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We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , Leonidas Mindrinos

A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , B. Tomas Johansson , Leonidas Mindrinos

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…

Analysis of PDEs · Mathematics 2022-12-28 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , Leonidas Mindrinos

In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this…

Numerical Analysis · Mathematics 2023-11-20 Roman Chapko , Leonidas Mindrinos

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…

Numerical Analysis · Mathematics 2017-12-21 Larisa Beilina , Kati Niinimäki

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a…

Analysis of PDEs · Mathematics 2022-10-12 Lauri Oksanen , Tianyu Yang , Yang Yang

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2019-01-15 Gen Nakamura , Manmohan Vashisth

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

Analysis of PDEs · Mathematics 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Numerical Analysis · Mathematics 2015-05-28 Carlos Borges , Leslie Greengard

This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…

Analysis of PDEs · Mathematics 2021-11-12 Masaru Ikehata

We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…

Optimization and Control · Mathematics 2015-05-12 Nicolae Cindea , Arnaud Munch

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…

Analysis of PDEs · Mathematics 2017-05-12 Kiril Datchev , Maarten V. de Hoop

In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.

Mathematical Physics · Physics 2009-09-30 Leonid Pestov , Victoria Bolgova , Oksana Kazarina

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

Numerical Analysis · Mathematics 2023-01-25 Heping Dong , Peijun Li

We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…

Analysis of PDEs · Mathematics 2026-03-11 Tianyu Yang , Yang Yang

We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…

Numerical Analysis · Mathematics 2016-09-21 Lauri Mustonen

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Analysis of PDEs · Mathematics 2025-11-27 Xiaoxu Xu , Guanghui Hu

We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…

Numerical Analysis · Mathematics 2024-08-19 Jesse Cherry , Alan E. Lindsay , Bryan D. Quaife
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