Haiwen Zhang

Haiwen Zhang
Chinese Academy of Sciences | CAS · Academy of Mathematics and Systems Science

PhD

About

37
Publications
3,625
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411
Citations
Introduction
Additional affiliations
May 2015 - present
Chinese Academy of Sciences
Position
  • Professor (Assistant)

Publications

Publications (37)
Preprint
This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data corresponding to infinitely many incident plane waves with distinct directions at a fixed frequency. Our proof is ba...
Preprint
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We consider the numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nystr\"{o}m method is proposed for the scattering problem based on the integral equation method. Convergence of the Nystr\"{o}m method is established with convergence rate depending on th...
Article
This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work (2018,SIAM J. Appl. Math. 78, 3024–3039), by adding a known reference ball into the acoustic scattering system, it was proved that the impenetrable obstacle and the index of refraction of an inhom...
Preprint
Full-text available
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is that the translation invariance property of the modulus of the far field pattern is unavoidable, which is simila...
Article
In this paper, we consider the inverse acoustic scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surfaces from scattered-field data for incident plane waves and the performance analysis is also presented. The reconstruction method is very robust to noises of measured data and does’t need...
Preprint
Full-text available
This paper is concerned with the inverse acoustic scattering problem with phaseless near-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the unknown scatterer from the phaseless near-field data generated by incident plane waves at a fixed frequency and measu...
Preprint
Full-text available
This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work [{\em SIAM J. Appl. Math.} {\bf 78} (2018), 3024-3039], by adding a known reference ball into the acoustic scattering system, it was proved that the impenetrable obstacle and the index of refracti...
Preprint
Full-text available
This paper is concerned with uniqueness results in inverse acoustic and electromagnetic scattering problems with phaseless total-field data at a fixed frequency. Motivated by our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), where uniqueness results were proved for inverse acoustic scattering with phaseless far-field data gener...
Preprint
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This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is proposed for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the...
Article
Full-text available
This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locall...
Article
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface in a half plane. The elastic scattered field is measured within a finite distance above the rough surface. A...
Preprint
Full-text available
Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex inhomogeneous medium from the far-field data. Numerical examples are also provided to illustrate the practicabi...
Preprint
Full-text available
This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locall...
Article
Full-text available
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that t...
Preprint
Full-text available
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the far-field operator we proved for the first time that the obstacle and the index of refraction of an inhomogeneous...
Preprint
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that t...
Article
Full-text available
This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered near-field Cauchy data generated by point sources. A Helmholtz-Kirchhoff-type identity is derived and then used to...
Article
Full-text available
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface in a half plane. The elastic scattered field is measured on a horizontal straight line segment within a finit...
Article
Full-text available
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and measured on a horizontal straight line segment at a finite distance above the rough surface. Theoretical analysis of...
Article
Full-text available
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work [SIAM J. Appl. Math., 78 (2018), pp. 1737–1753], by utilizing spectral properties of the far-field operator we proved for the first time that the obstacle and the index of refraction of an inhomogeneous med...
Article
Full-text available
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern generated by one plane wave as the incident field. Based on our previous work (J. Comput. Phys. 345 (2...
Article
Full-text available
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location of the obstacle can be recovered from the phaseless far-field data. In this paper, it is proved that the transl...
Article
Full-text available
This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration algorithm in frequencies is developed to reconstruct the locally rough surface from multi-frequency intensity-only...
Article
Full-text available
In this paper we establish a factorization method for recovering the location and shape of an acoustic bounded obstacle with using the near-field data, corresponding to infinitely many incident point sources. The obstacle is allowed to be an impenetrable scatterer of sound-soft, sound-hard or impedance type or a penetrable scatterer. An outgoing-to...
Article
Full-text available
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic plane waves from a complex obstacle in the sense that a so-called generalized impedance boundary condition (GIBC) is satisfied on the boundary of the obstacle. The factorization method is established to reconstruct the complex obstacle from the far-field data a...
Article
Full-text available
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by bounded, inhomogeneous, penetrable obstacles in a homogeneous background medium. A new method is proposed to prove the unique determination of the penetrable, inhomogeneous obstacle from the far-field pattern for all incident plane wa...
Article
Full-text available
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle with buried objects inside. We prove under certain conditions that the factorization method can be applied to reconstruct the penetrable obstacle from far-field data without knowing the buried objects inside. Numeri...
Article
Full-text available
This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting o...
Article
Full-text available
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. A main...

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