电磁反向散射中各向异性周期介质的稳定成像函数

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-29 DOI:10.1137/23m1577080

Dinh-Liem Nguyen, Trung Truong

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引用次数: 0

摘要

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1631-1657 页，2024 年 8 月。摘要本文探讨了三维各向异性周期介质中麦克斯韦方程的反散射问题。我们研究了一种新的成像函数，用于从散射场的边界测量中快速、稳健地重建各向异性周期散射体的形状。这种成像函数的实现非常简单，而且无需解决求解困难的问题。我们研究了成像函数的分辨率和稳定性分析。数值研究结果表明，在重建周期性散射体方面，该成像函数比因式分解法更稳定，比正交采样法更精确。

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A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024.
Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.