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

Xianchao Wang; Jiaqi Zhu; Minghui Song; Wei Wu

doi:10.3934/ipi.2021052

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

Xianchao Wang
, Jiaqi Zhu^*
, Minghui Song^*
, Wei Wu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

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 appropri-ate 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.

Original language	English
Pages (from-to)	325-340
Number of pages	16
Journal	Inverse Problems and Imaging
Volume	16
Issue number	2
Early online date	Jul 2021
DOIs	https://doi.org/10.3934/ipi.2021052
Publication status	Published - Apr 2022

User-Defined Keywords

Coupled-wave field
Elastic body force
Fourier method
Inverse source problem

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10.3934/ipi.2021052

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title = "Fourier method for reconstructing elastic body force from the coupled-wave field",

abstract = "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 appropri-ate 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.",

keywords = "Coupled-wave field, Elastic body force, Fourier method, Inverse source problem",

author = "Xianchao Wang and Jiaqi Zhu and Minghui Song and Wei Wu",

note = "Funding Information: Acknowledgments. The work of X. Wang was supported by the NSFC grants under Nos. 11971133, 12001140. The work of J. Zhu was financially supported by the National Science Fund for Distinguished Young Scholars (Grant No. 51625201) and the Key Program of National Natural Science Foundation of China (Grant No. 52032004). The work of M. Song was supported by NSFC grants under Nos. 11671113, 12071101. The work of W. Wu was supported by the Hong Kong RGC grant No. 12302219 and Tier 2 Startup fund from Hong Kong Baptist University. Publisher Copyright: {\textcopyright} 2022, American Institute of Mathematical Sciences. All rights reserved.",

year = "2022",

month = apr,

doi = "10.3934/ipi.2021052",

language = "English",

volume = "16",

pages = "325--340",

journal = "Inverse Problems and Imaging",

issn = "1930-8337",

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T1 - Fourier method for reconstructing elastic body force from the coupled-wave field

AU - Wang, Xianchao

AU - Zhu, Jiaqi

AU - Song, Minghui

AU - Wu, Wei

N1 - Funding Information: Acknowledgments. The work of X. Wang was supported by the NSFC grants under Nos. 11971133, 12001140. The work of J. Zhu was financially supported by the National Science Fund for Distinguished Young Scholars (Grant No. 51625201) and the Key Program of National Natural Science Foundation of China (Grant No. 52032004). The work of M. Song was supported by NSFC grants under Nos. 11671113, 12071101. The work of W. Wu was supported by the Hong Kong RGC grant No. 12302219 and Tier 2 Startup fund from Hong Kong Baptist University. Publisher Copyright: © 2022, American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/4

Y1 - 2022/4

N2 - 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 appropri-ate 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.

AB - 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 appropri-ate 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.

KW - Coupled-wave field

KW - Elastic body force

KW - Fourier method

KW - Inverse source problem

UR - https://www.scopus.com/pages/publications/85123525982

U2 - 10.3934/ipi.2021052

DO - 10.3934/ipi.2021052

M3 - Journal article

AN - SCOPUS:85123525982

SN - 1930-8337

VL - 16

SP - 325

EP - 340

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 2

ER -

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

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