Scattering Problems Research Articles

Investigation and Methods for Solving Problems of Scattering of Electromagnetic Waves on Three-Dimensional Anisotropic Dielectric Structures

Investigation and Methods for Solving Problems of Scattering of Electromagnetic Waves on Three-Dimensional Anisotropic Dielectric Structures

Investigation and Methods for Solving Problems of Scattering of Electromagnetic Waves on Three-Dimensional Anisotropic Dielectric Structures

The problems of scattering of electromagnetic waves by anisotropic dielectric structures are studied on the basis of volumetric singular integral equations. Existence and uniqueness theorems for solutions are given for a wide class of media, including lossless media. An efficient method for solving integral equations based on the collocation method and fast discrete Fourier transform algorithms is described.

A Novel Deep Neural Network Algorithm for the Helmholtz Scattering Problem In the Unbounded Domain

A Novel Deep Neural Network Algorithm for the Helmholtz Scattering Problem In the Unbounded Domain

Wideband Sherman–Morrison–Woodbury Formula-Based Algorithm for Electromagnetic Scattering Problems

In this paper, a wideband Sherman-Morrison-Woodbury formula-based algorithm (WSMWA) is proposed to efficiently compute the wideband and wide-angle electromagnetic scattering problems. In the proposed algorithm, the standard adaptive cross approximation (ACA) decomposition is only performed at the highest frequency of the frequency band of interest to find the dominant basis functions for each far-block pair. Then, at any frequency within the entire frequency band, the approximate compression of the impedance matrix can be efficiently constructed by using the impedance interpolation method with the dominant basis functions selected at the highest frequency. As a result, the WSMWA avoids performing the standard ACA repeatedly and saves a lot of computational time in comparison with the conventional Sherman-Morrison-Woodbury formula-based algorithm (SMWA) for wideband and wide-angle applications. Numerical results for electromagnetic scattering are given to demonstrate the efficiency and accuracy of the proposed algorithm.

Application of the Generalized Method of Eigenoscillations to the Solution of the Problems of Scattering on Nanostructures

We study the problem of scattering of electromagnetic waves on small-sized dielectric bodies by using the generalized method of eigenoscillations. The inhomogeneous problem is formulated on the basis of a version of the generalized method of eigenoscillations in which the dielectric permittivity plays the role of an eigenvalue. The corresponding homogeneous problem is solved with the use of Debye potentials. We obtain a system of linear algebraic equations for the unknown expansion coefficients. For the solution of this system, we use the method of successive approximations. The results of the performed numerical analyses confirm the efficiency of the proposed method.

Hybrid Method for Inverse Elastic Obstacle Scattering Problems

The problem of determining the shape of an object from knowledge of the far-field of a single incident wave in two-dimensional elasticity was considered. We applied an iterative hybrid method to tackle this problem. An advantage of this method is that it does not need a forward solver, and therefore, the exact boundary condition is not essential. By deriving the Fréchet derivatives of two boundary operators, we established reconstruction algorithms for objects with Dirichlet, Neumann, and Robin boundary conditions; by introducing a general boundary condition, we also established the reconstruction algorithm for objects with unknown physical properties. Numerical experiments showed the effectiveness of the proposed method.

Constructive Solution to Inverse Scattering Problem for Differential Systems with a Singularity

Constructive Solution to Inverse Scattering Problem for Differential Systems with a Singularity

Physics-Informed Supervised Residual Learning for 2-D Inverse Scattering Problems

In this communication, we propose a new physics-constrained approach to solve 2-D inverse scattering problems (ISPs) by extending physics-informed supervised residual learning (PhiSRL) with Born approximation (BA). By embedding the fixed-point iteration method in residual neural network (ResNet), PhiSRL aims to solve ISPs iteratively by applying the convolutional neural networks (CNNs) to learn the update rules of reconstructions. PhiSRL is employed to invert lossy scatterers by introducing BA to linearize ISPs and further reduce the computational burden of forward modeling. Both numerical and experimental results validate the effectiveness of the proposed approach.

Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition

Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition

Bayesian Method for Inverse Scattering Problem of Interior Cavity with Phaseless Data

This paper is concerned with the inverse acoustic scattering problem of a sound soft cavity based on phaseless near-field data. By combining the reference circle technique with the Bayesian method, this paper presents a numerical algorithm to retrieve the shape of the interior cavity from phaseless data. In this paper, the well-posedness of the Bayesian method is discussed. The posterior distribution of the shape parameters is obtained by DRAM algorithm and the reconstruction of the cavity boundary is acquired by taking the average value of the posterior distribution.

Solving Electromagnetic Inverse Scattering Problems in Inhomogeneous Media by Deep Convolutional Encoder–Decoder Structure

This communication proposes a novel deep learning (DL) approach to solve electromagnetic inverse scattering (EMIS) problems in inhomogeneous media. The conventional approaches for solving inhomogeneous EMIS problems generally have to consider inhomogeneous Green’s functions or conduct approximation operations to media, which inevitably introduces various challenges, including complex mathematical derivation, high computation cost, unavoidable nonlinearity, and even strong ill-posedness. To avoid these challenges, we propose a DL approach based on the complex-valued deep convolutional neural networks (DConvNets), which comprise the deep convolutional encoder–decoder (DCED) structure. Its training data are collected based on the simple synthetic dataset. While the scattered fields received in the measurement domain are utilized as the input for the encoder to extract feature fragments, the final output for the counterpart decoder is the contrasts (permittivities) of dielectric scatterers in the target domain. In this way, unlike the conventional methods, the unknown domain between the target domain and measurement domain never has to be considered to compute inhomogeneous Green’s functions. Consequently, the inhomogeneous EMIS problems could be solved with higher accuracy even for extremely high-contrast targets. Numerical examples illustrate the feasibility of the proposed DL approach. It acts as a new candidate for solving EMIS problems in inhomogeneous media.

Theoretic Study of Antenna Scattering Problems Based on Characteristic Modes and its Applications in Reducing Antenna Scattering

A new antenna scattering theory based on characteristic modes (AST-CMs) is proposed to analyze the antenna scattering mechanism and guide the design of antenna scattering reduction in this article. A specific set of modal electric fields, which of an antenna loaded with a short circuit, is used to express the structure mode and antenna mode scattering fields of the antenna with arbitrary loads. The contribution of each characteristic mode to the structure mode and antenna mode scattering fields can be clearly analyzed, which efficiently guides the antenna scattering reduction under the incident plane waves with arbitrary propagation direction and polarization. A typical microstrip antenna is given as an example to validate the proposed AST-CM. The radar cross section (RCS) of the microstrip antenna calculated by AST-CM agrees well with the result simulated by commercial simulation software Altair FEKO. Moreover, the design procedure based on AST-CM is used to guide the in- band RCS reduction of the microstrip antenna under both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${y}$ </tex-math></inline-formula> -polarized normally incident plane waves. Compared with the reference antenna, the proposed antenna achieves a notable RCS reduction in its operation band with the radiation performance well preserved. The proposed low-RCS antenna is fabricated and measured, and the experimental results are in good agreement with the numerical simulated results.

A Study on Characteristic Mode Equations of Radiation Problems Contrasted with Scattering Problems for Dielectric Bodies

This paper is concerned with the extractions of electromagnetic characteristic modes (CMs) for lossless dielectric bodies, for which spurious modes are prone to generate using the traditional definition of CMs based on the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) equations. It is found that the impedance matrix of PMCHWT equations cannot distinguish (i) which domain is the dielectric body and which domain is the background and (ii) from which domain the excitation source was applied. If the system is taken as a scattering problem, the spurious modes are solutions to a reverse media problem, i.e., exchanging the media of the dielectric body and the background space. However, if the system is taken as a radiation problem, no appropriate CMs that meet the specified boundary conditions are obtained. These phenomena indicate that CMs developed from scattering systems are not suitable for radiation systems. To clarify the issue, four cases with reverse media and with excitation sources in either domain are examined. The four cases are distinct in essence, but the PMCHWT equations cannot distinguish them. As a result, definitions of CMs for the four cases should be given along with their specific boundary conditions. Especially, the CMs for the radiation problems we consider here show that the excitation source inside the material object should be properly defined in order to be distinguished from scattering problems.

The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials

The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

Neural Born Iterative Method for Solving Inverse Scattering Problems: 2D Cases

In this article, we propose the neural Born iterative method (NeuralBIM) for solving 2-D inverse scattering problems (ISPs) by drawing on the scheme of the physics-informed supervised residual learning (PhiSRL) to emulate the computing process of the traditional Born iterative method (TBIM). NeuralBIM uses independent convolutional neural networks (CNNs) to learn the alternate update rules of two different candidate solutions regarding the residuals. Two different schemes are presented in this article, including the supervised and unsupervised learning schemes. With the dataset generated by the method of moments (MoM), supervised NeuralBIM is trained with the knowledge of the total fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded objective function founding on the governing equations of ISPs, which results in no requirement of the total fields and contrasts for training. Numerical and experimental results further validate the efficacy of NeuralBIM.

Solving Inverse Scattering Problem with a Crack in Inhomogeneous Medium Based on a Convolutional Neural Network

The direct and inverse scattering problems are a type of classical problem with symmetry. Numerical methods combined with machine learning are continuously being developed, and obtain good results in obstacle inversion problems. In this paper, we consider a crack shape with asymmetry; such problems are often ill-posed and nonlinear. Focusing on the inhomogeneous medium and limited-aperture far-field data, we propose a new sequence-to-sequence asymmetric convolutional neural network for recovering a crack via correlative far-field measurements. Taking the far-field data as the input and the shape parameters of a crack as the output, the features are quickly extracted using the convolutional and pooling layers. The Adam optimization algorithm is employed to update the weights and offsets of the neural network. Numerical experiments show that the proposed method can quickly and effectively reconstruct the shape of the crack.

Principal Component Analysis Accelerated the Iterative Convergence of the Characteristic Mode Basis Function Method for Analyzing Electromagnetic Scattering Problems

Principal Component Analysis Accelerated the Iterative Convergence of the Characteristic Mode Basis Function Method for Analyzing Electromagnetic Scattering Problems

Uncertainty Calibrations of Deep-Learning Schemes for Full-Wave Inverse Scattering Problems

Uncertainty Calibrations of Deep-Learning Schemes for Full-Wave Inverse Scattering Problems

From the Ray Approximation to the Exact Method of Random Rays for Wave Scattering Problems

From the Ray Approximation to the Exact Method of Random Rays for Wave Scattering Problems