从耦合波场重构弹性体力的傅立叶方法

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2021052

Xianchao Wang, Jiaqi Zhu, Minghui Song, Wei Wu

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引用次数: 1

摘要

本文研究时谐弹性波的逆源问题。提出了一种利用多频傅里叶展开确定弹性体力的非迭代重建方法。该方法的关键是选择合适的允许频率，建立纵波和横波耦合波场与傅里叶系数之间的关系。通过理论论证和数值算例验证了所提方法的有效性和鲁棒性。

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Fourier method for reconstructing elastic body force from the coupled-wave field

This paper is concerned with the inverse source problem of the time-harmonic elastic waves. A novel non-iterative reconstruction scheme is proposed for determining the elastic body force by using the multi-frequency Fourier expansion. The key ingredient of the approach is to choose appropriate admissible frequencies and establish an relationship between the Fourier coefficients and the coupled-wave field of compressional wave and shear wave. Both theoretical justifications and numerical examples are presented to verify the validity and robustness of the proposed method.

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.