{"title":"Determination of the modified exterior Steklov eigenvalues via the reciprocity gap method","authors":"Wensong Qiu, Hongyan Wang, Yuan Li, Lixin Feng","doi":"10.1016/j.cam.2024.116360","DOIUrl":null,"url":null,"abstract":"<div><div>The modified exterior Steklov eigenvalues (MESEs) arise from the inverse scattering problem for inhomogeneous media with a cavity and may serve as potential target signatures in nondestructive testing. In this paper we are interested in the determination of the MESEs from the measured Cauchy data of the total field on some manifold inside the cavity due to interior point sources. To this end, the reciprocity gap (RG) method based on a linear integral equation is employed. We provide the related theory and show that the blow-up property of the approximate solution to the integral equation can be used to characterize the MESEs. Numerical examples are presented to demonstrate the viability of our method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116360"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006083","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
The modified exterior Steklov eigenvalues (MESEs) arise from the inverse scattering problem for inhomogeneous media with a cavity and may serve as potential target signatures in nondestructive testing. In this paper we are interested in the determination of the MESEs from the measured Cauchy data of the total field on some manifold inside the cavity due to interior point sources. To this end, the reciprocity gap (RG) method based on a linear integral equation is employed. We provide the related theory and show that the blow-up property of the approximate solution to the integral equation can be used to characterize the MESEs. Numerical examples are presented to demonstrate the viability of our method.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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