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A version of the convexification globally convergent numerical method is constructed for a coefficient inverse problem for a wave-like partial differential equation. The presence of the Carleman Weight Function in the corresponding…

Numerical Analysis · Mathematics 2021-11-09 Michael V. Klibanov , Jingzhi Li , Wenlong Zhang

In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…

Numerical Analysis · Mathematics 2024-01-26 A. S. Shurup

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…

Numerical Analysis · Mathematics 2023-07-05 Youzi He , Hongyu Liu , Xianchao Wang

Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…

Analysis of PDEs · Mathematics 2016-12-21 Gang Bao , Guanghui Hu , Jiguang Sun , Tao Yin

In the present paper we describe a simple black box algorithm for efficiently and accurately solving scattering problems related to the scattering of time-harmonic waves from radially-symmetric potentials in two dimensions. The method uses…

Numerical Analysis · Mathematics 2020-08-03 Jeremy Hoskins , Vladimir Rokhlin

We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…

Analysis of PDEs · Mathematics 2018-12-26 Otar Chkadua , Sergey E. Mikhailov , David Natroshvili

Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimental data of a newly developed…

A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…

Numerical Analysis · Mathematics 2018-01-16 Michael V. Klibanov , Aleksandr E. Kolesov

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…

Numerical Analysis · Mathematics 2022-07-14 Mert Hidayetoglu , Michael Oelze , Erhan Kudeki , Weng Cho Chew

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…

Analysis of PDEs · Mathematics 2023-08-01 Li Li , Yang Zhang

This paper is concerned with the problem of scattering of a time-harmonic electromagnetic field by a three-dimensional elastic body. General transmission conditions are considered to model the interaction between the electromagnetic field…

Analysis of PDEs · Mathematics 2019-08-27 Tielei Zhu , Jiaqing Yang , Bo Zhang

We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.

Analysis of PDEs · Mathematics 2017-08-30 Peter C. Gibson

The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…

Numerical Analysis · Mathematics 2016-09-14 Balgaisha Mukanova , Vladimir G. Romanov

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…

Analysis of PDEs · Mathematics 2021-06-08 Mine Aylin Bayrak , Ali Demir

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

Computer Vision and Pattern Recognition · Computer Science 2016-10-07 Hsiou-Yuan Liu , Ulugbek S. Kamilov , Dehong Liu , Hassan Mansour , Petros T. Boufounos

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…

Computational Physics · Physics 2017-10-11 Evert Klaseboer , Shahrokh Sepehrirahnama , Derek Y. C. Chan

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed…

Numerical Analysis · Mathematics 2020-04-30 Thomas G. Anderson , Oscar P. Bruno , Mark Lyon

Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…

Geophysics · Physics 2009-05-05 R. B. Schlottmann