Fast numerical method for electromagnetic scattering from an object above a large-scale layered rough surface at large incident angle: vertical polarization

A fast numerical method has been proposed in this paper for calculating the electromagnetic scattering from a perfectly electric conducting object above a two-layered dielectric rough surface. The focus in this study is large incidence. The parallel fast multipole method is combined with the method of moments for fast implementation of the scattering from this composite model. The biconjugate gradient method is adopted to solve the unsymmetrical matrix equation and parallelized. The simulating time and parallel speedup ratio with different processors are provided. Several numerical results are shown and analyzed to discuss the influences of the parameters of the rough surface, the object, and the intermediate medium on the bistatic scattering.     

Fast method to compute scattering by a buried object under a randomly rough surface: PILE combined with FB-SA

A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.     

An efficient method for electromagnetic scattering analysis

We present a novel method to solve the magnetic field integral equation (MFIE) using the method of moments (MoM) efficiently. This method employs a linear combination of the divergence-conforming Rao-Wilton-Glisson (RWG) function and the curl-conforming n×RWG function to test the MFIE in MoM. The discretization process and the relationship of this new testing function with the previously employed RWG and n×RWG testing functions are presented. Numerical results of radar cross section (RCS) data for objects with sharp edges and corners show that accuracy of the MFIE can be improved significantly through the use of the new testing functions. At the same time, only the commonly used RWG basis functions are needed for this method.     

Fast spectral-domain method for acoustic scattering problems

This paper presents the application of the conjugate-gradient (CG) fast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFT (CG-NUFFT) method for the integral equation arising from acoustic scattering problems. In the conventional method of moments (MoM) for integral equations, the CPU and memory requirements are O(N³) and O(N²), respectively, where N is the number of unknowns in the problem. The CG-FFT method, which combines the iterative conjugate-gradient method with FFT, reduces these requirements to O(KN log₂N) and O(N), respectively, where K is the number of CG iterations. The CG-NUFFT method differs from the CG-FFT method in that it makes use of nonuniform FFT algorithms instead of FFT to allow a nonuniform discretization. Therefore, the CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method. These two methods are applied to solve for two-dimensional constant density acoustic scattering problems. Numerical. results demonstrate that they can solve much larger problems than the MoM     

A fast numerical method for analysis of one- and two-dimensional electromagnetic scattering using a set of cardinal functions

Since many problems in one- and two-dimensional scattering from perfectly conducting bodies can be modeled by linear Fredholm integral equations, the main focus of this paper is to present a fast numerical method for solving them. The method uses Whittaker cardinal functions as a set of basis functions. By using the properties of these cardinal functions together with an appropriate quadrature rule, the computational cost of the method becomes low and the calculations are done quickly. This is due to the fact that the method uses just sampling of functions instead of integration. To show computational efficiency of this approach, some practical one- and two-dimensional scatterers are analyzed by it and the results are compared with those of two other numerical methods.     

A numerical method for determining electromagnetic fields in cracked metals

We improve the numerical algorithm of the solution of a three-dimensional hypersingular integral equation of first kind based on the collocation method. The efficiency of the developed approach is shown. We also give some numerical results and their interpretation. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 85–93, March–April, 2007.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part I. Stochastic interface models

A theoretical model for ultrasonic wave scattering by geometrically irregular and imperfectly bonded interfaces is presented. In Part I, the normal stiffness of interfaces formed by the partial contact of solids with rough surfaces is estimated for two models of contacting surfaces with random roughness in one dimension only. The first model considers nonconforming surfaces with a single-scale of roughness, while double-scale roughness characterizes the surfaces of the second model, which are conforming at the large scale and nonconforming at the smaller scale. The surfaces' profiles are described by Gaussian probability and spectral densities. The surfaces at each contact are modeled by two cylinders under a compressive load and the normal stiffness per unit area of the interface is evaluated by averaging the stiffness of all the contacts, assuming they do not interact with each other. It is shown that the smaller the roughness, the softer the interface; the larger the autocorrelation length, the softer the interface; and the smaller the initial aperture, the stiffer the interface. Furthermore, interfaces described by the second model appear much stiffer than those described by the first model. The interface characterizations and normal stiffness models developed in Part I will be used in Part II to study the scattering of ultrasonic plane waves by such an interface.     

A numerical reconstruction method in inverse elastic scattering

In this paper a new numerical method for the shape reconstruction of obstacles in elastic scattering is proposed. Initially, the direct scattering problem for a rigid body and the mathematical setting for the corresponding inverse one are presented. Inverse uniqueness issues for the general case of mixed boundary conditions on the boundary of our obstacle, which are valid for a rigid body as well are established. The inversion algorithm based on the factorization method is presented into a suitable form and a new numerical scheme for the reconstruction of the shape of the scatterer, using far-field measurements, is given. In particular, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) and its linchpin within the framework of the factorization method is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples involving a kite, an acorn, and a peanut-shaped object.     

Light scattering by randomly rough isotropic dielectric surfaces

Abstract

An experimental investigation of the angular distribution of the light scattered by randomly rough, two-dimensional, isotropic dielectric surfaces is presented. The surfaces, whose profiles constitute good approximations to Gaussian random processes with Gaussian correlation functions, are fabricated in a photoresist and characterized by means of a mechanical profilometer. The substrates employed in the fabrication of the samples consist of thick parallel plates of filter glass that absorb the incident light and whose refractive index is close to that of the photoresist. This allows us to approximate experimentally a situation in which the light is scattered by a randomly rough interface between two semi-infinite dielectric media, illuminated from the air side. The results display features that can be attributed to multiple scattering. In particular, significant amounts of cross-polarized scattered light, as well as an enhanced backscattering peak, were observed in the scattering measurements.     

Coherent scattering by one-dimensional randomly rough metallic surfaces

A critical evaluation of various theoretical techniques for calculating the reflectivity of one-dimensional metallic randomly rough surfaces is presented. We proceed by comparing experimental and rigorous numerical results with those obtained with three perturbation theories and the Kirchhoff approximation. The samples were fabricated in photoresist, and their metallized surface profiles constitute good approximations to Gaussian-correlated, Gaussian random processes. The correlation lengths of these surfaces range from approximately one third to approximately three times the infrared wavelengths employed. The results show that the phase-perturbation theory has wider applicability than the other perturbation theories and the results based on the Kirchhoff approximation.     

Reducing computational costs using a multi-region finite element method for electromagnetic scattering

Electromagnetic scattering problems involving multiple scatterers can be solved by the finite element method using a single domain truncated with an absorbing boundary condition, but often it is more efficient to separate the single domain into several subdomains, separated by free-space, and to solve the set of subdomains iteratively. This multi-region method has been reported in the literature. Its relative computational cost is investigated and formulas for determining are provided when it is advantageous to use a multi-region against a single-region method.     

Design method of the layered active magnetic regenerator (AMR) for hydrogen liquefaction by numerical simulation

The design procedure of an active magnetic regenerator (AMR) operating between liquid nitrogen temperature and liquid hydrogen temperature is discussed with the selected magnetic refrigerants. Selected magnetic refrigerants (GdNi₂, Dy_0.85Er_0.15Al₂, Dy_0.5Er_0.5Al₂, and Gd_0.1Dy_0.9Ni₂) that have different transition temperatures are layered in an AMR to widen the temperature span. The optimum volume fraction of the layered refrigerants for the maximum COP with minimum volume is designed in a two-stage active magnetic regenerative refrigerator (AMRR) using one dimensional numerical simulation. The entropy generation in each stage of the AMR is calculated by the numerical simulation to optimize the proposed design. The main sources of the entropy generation in the AMR are pressure drop, convection and conduction heat transfers in the AMR. However, the entropy generation by the convective heat transfer is mostly dominant in the optimized cases. In this paper, the design parameters and the operating conditions such as the distribution of the selected refrigerants in the layered AMR, the intermediate temperature between two stages and the mass flow rate of heat transfer fluid are specifically determined to maximize the performance of the AMR. The proposed design method will facilitate the construction of AMR systems with various magnetic refrigerants and conditions such as AMR size, operating temperature range, and magnetic field variation.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

An efficient numerical method for modelling initiation and propagation of cracks along material interfaces

A numerical method, based on the multiregion concept in the boundary element method, is presented for modelling crack propagation. The advantage of the method is that the non-linear iterations only involve interface degrees of freedom and that the propagation of cracks is modelled by disconnecting degrees of freedom and no remeshing is necessary.     

Computations of the Mueller matrix elements for scattering from layered structures with rough surfaces, with applications to optical detection

A full-wave method is used to evaluate the Mueller matrix elements for scattering from layered structures with random rough surfaces. These provide a database for applications in optical detection over a broad range of rough surface statistical parameters. They can be used to determine the optimal frequencies and incident angles that provide most reliable measurements for optical detection. The elements of the Mueller matrix that are most sensitive to medium parameters of the layered structures can also be identified. Contributions from individual terms of the full-wave solutions are shown to have distinct physical interpretations.     

Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem

This paper investigates the signal-subspace method approach to solve the electromagnetic inverse scattering problem using intensity-only (phase-free) data. Due to the polarization of electromagnetic fields, the relationship between the rank of the multistatic matrix and the number of small scatterers is different from that associated with the scalar wave. Multiple scattering between scatterers is considered, and the inverse scattering problem of determining the polarization tensors is nonlinear, which, however, is solved by the proposed analytical approach where no associated forward problem is iteratively evaluated.     

A differential-equation method for the computation of the electromagnetic scattering by an inhomogeneity in a cylindrical waveguide

Summary In this paper an exact method is described for computing numerically the scattering by an inhomogeneity in a cylindrical waveguide. The Generalized Telegraphist's Equations are used to transform the electromagnetic-field equations into a system of ordinary differential equations. The latter system behaves numerically unstable. A method is given to cope with this difficulty. Numerical results are presented for two- and three-dimensional obstacles in a waveguide of rectangular cross-section and they are compared with those obtained by other methods. Our method requires, in general, a relatively small amount of computation time and storage capacity. Another advantage of the method is its flexibility.     

Quasi-three-dimensional method of moments for analyzing electromagnetic wave scattering in microwave tomography systems

A new quasi-three-dimensional method of moments (Quasi-3-D MoM) for analyzing electromagnetic wave scattering from a cylindrical dielectric object surrounded by a dipole array in microwave tomography systems is presented in this paper. A wire-volumetric electric field integral equation is derived for the electromagnetic wave scattering phenomena in microwave tomography systems. The new method is based on the MoM and involves rectangular cylindrical cells modeling the cylindrical object. The distribution of electric flux densities along the axial direction of cylindrical cells is expanded as a Fourier series multiplied by an attenuation factor, which is one part of basis functions. Therefore, the Quasi-3-D MoM is performed in a two-dimensional discretization, and the computational complexity is reduced. Detailed mathematical steps along with some numerical results are presented to illustrate the efficacy and accuracy of this approach.     

基于微分求积法及V-变换的大规模动力系统快速数值计算方法

针对大规模动力系统动态响应的数值计算,传统的微分求积法通常在时间域上逐步离散、整体求解,存在“维数灾”问题。在多级高阶时域微分求积法的基础上,提出了基于V-变换的大规模动力系统动态响应的快速数值计算方法。利用微分求积法的加权系数矩阵满足V-变换这一重要特性,将离散后的雅可比矩阵方程进行解耦分块,推导形成了多级分块递推计算方法。数值算例表明,即使采用相当于Newmark方法2s倍的步长,微分求积法的计算精度仍比Newmark方法要高出2~3个数量级。进一步对3个不同规模的算例系统进行了测试,结果表明：相对于传统的数值计算方法,多级分块递推计算方法可以获得较大的加速比,能够显著提高大规模动力系统动态响应的计算效率。     

Development of numerical phantoms by MRI for RF electromagnetic dosimetry: a female model

Numerical human models for electromagnetic dosimetry are commonly obtained by segmentation of CT or MRI images and complex permittivity values are ascribed to each issue according to literature values. The aim of this study is to provide an alternative semi-automatic method by which non-segmented images, obtained by a MRI tomographer, can be automatically related to the complex permittivity values through two frequency dependent transfer functions. In this way permittivity and conductivity vary with continuity--even in the same tissue--reflecting the intrinsic realistic spatial dispersion of such parameters. A female human model impinged by a plane wave is tested using finite-difference time-domain algorithm and the results of the total body and layer-averaged specific absorption rate are reported.