Determination of the modified exterior Steklov eigenvalues via the reciprocity gap method

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-11-12 DOI:10.1016/j.cam.2024.116360

Wensong Qiu, Hongyan Wang, Yuan Li, Lixin Feng

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.

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通过互易差距法确定修正的外部斯特克洛夫特征值

修正的外部斯特克洛夫特征值（MESEs）产生于带空腔的不均匀介质的反散射问题，可作为无损检测中的潜在目标特征。在本文中，我们感兴趣的是如何从空腔内部点源引起的某些流形上总场的 Cauchy 测量数据中确定 MESE。为此，我们采用了基于线性积分方程的互易差距 (RG) 方法。我们提供了相关理论，并证明积分方程近似解的吹胀特性可用来描述 MESE。我们还列举了数值示例来证明我们方法的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

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.