声波方程反问题数值解边界控制方法的正则化

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2020-12-10 DOI:10.1080/17415977.2020.1858077

A. Timonov

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引用次数: 1

摘要

通过边界控制方法的动力学版本，提出了总变化最小化用于从背散射声波中恢复流体介质的质量密度。这可能对水下声学成像或超声断层扫描特别感兴趣。特别地，提出并发展了正则化平均曲率流方程的类似物，以获得具有病态Gram矩阵的线性方程组的数值解。为了证明所提出的数值技术的计算有效性，我们对1 + 一维声波方程。

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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Regularization of the boundary control method for numerical solutions of the inverse problem for an acoustic wave equation

The total variation minimization is proposed for use in recovering the mass density of a fluid medium from back-scattered acoustic waves by the dynamical version of the boundary control method. This may be of particular interest to underwater acoustic imaging or ultrasound tomography. In particular, an analogue of the regularized mean curvature flow equation is proposed and developed to obtain numerical solution of the system of linear equations with the ill-conditioned Gram matrix. To demonstrate the computational effectiveness of the proposed numerical technique, we conduct a series of numerical experiments with the inverse problem for a 1 + 1 dimensional acoustic wave equation.

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.