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Bo Zhang - One of the best experts on this subject based on the ideXlab platform.

  • uniqueness in inverse Electromagnetic Scattering Problem with phaseless far field data at a fixed frequency
    Ima Journal of Applied Mathematics, 2020
    Co-Authors: Bo Zhang, Haiwen Zhang
    Abstract:

    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 refraction of an inhomogeneous medium can be uniquely determined by the acoustic phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency. In this paper, we extend these uniqueness results to the inverse Electromagnetic Scattering case. The phaseless far-field data are the modulus of the tangential component in the orientations $\mathbf{e}_\phi$ and $\mathbf{e}_\theta$, respectively, of the electric far-field pattern measured on the unit sphere and generated by infinitely many sets of superpositions of two Electromagnetic plane waves with different directions and polarizations. Our proof is mainly based on Rellich's lemma and the Stratton--Chu formula for radiating solutions to the Maxwell equations.

  • an inverse Electromagnetic Scattering Problem for a bi periodic inhomogeneous layer on a perfectly conducting plate
    Applicable Analysis, 2011
    Co-Authors: Jiaqing Yang, Bo Zhang
    Abstract:

    This article is concerned with uniqueness for reconstructing a periodic inhomogeneous medium sitting on a perfectly conducting plate. We deal with the Problem in the framework of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation is obtained for two refractive indices and then used to prove that the refractive index can be uniquely identified from a knowledge of the incident fields and the total tangential electric field on a plane above the inhomogeneous medium, utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm–Liouville eigenvalue Problem.

  • the inverse Electromagnetic Scattering Problem in a piecewise homogeneous medium
    Inverse Problems, 2010
    Co-Authors: Xiaodong Liu, Bo Zhang, Jiaqing Yang
    Abstract:

    This paper is concerned with the Problem of Scattering of time-harmonic Electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct Problem is established, employing the integral equation method. In Liu and Zhang (2009 Appl. Anal. 88 1339–55) it was proved, under the condition that the wave numbers in the innermost and outermost homogeneous layers coincide and S0 is known in advance, that the obstacle with its physical property can be uniquely determined from knowledge of the electric far-field pattern for incident plane waves. In this paper, we will remove this restriction by establishing a new mixed reciprocity relation. Furthermore, inspired by Hahner's idea in Hahner (1993 Inverse Problems 9 667–78), we prove that the penetrable interface between layers can also be uniquely determined.

  • a uniqueness result for the inverse Electromagnetic Scattering Problem in a two layered medium
    Inverse Problems, 2010
    Co-Authors: Xiaodong Liu, Bo Zhang
    Abstract:

    This paper is concerned with the inverse Problem of Scattering of time-harmonic Electromagnetic waves by an impenetrable obstacle buried in the lower half-space of a two-layered background medium. We prove that the buried obstacle and its physical property can be uniquely determined from a knowledge of the tangential component of the electric field on some two-dimensional device in the upper half-space corresponding to all incident electric dipoles located on another two-dimensional device in the upper half-space with two different polarizations. The key ingredient of our proof is a novel reciprocity relation established in this paper for the solution of the Scattering Problem of the electric dipole located at two different source points.

  • an inverse Electromagnetic Scattering Problem for a bi periodic inhomogeneous layer on a perfectly conducting plate
    arXiv: Analysis of PDEs, 2010
    Co-Authors: Jiaqing Yang, Bo Zhang
    Abstract:

    This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the Problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation for two refractive indices is obtained, and then inspired by Kirsch's idea, the refractive index can be identified by utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm-Liouville eigenvalue Problem.

Jiaqing Yang - One of the best experts on this subject based on the ideXlab platform.

  • an inverse Electromagnetic Scattering Problem for a bi periodic inhomogeneous layer on a perfectly conducting plate
    Applicable Analysis, 2011
    Co-Authors: Jiaqing Yang, Bo Zhang
    Abstract:

    This article is concerned with uniqueness for reconstructing a periodic inhomogeneous medium sitting on a perfectly conducting plate. We deal with the Problem in the framework of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation is obtained for two refractive indices and then used to prove that the refractive index can be uniquely identified from a knowledge of the incident fields and the total tangential electric field on a plane above the inhomogeneous medium, utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm–Liouville eigenvalue Problem.

  • the inverse Electromagnetic Scattering Problem in a piecewise homogeneous medium
    Inverse Problems, 2010
    Co-Authors: Xiaodong Liu, Bo Zhang, Jiaqing Yang
    Abstract:

    This paper is concerned with the Problem of Scattering of time-harmonic Electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct Problem is established, employing the integral equation method. In Liu and Zhang (2009 Appl. Anal. 88 1339–55) it was proved, under the condition that the wave numbers in the innermost and outermost homogeneous layers coincide and S0 is known in advance, that the obstacle with its physical property can be uniquely determined from knowledge of the electric far-field pattern for incident plane waves. In this paper, we will remove this restriction by establishing a new mixed reciprocity relation. Furthermore, inspired by Hahner's idea in Hahner (1993 Inverse Problems 9 667–78), we prove that the penetrable interface between layers can also be uniquely determined.

  • an inverse Electromagnetic Scattering Problem for a bi periodic inhomogeneous layer on a perfectly conducting plate
    arXiv: Analysis of PDEs, 2010
    Co-Authors: Jiaqing Yang, Bo Zhang
    Abstract:

    This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the Problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation for two refractive indices is obtained, and then inspired by Kirsch's idea, the refractive index can be identified by utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm-Liouville eigenvalue Problem.

  • the inverse Electromagnetic Scattering Problem in a piecewise homogeneous medium
    arXiv: Analysis of PDEs, 2010
    Co-Authors: Xiaodong Liu, Bo Zhang, Jiaqing Yang
    Abstract:

    This paper is concerned with the Problem of Scattering of time-harmonic Electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct Problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].

Yixian Gao - One of the best experts on this subject based on the ideXlab platform.

  • analysis of time domain Electromagnetic Scattering Problem by multiple cavities
    Acta Mathematicae Applicatae Sinica, 2020
    Co-Authors: Yang Liu, Yixian Gao
    Abstract:

    The time-domain multiple cavity Scattering Problem, which arises in diverse scientific areas, has significant industrial and military applications. The multiple cavities, embedded in an infinite ground plane, is filled with inhomogeneous media characterized by variable dielectric permittivities and magnetic permeabilities. Corresponding to the transverse electric, the Scattering Problem can be studied by the Helmholtz equation in frequency domain and wave equation in time-domain respectively. A novel transparent boundary condition in time-domain is developed to reformulate the cavity Scattering Problem into an initial-boundary value Problem in a bounded domain. The well-posedness and stability of the reduced Problem are established. Moreover, a priori energy estimates for the electric field is obtained with minimum regularity requirement for the data and an explicit dependence on the time by studying the wave equation directly.

  • analysis of time domain Electromagnetic Scattering Problem by multiple cavities
    arXiv: Analysis of PDEs, 2019
    Co-Authors: Yang Liu, Yixian Gao
    Abstract:

    Consider the time-domain multiple cavity Scattering Problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with inhomogeneous media characterized by variable dielectric permittivities and magnetic permeabilities. Corresponding to the transverse electric or magnetic polarization, the Scattering Problem can be studied for the Helmholtz equation in frequency domain and wave equation in time-domain, respectively. A novel transparent boundary condition in time-domain is developed to reformulate the cavity Scattering Problem into an initial-boundary value Problem in a bounded domain. The well-posedness and stability are established for the reduced Problem. Moreover, a priori estimates for the electric field is obtained with a minimum requirement for the data by directly studying the wave equation.

  • Electromagnetic Scattering for time domain maxwell s equations in an unbounded structure
    Mathematical Models and Methods in Applied Sciences, 2017
    Co-Authors: Yixian Gao
    Abstract:

    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 initial-boundary value Problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced Problem. Our proof is based on the method of energy, the Lax–Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.

Jun Zou - One of the best experts on this subject based on the ideXlab platform.

  • unique continuation from a generalized impedance edge corner for maxwell s system and applications to inverse Problems
    arXiv: Analysis of PDEs, 2020
    Co-Authors: Huaian Diao, Hongyu Liu, Long Zhang, Jun Zou
    Abstract:

    We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite non-identically vanishing variable function. We establish an accurate relationship between the vanishing order of the solutions to the Maxwell system and the dihedral angle of the edge-corner. In particular, if the angle is irrational, the vanishing order is infinity, i.e. strong unique continuation holds from the edge-corner. The establishment of those new quantitative results involve a highly intricate and subtle algebraic argument. The unique continuation study is strongly motivated by our study of a longstanding inverse Electromagnetic Scattering Problem. As a significant application, we derive several novel unique identifiability results in determining a polyhedral obstacle as well as it surface impedance by a single far-field measurement. We also discuss another potential and interesting application of our result in the inverse Scattering theory related to the information encoding.

  • analysis on block diagonal and triangular preconditioners for a pml system of an Electromagnetic Scattering Problem
    Computers & Mathematics With Applications, 2017
    Co-Authors: Na Huang, Jun Zou
    Abstract:

    Abstract We shall propose several block triangular preconditioners for a PML system of an Electromagnetic wave Scattering Problem and analyze the spectral behavior of the preconditioned systems. When the PML system is discretized by edge element methods, it results in a discrete system with its stiffness matrix being complex, symmetric but indefinite, which can be formulated into a real symmetric but indefinite saddle-point system. In order to preserve the symmetry of the coefficient matrix, we present block triangular preconditioners with two-sided preconditioning for the discrete PML system. We will estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. On the other hand, one may also like to apply some iteration methods for nonsymmetric linear systems in applications although the discrete systems are symmetric. To this end, we propose a block triangular preconditioner to precondition the systems only from one side and analyze the spectrum of the preconditioned systems. In addition, we have also established a spectral estimate of the preconditioned system by an effective preconditioner that was recently developed in literature. Numerical experiments are presented to demonstrate the effectiveness and robustness of these new preconditioners and our theoretical predictions on the spectral bounds of the preconditioned systems.

  • an effective preconditioner for a pml system for Electromagnetic Scattering Problem
    Mathematical Modelling and Numerical Analysis, 2015
    Co-Authors: Chunmei Liu, Shi Shu, Jun Zou
    Abstract:

    In this work we are concerned with an efficient numerical solution of a perfectly matched layer (PML) system for a Maxwell Scattering Problem. The PML system is discretized by the edge finite element method, resulting in a symmetric but indefinite complex algebraic system. When the real and imaginary parts are considered independently, the complex algebraic system can be further transformed into a real generalized saddle-point system with some special structure. Based on an crucial observation to its Schur complement, we construct a symmetric and positive definite block diagonal preconditioner for the saddle-point system. Numerical experiments are presented to demonstrate the effectiveness and robustness of the new preconditioner.

Leonidas Mindrinos - One of the best experts on this subject based on the ideXlab platform.

  • the direct Electromagnetic Scattering Problem by a piecewise constant inhomogeneous cylinder at oblique incidence
    arXiv: Analysis of PDEs, 2020
    Co-Authors: Drossos Gintides, Sotiris Giogiakas, Leonidas Mindrinos
    Abstract:

    We consider the solvability of the direct Scattering Problem of an obliquely incident time-harmonic Electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness of the solution using properties of the boundary value operators and the integral equation method. For the numerical solution, we apply a collocation method and we approximate the singular integral operators using quadrature rules. We show convergence of the numerical scheme for the interior and the scattered fields both in the near- and far-field regime.

  • the Electromagnetic Scattering Problem by a cylindrical doubly connected domain at oblique incidence the direct Problem
    Ima Journal of Applied Mathematics, 2019
    Co-Authors: Leonidas Mindrinos
    Abstract:

    We consider the direct Electromagnetic Scattering Problem of time-harmonic obliquely incident waves by a infinitely long, homogeneous and doubly-connected cylinder in three dimensions. We apply a hybrid integral equation method (combination of the direct and indirect methods) and we transform the Scattering Problem to a system of singular and hypersingular integral equations. The well-posedness of the corresponding Problem is proven. We use trigonometric polynomial approximations and we solve the system of the discretized integral operators by a collocation method.

  • the inverse Electromagnetic Scattering Problem by a penetrable cylinder at oblique incidence
    Applicable Analysis, 2019
    Co-Authors: Drossos Gintides, Leonidas Mindrinos
    Abstract:

    In this work, we consider the method of non-linear boundary integral equation for solving numerically the inverse Scattering Problem of obliquely incident Electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We consider the indirect method and simple representations for the electric and the magnetic fields in order to derive a system of five integral equations, four on the boundary of the cylinder and one on the unit circle where we measure the far-field pattern of the scattered wave. We solve the system iteratively by linearizing only the far-field equation. Numerical results illustrate the feasibility of the proposed scheme.