利用实验数据对凸化法处理频率相关反向散射问题进行数值验证

IF 0.58 Q3 Engineering
T. Le, V. A. Khoa, M. V. Klibanov, L. H. Nguyen, G. W. Bidney, V. N. Astratov
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引用次数: 0

摘要

摘要 根据边界测量结果重建介质的物理特性(即反向散射问题)是一项重大挑战。本研究旨在利用北卡罗来纳大学夏洛特分校微波散射设施收集的实验数据,验证针对沙箱中埋藏未知物体的三维系数反问题新开发的凸化方法。我们的研究考虑了基于多频率的耦合准线性椭圆系统的形式。该系统可以通过最小化加权提霍诺夫函数来求解,这就是我们的凸化方法。与凸化相关的理论结果也在这项工作中得到了重新审视。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Numerical Verification of the Convexification Method for a Frequency-Dependent Inverse Scattering Problem with Experimental Data

Numerical Verification of the Convexification Method for a Frequency-Dependent Inverse Scattering Problem with Experimental Data

The reconstruction of physical properties of a medium from boundary measurements, known as inverse scattering problems, presents significant challenges. The present study aims to validate a newly developed convexification method for a 3D coefficient inverse problem in the case of buried unknown objects in a sandbox, using experimental data collected by a microwave scattering facility at The University of North Carolina at Charlotte. Our study considers the formulation of a coupled quasilinear elliptic system based on multiple frequencies. The system can be solved by minimizing a weighted Tikhonov-like functional, which forms our convexification method. Theoretical results related to the convexification are also revisited in this work.

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来源期刊
Journal of Applied and Industrial Mathematics
Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering
CiteScore
1.00
自引率
0.00%
发文量
16
期刊介绍: Journal of Applied and Industrial Mathematics  is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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