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The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…

Mathematical Physics · Physics 2016-01-20 Michael V. Klibanov , Vladimir G. Romanov

This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…

Analysis of PDEs · Mathematics 2020-08-18 Henrik Garde

Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…

Numerical Analysis · Mathematics 2015-07-13 Martin Burger , Ole Loseth Elvetun , Matthias Schlottbom

We analyze the factorization method (introduced by Kirsch in 1998 to solve inverse scattering problems at fixed frequency from the far field operator) for a general class of boundary conditions that generalizes impedance boundary…

Analysis of PDEs · Mathematics 2013-09-17 Mathieu Chamaillard , Nicolas Chaulet , Houssem Haddar

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…

Analysis of PDEs · Mathematics 2018-01-18 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…

Analysis of PDEs · Mathematics 2020-10-13 Loc H. Nguyen , Qitong Li , Michael V. Klibanov

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

Numerical Analysis · Mathematics 2018-03-29 Antti Hannukainen , Nuutti Hyvönen , Lauri Mustonen

Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the…

Numerical Analysis · Mathematics 2020-04-22 Heping Dong , Jun Lai , Peijun Li

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the locations of small conductivity inclusions in the model from…

Numerical Analysis · Mathematics 2025-05-29 Jiho Hong , Bangti Jin , Zhizhang Wu

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to…

Numerical Analysis · Mathematics 2015-06-12 Haiwen Zhang , Bo Zhang

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…

Numerical Analysis · Mathematics 2022-12-20 Deyue Zhang , Yue Wu , Yukun Guo

This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…

Analysis of PDEs · Mathematics 2025-09-04 Isaac Harris , Peijun Li , General Ozochiawaeze

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…

Analysis of PDEs · Mathematics 2022-04-12 Giovanni Covi , Jesse Railo , Philipp Zimmermann

We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…

Numerical Analysis · Mathematics 2019-04-11 Emanuel H. Rubensson , Anton G. Artemov , Anastasia Kruchinina , Elias Rudberg

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…

Analysis of PDEs · Mathematics 2021-02-10 Isaac Harris
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