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This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…

Numerical Analysis · Mathematics 2023-08-14 Peijun Li , Xiaokai Yuan

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…

Analysis of PDEs · Mathematics 2026-02-20 Rafael Ceja Ayala , Isaac Harris , Tonatiuh Sánchez-Vizuet

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

Numerical Analysis · Mathematics 2024-08-07 Borong Zhang , Leonardo Zepeda-Núñez , Qin Li

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…

Statistical Mechanics · Physics 2026-05-12 Carolina Garcia , Lucía Perea Durán , Agnese Venezia , Alex Conradie

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…

Numerical Analysis · Mathematics 2025-04-09 Carolina Abugattas , Ana Carpio , Elena Cebrián , Gerardo Oleaga

We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…

Numerical Analysis · Mathematics 2025-08-18 Sarah Eberle-Blick , Bastian Harrach , Xianchao Wang

Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…

Optics · Physics 2025-03-03 Ilya A. Kudryavtsev

In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic…

Numerical Analysis · Mathematics 2025-08-05 Guanghui Hu , Jiayi Zhang , Linlin Zhu

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

In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…

Numerical Analysis · Mathematics 2022-05-26 Fortino Garcia , Daniel Appelö , Olof Runborg

We study inverse boundary problems for the advection diffusion equation on an admissible manifold, i.e. a compact Riemannian manifold with boundary of dimension $\ge 3$, which is conformally embedded in a product of the Euclidean real line…

Analysis of PDEs · Mathematics 2017-04-20 Katya Krupchyk , Gunther Uhlmann

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…

Numerical Analysis · Mathematics 2022-02-21 Deyue Zhang , Yue Wu , Yinglin Wang , Yukun Guo

Based on the classical Lorentz model of the index of refraction, a new method is presented for the extraction of the complex index of refraction from the extinction efficiency of homogeneous and layered dielectric spheres that…

Optics · Physics 2022-06-28 Kalpa de Silva , Proity Akbar , Reinhold Blümel

This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…

Computational Physics · Physics 2015-06-19 Carlos Pérez-Arancibia , Oscar P. Bruno

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

Consider the elastic scattering of an incident wave by a rigid obstacle in three dimensions, which is formulated as an exterior problem for the Navier equation. By constructing a Dirichlet-to-Neumann (DtN) operator and introducing a…

Numerical Analysis · Mathematics 2021-01-18 Gang Bao , Peijun Li , Xiaokai Yuan

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

Numerical Analysis · Mathematics 2023-07-31 Oscar P. Bruno , Ambuj Pandey

Electromagnetic Inverse Scattering Problems (EISP) have gained wide applications in computational imaging. By solving EISP, the internal relative permittivity of the scatterer can be non-invasively determined based on the scattered…

Computer Vision and Pattern Recognition · Computer Science 2024-07-15 Ziyuan Luo , Boxin Shi , Haoliang Li , Renjie Wan