Integrating the probe and singular sources methods

IF 0.9 4区 数学 Q2 MATHEMATICS
Masaru Ikehata
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引用次数: 0

Abstract

The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods.
整合探针法和奇异源法
探针法和奇异源法是偏微分方程反障碍问题中两种著名的经典直接重构方法。本文以拉普拉斯方程控制的有界域逆障碍问题为原型,提出了探针法和奇异源法的综合理论。该理论由三部分组成:(i) 引入奇异源方法与探针方法的概念;(ii) 寻找第三个指标函数,其双向分解可得到探针方法和奇异源方法中的指标函数;(iii) 寻找探针方法和奇异源方法的完全集成版本。
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来源期刊
Journal of Inverse and Ill-Posed Problems
Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.60
自引率
9.10%
发文量
48
审稿时长
>12 weeks
期刊介绍: This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography
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