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The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…

Analysis of PDEs · Mathematics 2016-04-27 Yixian Gao , Peijun Li

Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…

Computational Physics · Physics 2025-02-06 Georgios E. Pavlou , Vasiliki Pavlidou , Vagelis Harmandaris

The inverse wave scattering problem seeks to estimate a heterogeneous, inaccessible medium, modeled by unknown variable coefficients in wave equations, from transient recordings of waves generated by probing signals. It is a widely studied…

Numerical Analysis · Mathematics 2024-03-07 Liliana Borcea , Yiyang Liu , Jörn Zimmerling

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse…

Analysis of PDEs · Mathematics 2018-01-11 Xianchao Wang , Minghui Song , Yukun Guo , Hongjie Li , Hongyu Liu

This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is…

Numerical Analysis · Mathematics 2019-11-07 Marion Darbas , Jérémy Heleine , Stephanie Lohrengel

We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate…

Analysis of PDEs · Mathematics 2018-10-31 Irena Lasiecka , Michael Pokojovy , Roland Schnaubelt

We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…

Fluid Dynamics · Physics 2007-05-23 Frank Stefani , Thomas Gundrum , Gunter Gerbeth , Uwe Guenther , Mingtian Xu

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…

Analysis of PDEs · Mathematics 2020-02-21 Peijun Li , Xu Wang

In this note we discuss the numerical solution of the eddy current approximation of the Maxwell equations using the simple Pragmatic Algebraic Model to include hysteresis effects. In addition to the more standard time-stepping approach we…

Numerical Analysis · Mathematics 2025-04-17 Mario Gobrial , Lukas Domenig , Michael Reichelt , Manfred Kaltenbacher , Olaf Steinbach

We study an inverse initial-density problem for a nonlinear diffusive coagulation--fragmentation equation with known coagulation and fragmentation kernels. The objective is to recover the unknown initial particle-size distribution on a…

Numerical Analysis · Mathematics 2026-03-24 Thuy T. Le , Minh-Binh Tran , Loc H. Nguyen

We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…

Numerical Analysis · Mathematics 2015-06-19 Larisa Beilina , Nguyen Trung Thành , Michael V. Klibanov , John Bondestam Malmberg

We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…

Analysis of PDEs · Mathematics 2018-06-25 Monika Pichler

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

Optimization and Control · Mathematics 2024-02-11 Arnaud Munch , Diego Souza

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards…

Analysis of PDEs · Mathematics 2011-05-23 Dirk Pauly

This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher…

Numerical Analysis · Mathematics 2024-09-10 Zixuan Gao , Zhenli Xu , Zhiguo Yang

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…