Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.     

Determination of the Parameters of the Equivalent Two-Pole Circuit for an Electric Discharge Induced by Voltage Pulses

An algorithm (method) of determining the parameters of the two-pole equivalent electric circuit for an electric discharge is described in the present paper. The algorithm (method) is based on a solution of the ill-posed inverse problem of determining a kernel of the Duhamel integral for the first-order Fredholm integral equation. The fast Fourier transform (FFT) algorithm used to solve this problem reduces significantly the execution time of the algorithm. Examples of solving model problems for first- and second-order electric equivalent circuits are presented which demonstrate the universality and efficiency of the suggested algorithm.     

非稳腔傍轴波动方程高斯球面波修正方法的数值研究

在分析用差分方法求解虚共焦非稳腔三维傍轴波动方程,及用数值积分方法与快速付氏变换(FFT)方法求解三维菲涅耳积分方程优缺点的基础上,从激光束在虚共焦非稳腔中以修正高斯球面波形式传输的特征出发,经坐标变换把发散(或会聚)的光束拉直成平行光束,然后用FFT方法求解了在新坐标系中修正函数满足的傍轴波动方程.把相同条件下得到的结果与国内外文献给出的结果进行了比较;计算COIL实验非稳腔给出的近远场结果图象合理正确.     

A quantum search algorithm of two entangled registers to realize quantum discrete Fouriertransform of signal processing

The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT （1D QDFT） and two-dimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.     

Improved diagonal tensor approximation (DTA) and hybrid DTA/BCGS-FFT method for accurate simulation of 3D inhomogeneous objects in layered media

This paper presents an improved diagonal tensor approximation (DTA) and its hybridization with the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm to solve a volume integral equation for three-dimensional (3D) objects in layered media. The improvement in DTA is obtained for lossy media through a higher-order approximation. The interaction between the dyadic Green's function and the contrast source is efficiently evaluated by the (FFT) algorithm through the convolution and correlation theorems. For the hybrid implementation, the DTA solution is used as an initial estimate and a preconditioner in the BCGS-FFT algorithm in order to solve the forwards modelling problem accurately with fewer iterations than the conventional BCGS-FFT algorithm. The accuracy and convergence of the DTA, BCGS-FFT and hybrid DTA/BCGS-FFT methods are compared extensively with several numerical examples. Numerical results show that (a) the improved DTA formulation enhances the accuracy and (b) the DTA/BCGS-FFT method can produce results as accurate as the conventional BCGS-FFT but with fewer iterations if the contrast is moderate. For very high contrasts, the hybrid method does not seem to improve further on the BCGS-FFT iteration convergence.     

复化辛普森法和傅里叶法在衍射计算上的比较

通过快速傅里叶变换(FFT)法和复化辛普森法对衍射的数值进行计算,可以看出快速傅里叶变换法是一种积分变换法,而复化辛普森法则是迭代相加的方法.通过计算得出了FFT法的计算速度高于复化辛普森法,计算精度则远低于复化辛普森法;复化辛普森法适合近距离菲涅尔衍射和近场衍射,而FFT法不适合.     

Fast reconstruction of multiple off-axis holograms based on a combination of complex encoding and digital spatial multiplexing

An algorithm is proposed for the fast reconstruction of off-axis digital holograms based on a combination of complex encoding(CE) and spatial multiplexing(SM). In this algorithm, every two off-axis holograms recorded in sequence are first assembled into a CE hologram using the CE method, and then four of the CE holograms are again encoded into one complex spatial multiplexing(CSM) hologram based on the SM algorithm. It is demonstrated that the eight holograms encoded into such one CSM hologram can be quickly reconstructed by performing a two-dimensional(2D) Fourier transform(FT) on the CSM hologram. Using this method, the eight 2D FTs required for the reconstruction of the eight holograms in the conventional spatial filtering methods can be simplified to a process with only one 2D FT, which can largely improve the computation efficiency with the     

求解分数傅里叶变换衍射积分的一种快速算法

在对Lohmann 二型分数傅里叶变换(FRT)和菲涅耳衍射积分进行比较的基础上,给出基于快速傅里叶变换(FFT)求解该分数傅里叶变换和菲涅耳衍射积分的快速算法及算法适用范围.数值模拟实验证明了理论的可靠性和算法的高效性.此快速算法为分数傅里叶变换在工程实际中的进一步广泛应用奠定了基础.     

Cochlear macromechanics: time domain solutions.

In this paper we report on a new method of solving a previous derived, two-dimensional model, integral equation for basilar membrane (BM) motion. The method uses a recursive algorithm for the solution of an initial-value problem in the time domain, combined with a fast Fourier transform (FFT) convolution in the space domain at each time step. Thus, the method capitalizes on the high speed and accuracy of the FFT yet allows the BM to have nonlinear mechanical properties. Using the new method we compute (linear) solutions for various choices of model parameters and compare the results to the experimental measurements of Rhode. [J. Acoust. Soc. Am. 49, 1218-1231 (1971)]. We also demonstrate the effect of including longitudinal stiffness along the BM and conclude that it is useful in matching the high-frequency slope as measured by Rhode.     

光学图像加密与多参数加权类分数傅里叶变换

为了提高图像加密的安全性, 提出了一种多参数加权类分数傅里叶变换。此类多参数加权类分数傅里叶变换是C.C.Shih提出的四项加权类分数傅里叶变换的一种扩展, 除了分数阶数, 还有四个在四项加权系数之中的自由参数, 称其为向量参数。同时给出此多参数加权类分数傅里叶变换的离散形式, 并把这种算法应用到光学图像加密中。此算法在应用一次二维分数傅里叶变换可以有十个密键：一类为阶数参数; 另一类为向量参数, 因此这种加密算法在增加了安全性的同时, 加密过程的复杂度降低。数值仿真验证了此算法的有效性和可靠性。     

一种高效的高合成数快速Fourier变换算法

本文概述了快速Fourier变换(FFT)的基本方法,着重讨论了高合成数FFT旋转因子算法。试验表明,由此编制的程序计算速度快、通用性强,具有实用价值。     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

A geometric nonuniform fast Fourier transform

An efficient algorithm is presented for the computation of Fourier coefficients of piecewise-polynomial densities on flat geometric objects in arbitrary dimension and codimension. Applications range from standard nonuniform FFTs of scattered point data, through line and surface potentials in two and three dimensions, to volumetric transforms in three dimensions. Input densities are smoothed with a B-spline kernel, sampled on a uniform grid, and transformed by a standard FFT, and the resulting coefficients are unsmoothed by division. Any specified accuracy can be achieved, and numerical experiments demonstrate the efficiency of the algorithm for a gallery of realistic examples.     

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.     

The radiation impedance of a rectangular piston

The radiation impedance of a rectangular piston is expressed as the Fourier transform of its impulse response, which is obtained from the recent work of Lindermann [1]. The analytical evaluation of the transform is performed and new integral expressions are presented for both the radiation resistance and reactance. The integrals are readily evaluated in terms of elementary functions at both the low and high frequency limits. The integrals are also expressed as series of Bessel functions which are valid for all frequencies and aspect ratios. Numerical results are presented to illustrate the behavior of the radiation resistance and reactance as a function of the aspect ratio of the piston and a normalized frequency parameter. Additional numerical results are then presented to illustrate the accuracy of the analytical expressions for the radiation resistance and reactance at low and high frequencies. Finally, numerical results are presented to illustrate the application and accuracy of using standard FFT algorithms to evaluate the radiation resistance and reactance directly from the impulse responses.     

Exact solution of three-dimensional acoustic field in a wedge with perfectly reflecting boundaries

An exact approach is presented to compute the three-dimensional(3D) acoustic field in a homogeneous wedge-shaped ocean with perfectly reflecting boundaries. This approach applies the Fourier synthesis technique, which reduces a 3D point-source ideal wedge problem into a sequence of two-dimensional(2D) line-source ideal wedge problems, whose analytical solution is well established. A comparison of numerical efficiency is provided between this solution and the solution proposed by Buckingham,which is obtained by a sequence of integral transforms. The details of numerical implementation of these two solutions are also given. To validate the present approach and at the same time compare numerical efficiency between this approach and Buckingham's analytical solution, two numerical examples are considered. One is the Acoustical Society of America(ASA) benchmark wedge problem and the other is a wide-angle wedge problem. Numerical results indicate that the present approach is efficient and capable of providing accurate 3D acoustic field results for arbitrary receiver locations, and hence can serve as a benchmark model for sound propagation in a homogeneous wedge-shaped ocean.     

基于小波的多极化机载合成孔径雷达海面风向反演

为了实现从合成孔径雷达(SAR)图像本身提取高精度的海面风向信息, 提高SAR海面风场反演精度,研究了多极化机载SAR海面风向反演技术, 借助小波分析相对傅里叶分析和局部梯度更精细的时-频分析能力, 将二维连续小波变换与快速傅里叶变换(FFT)相结合,提出一种新的机载SAR海面风向反演方法. 为验证反演方法的有效性,通过海上同步飞行试验获取多极化机载SAR数据及同步调查船实测风向数据,用于反演试验的数据比对.采用本文提出的方法, 利用多种小波基对机载C波段SAR的同极化和交叉极化数据进行风向反演, 将反演结果与美国国家环境预报中心再分析资料以及调查船实测风向进行比对. 结果表明,本文提出的基于小波分析的海面风向反演方法适用于机载SAR探测数据, 反演精度优于二维FFT法和局部梯度方法;小波基的选择对反演结果影响较大, Mexican-Hat小波基是机载SAR海面风向反演的最优小波基, 且同极化与交叉极化机载SAR数据均可用于海面风向的反演.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given.The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane,or a rotation and stretching transformation of the Wigner distribution function space.A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms.The algorithm,by which a good evaluation can be achieved,unifies the calculations of Fresnel diffraction,arbitrary fractionalorder Fourier transforms and other scalar diffraction systems.The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform,the Fresnel transform,the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm.The calculated results are in good agreement with the analytical results,both in the amplitude and phase.