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A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Numerical Analysis · Mathematics 2016-05-23 Michael V. Klibanov , Hui Liu , Loc H. Nguyen

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…

Numerical Analysis · Mathematics 2020-02-14 Vo Anh Khoa , Michael Victor Klibanov , Loc Hoang Nguyen

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

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

Numerical Analysis · Mathematics 2016-12-14 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen , Hui Liu

A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…

Numerical Analysis · Mathematics 2008-09-24 Hua Shan , M. V. Klibanov , Jianzhong Su , Natee Pantong , Hanli Liu

To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…

Numerical Analysis · Mathematics 2021-04-26 Michael V. Klibanov , Thuy T. Le , Loc H. Nguyen , Anders Sullivan , Lam Nguyen

We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

Numerical Analysis · Mathematics 2018-05-22 Michael V. Klibanov , Aleksandr E. Kolesov , Dinh-Liem Nguyen

This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…

It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…

Numerical Analysis · Mathematics 2022-03-23 Thuy T. Le , Michael V. Klibanov , Loc H. Nguyen , Anders Sullivan , Lam Nguyen

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

Numerical Analysis · Mathematics 2017-10-16 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen

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

A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…

Numerical Analysis · Mathematics 2018-10-17 Michael V. Klibanov , Aleksandr E. Kolesov , Anders Sullivan , Lam Nguyen

We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…

Numerical Analysis · Mathematics 2024-12-20 Thanh T. Nguyen , Michael V. Klibanov

A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problems with the initial condition the delta function concentrated at a single plane (i.e. the plane…

Analysis of PDEs · Mathematics 2022-03-23 Michael V. Klibanov , Vladimir G. Romanov

A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most…

Numerical Analysis · Mathematics 2020-07-14 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…

Numerical Analysis · Mathematics 2025-12-23 Michael V. Klibanov , Jingzhi Li , Vladimir G. Romanov , Zhipeng Yang

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…

Analysis of PDEs · Mathematics 2019-06-06 Phuong Mai Nguyen , Loc Hoang Nguyen

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…

We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…

Analysis of PDEs · Mathematics 2019-02-20 Loc Hoang Nguyen
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