A novel Newton method for inverse elastic scattering problems

IF 2 2区 数学 Q1 MATHEMATICS, APPLIED
Yan Chang, Yukun Guo, Hongyu Liu and Deyue Zhang
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引用次数: 0

Abstract

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier–Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method.
用于反弹性散射问题的新型牛顿法
本研究关注的是一个反弹性散射问题,即识别嵌入充满各向同性均质弹性介质的开放空间中的未知刚性障碍物。设计了一种基于边界条件的牛顿迭代法来识别障碍物的边界曲线。基于亥姆霍兹分解和傅立叶-贝塞尔展开,我们明确推导出了近似散射场及其在每条迭代曲线上的导数。我们为所提出的方法提供了严格的数学论证。我们还提供了数值示例来验证所提方法的有效性。
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来源期刊
Inverse Problems
Inverse Problems 数学-物理:数学物理
CiteScore
4.40
自引率
14.30%
发文量
115
审稿时长
2.3 months
期刊介绍: An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.
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