文： | 王青云,王连堂.用正则化方法求解声波散射反问题[J].纯粹数学与应用数学,2006,22(2):182-188. |
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| 作者姓名： | 王青云 王连堂 |
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| 作者单位： | 西北大学数学系,陕西,西安,710069;西北大学数学系,陕西,西安,710069 |
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| 基金项目： | 陕西省教委基金(01JK064)，陕西省自然科学基金(2002A10)资助 |
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| 摘 要： | 研究了从声波散射场的远场模式的信息来再现散射物边界形状的反问题.首先构造表达散射物特征的指示函数,然后利用该函数之特性,建立求解该类反问题的基本方程,从而确定散射物的边界形状.在这个算法中,不需预先知道散射物的边界类型和形状等知识,从T ikhonov正则化方法进行的数值计算结果表明了该方法是有效的和实用的.
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| 关 键 词： | 远场模式 指示函数 Tihkonov正则化 |
| 文章编号： | 1008-5513（2006）02-0182-07 |
| 收稿时间： | 2005-06-15 |
| 修稿时间： | 2005年6月15日 |
Regularization method for solving the inverse acoustic scattering problem |
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| WANG Qing-yun,WANG Lian-tang.Regularization method for solving the inverse acoustic scattering problem[J].Pure and Applied Mathematics,2006,22(2):182-188. |
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| Authors: | WANG Qing-yun WANG Lian-tang |
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| Abstract: | An inverse problem of recovering the shape of an obstacle from a knowledge of the far-field pattern of the acoustic scattering wave is investigated in this paper.First,the indicator function representing the scattering characteristics is constructed;then,based on the property of the function,the fundamental equation for solving the inverse problem is established;thereby,the shape of the obstacle is determined.The method requires no a prior knowledge of the type of boundary condition imposed on the objects and its shape.the results of the numerical computation which is using Tikhonov regularization method show the validity and practicality of the method. |
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| Keywords: | the far-field pattern indicator function Tikhonov regularization |
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