{"title":"Inverse Source Problem of the Biharmonic Equation from Multifrequency Phaseless Data","authors":"Yan Chang, Yukun Guo, Yue Zhao","doi":"10.1137/24m162889x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2799-A2818, October 2024. <br/> Abstract. This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless data. In the first stage, we introduce some artificial auxiliary point sources to the inverse source system and establish a phase retrieval formula. Theoretically, we point out that the phase can be uniquely determined and estimate the stability of this phase retrieval approach. Once the phase information is retrieved, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. The proposed method is easy to implement and there is no forward solver involved in the reconstruction. Numerical experiments are conducted to verify the performance of the proposed method.","PeriodicalId":49526,"journal":{"name":"SIAM Journal on Scientific Computing","volume":"163 1","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Scientific Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m162889x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2799-A2818, October 2024. Abstract. This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless data. In the first stage, we introduce some artificial auxiliary point sources to the inverse source system and establish a phase retrieval formula. Theoretically, we point out that the phase can be uniquely determined and estimate the stability of this phase retrieval approach. Once the phase information is retrieved, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. The proposed method is easy to implement and there is no forward solver involved in the reconstruction. Numerical experiments are conducted to verify the performance of the proposed method.
期刊介绍:
The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems.
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