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Volume 25, Issue 5
Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method

Deyue Zhang, Yukun Guo, Jingzhi Li & Hongyu Liu

DOI: 10.4208/cicp.OA-2018-0020

Commun. Comput. Phys., 25 (2019), pp. 1328-1356.

Published online: 2019-01

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  • Abstract

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.

  • Keywords

Inverse source problem, direct sampling method, Helmholtz equation, multipolar sources, acoustic wave.

  • AMS Subject Headings

49N45, 65M32, 74G75

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-25-1328, author = {Deyue Zhang, Yukun Guo, Jingzhi Li and Hongyu Liu}, title = {Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1328--1356}, abstract = {

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0020}, url = {http://global-sci.org/intro/article_detail/cicp/12953.html} }
TY - JOUR T1 - Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method AU - Deyue Zhang, Yukun Guo, Jingzhi Li & Hongyu Liu JO - Communications in Computational Physics VL - 5 SP - 1328 EP - 1356 PY - 2019 DA - 2019/01 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0020 UR - https://global-sci.org/intro/article_detail/cicp/12953.html KW - Inverse source problem, direct sampling method, Helmholtz equation, multipolar sources, acoustic wave. AB -

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.

Deyue Zhang, Yukun Guo, Jingzhi Li and Hongyu Liu. (2019). Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method. Communications in Computational Physics. 25 (5). 1328-1356. doi:10.4208/cicp.OA-2018-0020
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