Inverse Source Problem of the Biharmonic Equation from Multifrequency Phaseless Data

IF 3 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Scientific Computing Pub Date : 2024-09-03 DOI:10.1137/24m162889x

Yan Chang, Yukun Guo, Yue Zhao

引用次数: 0

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2799-A2818, October 2024.
Abstract. This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless data. In the first stage, we introduce some artificial auxiliary point sources to the inverse source system and establish a phase retrieval formula. Theoretically, we point out that the phase can be uniquely determined and estimate the stability of this phase retrieval approach. Once the phase information is retrieved, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. The proposed method is easy to implement and there is no forward solver involved in the reconstruction. Numerical experiments are conducted to verify the performance of the proposed method.

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从多频无相数据看比谐波方程的反源问题

SIAM 科学计算期刊》，第 46 卷第 5 期，第 A2799-A2818 页，2024 年 10 月。摘要本研究涉及双谐波方程的反源问题。提出了一种两阶段数值方法，以从多频无相数据中识别未知源。在第一阶段，我们在反源系统中引入了一些人工辅助点源，并建立了一个相位检索公式。我们从理论上指出相位可以唯一确定，并估计了这种相位检索方法的稳定性。一旦检索到相位信息，就可以采用傅立叶方法从相位多频数据中重建源函数。所提出的方法易于实施，重建过程中不涉及前向求解器。为验证所提方法的性能，我们进行了数值实验。

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

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.