Time-domain analysis of forward obstacle scattering for elastic wave

Zhao, Lu; Dong, Heping; Ma, Fai

doi:10.3934/dcdsb.2020276

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…The time domain inverse obstacle scattering problem is an important research topic with many potential applications such as geophysical exploration, biomedical imaging and noninvasive detecting. Since time domain broadband signals can be captured easier and these measurement data contain more information at discrete frequencies compared with frequency domain data, recently, time domain scattering and inverse scattering problems have attracted a lot of attention [5,16,17,19,25,26,32,33,35].…”

Section: Introductionmentioning

confidence: 99%

Inverse obstacle scattering for elastic waves in the time domain

Zhao¹,

Dong²,

Ma³

2022

Inverse Problems

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This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using the Helmholtz decomposition, we reduce the initial-boundary value problem for the time domain Navier equation to a coupled initial-boundary value problem for wave equations, and prove the uniqueness of the solution for the coupled problem by employing the energy method. The retarded single layer potential is introduced to establish a set of coupled boundary integral equations, and uniqueness is discussed for the solution of these boundary integral equations. Based on the convolution quadrature method for time discretization, the coupled boundary integral equations are reformulated into a system of boundary integral equations in the s-domain, and then a convolution quadrature based nonlinear integral equation method is proposed for the inverse problem. Numerical experiments are presented to show the feasibility and effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Inverse obstacle scattering for elastic waves in the time domain

Zhao¹,

Dong²,

Ma³

2022

Inverse Problems

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“…For some recent developments on path reconstructions of moving point sources, we refer to [8,35,39,40]. For other direct scattering problems in time domain with acoustic, elastic or electromagnetic wave, we refer to [3,2,6,10,11,18,19,21,20,34,43]. As for the frequency domain inverse scattering problem, we refer to [13,14,31,32,33,36,41,42].…”

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confidence: 99%

Inverse obstacle scattering for acoustic waves in the time domain

Zhao¹,

Dong²,

Ma³

2021

IPI

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<p style='text-indent:20px;'>This paper concerns an inverse acoustic scattering problem which is to determine the location and shape of a rigid obstacle from time domain scattered field data. An efficient convolution quadrature method combined with nonlinear integral equation method is proposed to solve the inverse problem. In particular, replacing the classic Fourier transform with the convolution quadrature method for time discretization, the boundary integral equations for the Helmholtz equation with complex wave numbers can be obtained to guarantee the numerically approximate causality property of the scattered field under some condition. Numerical experiments are presented to demonstrate the effectiveness and robustness of the proposed method.</p>

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Time-domain analysis of forward obstacle scattering for elastic wave

Cited by 2 publications

References 19 publications

Inverse obstacle scattering for elastic waves in the time domain

Inverse obstacle scattering for elastic waves in the time domain

Inverse obstacle scattering for acoustic waves in the time domain

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