A High-Order Accurate Algorithm for Electrostatics of Overlapping Disks

A fast and accurate algorithm for the computation of effective electric and mathematically equivalent properties of composites with nonsmooth interfaces is reported. The algorithm is based on an integral equation reformulation of the electrostatic partial differential equation and a fast hierarchical technique for potential field evaluation. In a numerical example, 200 large and strongly inhomogeneous aggregates of randomly overlapping disks are solved with a relative error of 0.0005.     

Polarization tomography of residual stress in monocrystals of YAG

An algorithm for determining the thermal stress in round cylindrical monocrystals by means of the integral photoelasticity method is analyzed. Transillumination in a cross section of a sample is assumed. The optical problem is solved within the framework of the paraxial approximation assuming weak birefringence. Reconstruction is based on the measurement of characteristic parameters of the polarized light propagated through the sample.     

Determination of unsteady heat release distribution from acoustic pressure measurements: a reformulation of the inverse problem

An integral method is developed to solve the inverse problem of determining the oscillatory heat release distribution from the knowledge of the acoustic pressure field within a combustor. Unlike earlier approaches, in which the problem is formulated in terms of Fredholm integral equation, the inverse problem is reformulated in terms of Volterra integral equation. This reformulation, valid for low Mach numbers (M2 < 1), facilitates the recovery of heat release at all frequencies. The resulting Volterra integral equation is solved using both direct numerical method and implicit least-squares method. The results show that the implicit least-squares method is superior to the direct numerical method and yields accurate determination of heat release at all frequencies.     

A novel stochastic collocation method for uncertainty propagation in complex mechanical systems

This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions’ statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it’s a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.     

Determination of the Coefficient of Light Absorption via Transformation of a Pulse in a Disperse Medium

We suggested and substantiated an algorithm for solving the inverse problem of determining the coefficient of absorption of light for the case of a disperse medium (body) V from the known time scans of the powers (fluxes) of radiation. The algorithm is based on strict integral relations and is applied when the coefficient of scattering, scattering indicatrix, and the optical dimensions of the body V are unknown. Using the properties of the solutions of direct boundary-value problems of radiation transfer theory and statistical modeling, the efficiency of the algorithm for disperse media of various configurations is shown.     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

三自由度二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法

用扩展Prelle-Singer法(扩展P-S法)求三自由度二阶非线性耦合动力学系统的守恒量,得到了6个积分乘子满足的确定方程、约束方程和守恒量的一般形式,并讨论了确定积分乘子的方法.最后,用扩展P-S法求得了三质点Tada晶格问题的两个守恒量.     

Improved transmission conditions for a one-dimensional domain decomposition method applied to the solution of the Helmholtz equation

The scattering problem of a time-harmonic electromagnetic wave from a perfect electric conductor (PEC) coated with materials is considered, and solved by coupling a finite element method with an integral equation prescribed on the outer boundary of the computational domain. To reduce the numerical complexity, a one-dimensional domain decomposition method (DDM) is employed: the computational domain is partitioned into concentric subdomains (SDs), and Robin transmission conditions (TCs) are prescribed on the interfaces. For some configurations and/or materials, the convergence of the corresponding DDM algorithm happens to be slow. A possible remedy is to enhance the efficiency of the TCs by approximating the exact ones more accurately. To this end, we first consider the simplified 2D problem of a circular PEC cylinder with an homogeneous coating and up to four SDs with circular interfaces, thus allowing to obtain the exact TCs in closed-form. Approximate local or non-local TCs are derived from these exact ones, and numerical examples demonstrate their superiority over the standard Robin TCs. Then, the case of an elliptical PEC cylinder with one interface in free-space is investigated. Also, the issues pertaining to the uniqueness of the solutions and convergence of the algorithm are addressed.     

基于改进确定采样型滤波的疲劳裂纹扩展预测

针对确定性采样滤波在进行状态估计预测时随维数增加时出现计算量增加且精度不高的问题,提出一种确定采样型滤波的算法并将其应用到疲劳裂纹扩展预测当中去。首先,阐述了确定采样型滤波器的基本原理;其次,从多维数值积分的角度出发,引入完全对称积分公式,根据不变容积法则选取容积节点作为基础采样点,计算积分节点、节点个数和权重;最后,将改进后的确定采样型滤波器应用到构件疲劳裂纹损伤扩展中去,并与无迹卡尔曼滤波算法、容积卡尔曼滤波算法进行比较,提升了裂纹扩展预测的精度,仿真分析验证了该方法的可行性和有效性。     

Depolarization of the electromagnetic field scattered by a three-dimensional large-scale irregularity of the lower ionosphere

This paper develops analytical and numerical methods for the solution of three-dimensional problems of radio wave propagation. We consider a three-dimensional vector problem for the electromagnetic field of a vertical electric dipole in a planar Earth-ionosphere waveguide with a largescale local irregularity of negative characteristics at the anisotropic ionospheric boundary. The field components at the boundary surfaces obey the Leontovich boundary conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr≫1, where r is the distance from the source or receiver to the nearest point of the irregularity, k=2π/λ, and λ is the radio wavelength) integration over the direction perpendicular to the ray path, we transform this system to one-dimensional integral equations where integration contours represent the geometric contour of the irregularity. The system is numerically solved in the diagonal approximation, combining direct inversion of the Volterra integral operator and subsequent iterations. The proposed numerical algorithm reduces the computer time required for the solution of this problem and is applicable for studying both small-scale and large-scale irregularities. We obtained novel estimates for the field components that are not excited by the source but result entirely from scattering by the sample three-dimensional ionospheric irregularity.     

Comparison of asynchronous particle swarm optimization and dynamic differential evolution for partially immersed conductor

The application of two techniques for the of shape reconstruction of a perfectly two-dimensional conducting cylinder from mimic measurement data is studied in the present paper. After an integral formulation, the microwave imaging is recast as a nonlinear optimization problem; a cost function is defined by the norm of a difference between the measured scattered electric fields and the calculated scattered fields for an estimated shape of a conductor. Thus, the shape of conductor can be obtained by minimizing the cost function. In order to solve this inverse scattering problem, transverse electric (TE) waves are incident upon the objects and two techniques are employed to solve these problems. The first is based on an asynchronous particle swarm optimization (APSO) and the second is a dynamic differential evolution (DDE). Both techniques have been tested in the case of simulated mimic measurement data contaminated by additive white Gaussian noise. Numerical results indicate that the DDE algorithm and the APSO have almost the same reconstructed accuracy.     

A variational approach to the reconstruction of galactic peculiar velocities

A variational method for determining the peculiar velocities of galaxies using a catalog of their positions and masses is suggested. The method is based on an approximate reconstruction of the dynamical history of the patch of the Universe covered by the catalog through the optimization of a suitable integral action functional and is an improvement on the method of the Monge-Kantorovich mass transportation problem developed in [1].     

用于电介质中空间电荷分布测量的Tikhonov反卷积算法

研究了使用压力波法测量平板电介质试样的空间电荷分布的数值解法,使用基于Tikhonov正则化方法的反卷积算法得到了真实的空间电荷分布.在反卷积算法中使用了相关的技术处理,如小波包过滤高频噪音,Tikhonov正则化方法处理积分方程等.利用数值实验研究了噪声对反卷积算法的影响,结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出电介质中的空间电荷分布;在处理有噪数据时,反卷积的结果受到明显的影响,但仍然有较高的计算精度.正则化参数α对空间电荷分布的数值解起着明显的光滑作用,但是对于解的积分值却影响不大.对实际测量数据进行处理的结果表明,反卷积算法成功地计算出了固体电介质中的空间电荷分布和电场分布.     

Structure of the electric field in the skin-effect problem

The structure of the electric field in a metal has been elucidated for the skin-effect problem. It is demonstrated that the electric field is the sum of the integral term and two (or one) exponentially decreasing particular solutions to the initial system and that one particular solution disappears depending on the anomality parameter. An expression for the distribution function profile in the half-space and at the metal boundary is obtained in the explicit form. The absolute value, the real part, and the imaginary part of the electric filed are analyzed in the case of the anomalous skin effect.     

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao–Wilton–Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.     

Vibrations of an elastic strip with a rough boundary

A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method.     

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model.     

Improved optimization strategies for autofocusing motion compensation in MRI via the analysis of image metric maps

Autofocusing is a postprocessing technique for motion correction, which optimizes an image quality metric against various trial motions. In this work, image metric maps, which are measures of image quality plotted as a function of in-plane 2-D trial translations, are systematically studied to develop improved autofocusing motion correction algorithms. It is shown that determining object motion with autofocusing is equivalent to an image metric map optimization problem. These maps provide insights into the motion compensation process and help improve several aspects of the correction algorithm, including the selection of the image metric and motion search strategy. A highly efficient and robust 2-D global optimization method is devised, exploiting the properties of the metric map pattern. The improved algorithm is used to correct phantom and clinical MR images with in-plane 2-D translational motion and is shown to be more effective than existing methods.     

Algorithm of parameters correction for solving the inverse problem of Mössbauer spectroscopy

An algorithm for correcting parameters in the kernel of an integral equation is proposed. This problem appears in particular in the estimation of the distribution of a hyperfine parameter from Mössbauer spectra. The problem is solved within the framework of Tikhonov variational method. The computational scheme and experimental example are presented.