Inverse Wave-Number-Dependent Source Problems for the Helmholtz Equation

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-06-06 DOI:10.1137/23m1572696

Hongxia Guo, Guanghui Hu

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引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1372-1393, June 2024.
Abstract. This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a [math]-convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.

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亥姆霍兹方程的反波数依赖源问题

SIAM 数值分析期刊》第 62 卷第 3 期第 1372-1393 页，2024 年 6 月。摘要本文主要研究多频因式分解法，用于对依赖波数的源函数的支持进行成像。假设该源函数是由某个先验给定辐射周期的随时间变化的源的反傅里叶变换给出的。利用固定观测方向的多频远场数据，我们提供了一个计算准则，用于描述包含支撑且垂直于观测方向的最小条带。来自稀疏观测方向的远场数据可用来恢复支撑点的[数学]凸多边形。即使是三维多频近场数据，反演算法也被证明是有效的。在近场情况下，讨论了与时间相关反源问题的联系。通过二维和三维数值测试，展示了该方法的有效性和可行性。本文提供了频域方法的数值分析，以恢复一类时间相关源的可容许支持。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.