Efficient method for solving the problems of wave diffraction by scatterers with broken boundaries

The pattern equations method is extended to solving the problems of wave scattering by bodies with piecewise smooth boundaries. The method is based on the reduction of the initial boundary-value problem to an integro-operator equation of the second kind in the scattering pattern of a body. With the use of the series expansion of the scattering pattern in angular spherical harmonics, the problem is ultimately reduced to solving an infinite algebraic system of equations in the expansion coefficients of the scattering pattern. The conditions at which this system can be solved by the method of reduction are formulated. Examples of solving the problems of wave scattering by bodies with impedance boundaries are considered. Essential advantages of the proposed method over other known methods are demonstrated.     

Solving the diffraction problem of electromagnetic waves on objects with a complex geometry by the pattern equations method

A new efficient method for solving the problems of waves diffraction on complex-shaped objects with the use of their replacement by a group of bodies with more simple form (fragments of complex objects) is offered. By the expansion of the scattering patterns of separate bodies in the series of vector spherical harmonics, the problem is reduced to solving the algebraic system of equations. It is shown that the method possesses a high convergence rate. Examples of modeling the scattering patterns of various complex objects are considered. Reliability of the results obtained is validated using the Optical theorem.     

Solving of problems of electromagnetic waves scattering by complex-shaped dielectric bodies via the pattern equations method

An efficient method is proposed for solving the problem of diffraction on complex-shaped dielectric bodies with the use of their replacement by a group of bodies with more simple form (fragments of complex objects). The initial problem is reduced to a system of algebraic equations by expanding the scattering patterns in vector angular spherical harmonics. It is shown that the method offers a high rate of convergence that weakly depends on the distances between the bodies. Examples of modeling the scattering characteristics of complex-shaped bodies are considered.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

The application of a modified method of discrete sources for solving the problem of wave scattering by group of bodies

A new universal and effective algorithm for solving the problems of wave diffraction on complicated structures composed of bodies of revolution is presented. The method is applied to diffraction on a group made of two impedance bodies of revolution. The method permits to get the pattern and the field with high accuracy.     

Scattering of E and H polarized waves from covered cylindrical structures

A modification of the method of discrete sources (MMDS) is applied for solving 2D scattering problems by metal (or dielectric) cylindrical structure covered with a dielectric layer. The scattering of E (or H) polarized incident plane and cylindrical wave was considered. The problems of accuracy, choosing auxiliary contours and impedance approximation in scattering problem are discussed.     

Analysis of diffraction of a plane wave on a grating consisting of impedance bodies of revolution

The problem of wave scattering by a grating consisting of coaxial impedance bodies of revolution is solved. The efficient numerical algorithm based on the modified null field method is offered. The method is applied both to scalar and vector formulations of the problem. The numerical results are obtained for various geometries of the grating elements.     

Electromagnetic wave scattering by small bodies

A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the characteristic size of the bodies tends to zero. The technique developed is used for solving the many-body EM wave scattering problem by rigorously reducing it to solving linear algebraic systems, completely bypassing the usage of integral equations. An equation is derived for the effective field in the medium, in which many small particles are embedded. A method for creating a desired refraction coefficient is outlined.     

轴对称体声振耦合的边界子波谱与有限元耦合方法

探讨了子波在Helmholtz积分方程及声振耦合中的应用,在建立了求解轴对称Helmholtz积分方程的子波谱方法的基础上,构造了轴对称子波谱与轴对称有限元的耦合方法,该方法可以处理轴对称问题的任意边界条件.进行了声振耦合问题的模态分析.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

介质涂覆位置对双S弯排气系统电磁散射特性影响研究

尾喷管作为飞行器后向强散射源之一, 可通过特殊结构设计和介质涂覆缩减其雷达散射截面(RCS). 本文采用迭代物理光学法和阻抗边界条件的混合计算模型, 研究了6种涂覆方案和不涂覆时双S弯排气系统的电磁散射特性, 采用所提出的射线行程追踪方法提高了几何消隐计算效率, 利用前后向迭代方法加速收敛并采用openMP和MPI并行技术缩短计算时间, 获得了在X波段下7种模型的RCS随探测角度的变化规律. 研究结果表明, 介质涂覆能够有效抑制双S弯排气系统的RCS; 合理的介质涂覆方案不仅具有明显的抑制效果, 同时又具有经济性好、重量轻及涂覆方便等优势; 相比全涂覆方案, 仅在喷管出口附近涂覆的方案, 可减少73.6%的涂覆材料, 且其RCS的最大增幅不超过15.6%, 相比未涂覆方案, RCS 至少降低18.5%. 同时所开发的计算程序可用于任意腔体电磁散射特性的计算, 可为带介质涂覆腔体试验提供技术支撑.     

On solving coupled equations for scattering problems under the many channel and short wavelength conditions of heavy ion collisions

An iterative method for solving coupled equations in scattering problems is presented. Radical wave functions are expressed in terms of amplitudes on regular and outgoing components. This is analogous to the semi-quantal approach and gives many of its convenient features for heavy ion collisions. One solves directly for the scattering matrix without generating a complete set of solutions. The amplitudes are smoothly varying compared to the total wave functions. The iteration is non-perturbative, as each step contains the interaction to all orders. The convergence improves as the wavelength of relative motion decreases. In the short wavelength limit only one iteration is required.     

Numerical analysis of electromagnetic wave diffraction on a three-dimensional magnetodielectric body

A variant of the method of discrete sources suitable for solving problems of electromagnetic wave scattering on three-dimensional magnetodielectric bodies having a smooth surface of arbitrary shape is suggested and realized. A computer program implementing the suggested variant is briefly described. Some results of numerical calculations that illustrate the opportunities of the method are presented. Special attention is given to a study of the influence of deviations of the body shape from axisymmetric one on the bistatic scattering cross sections. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 50–57, October, 2005.     

Spectral-energy characteristics of sound fields scattered by fine-structured inhomogeneities of sound velocity into the geometrical shadow zone

In analyzing experimental results obtained with explosive sources in the tropical zone of the Indian Ocean, a good agreement was obtained for spectral-energy characteristics of signals observed in the first geometrical shadow zone with computer calculations of the sound field scattered by fine structure inhomogeneities of the fractal type. From the comparison of the results of calculating the frequency characteristics of sound fields in the shadow zone by the wave code and by the method combining ray acoustics with the wave theory of sound scattering, it was found that both methods are appropriate for describing the real processes of scattering and propagation of sound in the ocean with fine-structured stratification and that these methods can be used for solving inverse problems.     

Enhanced plane wave expansion analysis for the band structure of bulk modes in two-dimensional high-contrast solid–solid phononic crystals

Plane wave expansion analyses that use the inverse rule to obtain the Fourier coefficients of the elastic tensor instead of the more conventional Laurent's rule, exhibit faster convergence rates for solid–solid phononic crystals. In this work, the band structure convergence of calculations using the inverse rule is investigated and applied to the case of high acoustic impedance contrast solid–solid phononic crystals, previously known for convergence difficulties. Results are contrasted to those obtained with the conventional plane wave expansion method. The inverse rule is found to converge at a much rate for all ranges of impedance contrast, and the ratio between the computational times needed to obtain a convergent band structure for a high-contrast solid–solid phononic crystal with the conventional plane wave expansion method using 1369 reciprocal lattice vectors is as large as 6800:1. This ratio decreases for material sets with lower impedance contrast; however, the inverse rule is still faster for a given error threshold for even the lowest impedance contrast phononic crystals reported in the literature. This convergence enhancement is a major factor in reconsidering the plane wave expansion method as an important tool in obtaining propagating elastic modes in phononic crystals.     

Scattering characteristics of conducting cylinder coated with nonuniform magnetized ferrite

An analytical technique, referred to as the scattering matrix method （SMM）, is developed to analyse the scattering of a planar wave from a conductolution for the nonuniform fering cylinder coated with nonuniform magnetized ferrite. The SMM srite coating can be reduced to the expressions for the scattering and penetrated coefficients in four particular cases： nonuniform magnetized ferrite cylinder, uniform magnetized ferrite-coated conducting cylinder, uniform ferrite cylinder as well as homogeneous dielectric-coated conducting cylinder. The resonant condition for the nonuniform ferrite coating is obtained. The distinctive differences in scattering between the nonuniform ferrite coating and the nonuniform dielectric coating are demonstrated. The effects of applied magnetic fields and wave frequencies on the scattering characteristics for two types of the linear profiles are revealed.     

A new version of the modified method of discrete sources in application to the problem of diffraction by a body of revolution

A new version of the modified method of discrete sources is proposed for solving the scalar problem of diffraction by an impedance body of revolution. The proposed approach allows the construction of effective algorithms that solve the aforementioned problem for bodies of revolution of different shapes, including the scatterers with broken boundaries. Numerical results are presented for bodies with different geometries and the high accuracy of the results is demonstrated.     

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

Scattering of electromagnetic waves by a perfectly conducting body with a chiral coating

We propose a numerical method for solving problems of electromagnetic scattering in the resonance spectrum of frequencies by a 3D ideally conducting arbitrary-shaped body covered by a homogeneous chiral coating. A program package for calculating the characteristics of the scattered field and checking the accuracy of the obtained solution based on the above method is described briefly. Some results of numerical calculations are given, which are useful for a study of the influence of “chirality” on the scattering properties of absorbing coatings. Siberian Physical-and-Technical Institute at Tomsk State University, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 4, pp. 495–506, April, 1998.     

Numerical Simulation of Plasma Antenna with FDTD Method

We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the chaxacteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconfigurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design.