arXiv subjects

Youzi He

Publications and source records attributed to Youzi He.

5 recordsLinked to original sources

arXiv2025

Uniqueness for phaseless inverse elastic scattering problem for periodic structures

This paper establishes uniqueness results of inverse elastic scattering problem with phaseless near-field data in periodic structures in $\mathbb{R}^2$ and periodic/biperiodic structures in $\mathbb{R}^3$. We use a superposition of two point sources in each periodic unit with different positions as the incident field, and measures the phaseless near-field data on a line parallel to $x_1$-axis in 2D, or on a plane parallel to $(x_1,x_2)$-plane in 3D. We first calculate the explicit formula of quasi-periodic/biperiodic Green's functions of Lam\'{e} system in $\mathbb{R}^3$. Then, to establish the uniqueness results, the reciprocity relations for point sources, scattered fields, and total fields are derived. Finally, with the help of Rayleigh's expansion, the uniqueness results are proved. The quasi-periodic/biperiodic Green's functions of Lam\'{e} system in $\mathbb{R}^3$, the reciprocity relations, and Rayleigh's expansion in $\mathbb{R}^3$ are novel results as important by-products in the proof process.

math.AP↗

arXiv2025

Mathematical Analysis of Subwavelength Resonance in Elastic Metascreen

The aim of this paper is to provide a comprehensive and mathematically rigorous analysis on determining the existence of subwavelength resonance in elastic metascreen and resonance frequency calculation based on asymptotic analysis of quasi-periodic layer potential operators. An elastic metascreen is a thin sheet with subwavelength structures, which nevertheless has a significant effect on elastic wave propagation at specific frequencies. Periodic subwavelength elastic scatterers positioned on a reflective plane are considered in this paper. Firstly an explicit formula of quasi-periodic Green's function of Lam\'{e} system with Dirichlet boundary condition is derived for the first time. The subsequent discussion is twofold. In the first part where the shear modulus of scatterers is assumed to tend to infinity, the subwavelength resonance frequencies are given and approximated field inside inclusions and far-away from metascreen are calculated to demonstrate the dramatic change of scattered field due to subwavelength resonance. In the second part where the shear modulus of background is assumed to go to infinity, the absence of subwavelength resonance is proved. Without imposing conditions on the material parameters, the discussion in this paper provides the necessary condition for the occurrence of subwavelength resonance.

math.AP↗

arXiv2022

A novel quantitative inverse scattering scheme using interior resonant modes

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown obstacle from the far-field data via the indicating behaviour of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme of Newton's type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton's iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the Newton's formula involves the geometric quantities of the unknown boundary surface in a natural way. We provide rigorous theoretical justifications of the proposed method. Numerical experiments in both 2D and 3D are conducted, which confirm the promising features of the proposed imaging scheme. In particular, it can produce quantitative reconstructions of high accuracy in a very efficient manner.

math.NA↗

arXiv2021

Invisibility enables super-visibility in electromagnetic imaging

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.

math.AP↗

arXiv2020

Surface-localized transmission eigenstates, super-resolution imaging and pseudo surface plasmon modes

We present the discovery of a novel and intriguing global geometric structure of the (interior) transmission eigenfunctions associated with the Helmholtz system. It is shown in generic scenarios that there always exists a sequence of transmission eigenfunctions with the corresponding eigenvalues going to infinity such that those eigenfunctions are localized around the boundary of the domain. We provide a comprehensive and rigorous justification in the case within the radial geometry, whereas for the non-radial case, we conduct extensive numerical experiments to quantitatively verify the localizing behaviours. The discovery provides a new perspective on wave localization. As significant applications, we develop a novel inverse scattering scheme that can produce super-resolution imaging effects and propose a method of generating the so-called pseudo surface plasmon resonant (PSPR) modes with a potential sensing application.

math.AP↗