An efficient surrogate-based method for computing rare failure probability

In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966–8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation—it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10⁻¹² ∼ 10⁻⁶ with only several hundreds samples.     

Design of ultra wideband microwave absorber effectual for objects of arbitrary shape

In this paper, we present the design of multilayer microwave absorbers comprised of Co Fe alloy nano-particles and nano-flakes as fillers. The thickness of the unite layer is optimized by using the Genetic Algorithm. Efficient microwave absorptions over a wide frequency band and a range of incident angles are achieved by using multilayer absorbers. We show that the absorbers are effective not only for a planar surface but also for arbitrarily shaped objects as well.     

An efficient method for computing atmospheric radiances in clear-sky and cloudy conditions

A computationally efficient method is developed to simulate the radiances in a scattering and absorbing atmosphere along an arbitrary path in the spectral region ranging from visible to far-infrared with a spectral resolution of 1 cm⁻¹. For a given spectral region, the method is based on fitting radiances pre-calculated from the discrete ordinate radiative transfer (DISORT) at several wavenumbers. Radiances at other wavenumbers are interpolated based on the pre-computed total absorption and scattering optical thicknesses and the surface albedo. The computational efficiency and accuracy of the method are tested in comparison with rigorous simulations for various scenarios under the same conditions. For both clear-sky and cloud atmospheres, the present method is at least 140 times faster than the direct application of DISORT. Across the spectral range, the standard relative differences between the new method and the DISORT are less than 2% for clear-sky conditions. Root-mean-square (RMS) differences of the top of the atmosphere (TOA) brightness temperatures between the new method and DISORT, for atmospheric infrared sounder (AIRS) channels over clear-sky, ice cloudy and water cloudy skies, are within the noise equivalent differential temperature (NEDT) of the AIRS sensor. The fast method is also applied to simulations of the spectral downwelling radiance measured by the Fourier transform infrared (FTIR) interferometer, and to the simulations of the AIRS upwelling radiances under clear-sky and cloudy conditions.     

An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher–Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.     

An efficient method of distinguishing chaos from noise

It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochastic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.     

Cutoff frequencies in planar optical waveguides with arbitrary index profiles: An efficient numerical method

A numerical method for obtaining mode cutoffs for planar waveguides with arbitrary index profiles is developed. The method is based on the Galerkin method in which the wave equation for modes at cutoff is converted to a matrix eigenvalue equation using a set of orthogonal basis functions. Due to different boundary conditions, we have identified two separate cases; one, in which the cover and the substrate indices are identical leading to same behavior of the field at cutoff in these two regions and, the other, in which the two indices are different and hence, the field behaves differently. We have accordingly chosen different basis functions for the two cases. The method results in a generalized matrix eigenvalue problem which has been converted to a standard symmetric matrix eigenvalue analytically. The method has been used to obtain mode cutoffs for waveguides with a variety of index profiles. Comparisons with available exact results show that very good accuracies can be obtained with moderate matrix sizes.     

Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.     

修正一阶Born近似改进水中弱散射目标的散射声场预报

在推导Fourier衍射定理中运用一阶Born近似时忽略了弱散射体内外的波数差异,使散射声场方向特性的预报产生较大误差,针对这一问题,对一阶Born近似进行修正。考虑散射体内外波数差异引起的幅度和相位误差,通过调整频域采样圆弧半径并移动圆心位置得到了修正的一阶Born近似解。由于更准确地反映了目标与周围水介质的声学性质,有效提高了散射声场的预报精度。根据修正的Born近似计算了弱散射条件下无限长圆柱目标的散射远场指向性,结果与严格解相吻合,对其它形状截面的柱状目标也得到了合理的计算结果。     

The R-function method for the free vibration analysis of thin orthotropic plates of arbitrary shape

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method. The proposed method is based on the use of the R-function theory and variational methods. In contrast to the widely used methods of the network type (finite differences, finite element, and boundary element methods), in the R-function method all the geometric information given in the boundary value problem statement is represented in an analytical form. This allows one to seek a solution in a form of some formulas called a solution structure. These solution structures contain some indefinite functional components that can be determined by using any variational method. A method of constructing the solution structures satisfying the required mixed boundary conditions for eigenvalue plate bending problems is described. Numerical examples for the vibration analysis of orthotropic plates of complex geometry with mixed boundary conditions for illustrating the aforementioned R-function method and comparison against the other methods are made to demonstrate its merits.     

An improved computing method for the image edge detection

The framework of detecting the image edge based on the sub-pixel multi-fractal measure (SPMM) is presented. The measure is defined, which gives the sub-pixel local distribution of the image gradient. The more precise singularity exponent of every pixel can be obtained by performing the SPMM analysis on the image. Using the singularity exponents and the multi-fractal spectrum of the image, the image can be segmented into a series of sets with different singularity exponents, thus the image edge can be detected automatically and easily. The simulation results show that the SPMM has higher quality factor in the image edge detection.     

层析法计算三维物体全息图的并行加速研究

随着计算空间光调制器的分辨率的尺寸逐渐变大，全息图三维动态显示的计算量也越来越大，使得对全息计算速度提出了新的要求。利用GPU并行计算处理的方式实现全息图的快速层析法计算，该方法利用GPU并行多线程和层析法中的图像二维傅里叶变换的优势对菲涅尔衍射变换算法加速计算；同时通过对GPU底层资源的调用和对CUDA中程序的流处理过程，有效减少中间的延时等待。通过对计算速度对比分析表明:与在CPU上运算相比，计算速度大幅提升，基于GPU并行计算的方法比基于CPU计算的方法速度快10倍左右。     

Transverse vibration of membranes of arbitrary shape by the method of constant-deflection contours

A method for approximate computation of the fundamental frequency of membranes of arbitrary shape vibrating harmonically is developed. The method is based upon the concept of contour lines of equal deflection on the surface of the membrane. A similar method for elastic plates has recently been developed by the author in a series of papers. As illustrations of the procedure, the method is applied to the calculation of the gravest mode of an annular, an elliptic, and a parabolic membrane.     

An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plates

In this paper, a new differential quadrature (DQ) methodology is employed to study free vibration of irregular quadrilateral straight-sided thin plates. A four-nodded super element is used to map the irregular physical domain into a square domain in the computational domain. Second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains. The only degree of freedom within the domain is the displacement, whereas along the boundaries, the displacement as well as the second order derivative of the displacement with respect to associated normal co-ordinate variable in computational domain are the two degrees of freedom. Implementing the method, the formulation for the DQ method for the free vibration analysis of plates of straight-sided shapes was presented together with the implementation procedure for the different boundary conditions. To demonstrate the accuracy, convergency and stability of the new methodology, detail studies are made on isotropic plates at acute angles with different geometries, boundary and loading conditions including DQ free-edge boundary condition implementations. Accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved.     

A vector raytracing equation for hologram lenses of arbitrary shape

A single vector equation is given, including the effect of wavelength change, for tracing rays in the geometrical optics approximation.     

An efficient shooting method for fiber amplifiers and lasers

A simple shooting method is proposed for the design of distributed multi-pumped Raman fiber amplifiers (RFAs) and Yb-doped double-clad fiber lasers (DCFLs). Using the proposed method a distributed RFA with 10 pump sources and 1700 mW total input pump power is simulated and high-power Yb-doped DCFL rate equations are solved numerically. The numerical simulation results show that the proposed method has good convergence in the condition of increasing numbers and power of input pump sources.     

An efficient method for solving highly anisotropic elliptic equations

Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterized by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest derivative in one direction is much larger than the terms in the remaining directions, the discretized elliptic operator often has a very large condition number – taking the solution even further out of reach using traditional methods. This paper will demonstrate a solution method for such ill-behaved problems. The high condition number of the D-dimensional discretized elliptic operator will be exploited to split the problem into a series of well-behaved one and (D − 1)-dimensional elliptic problems. This solution technique can be used alone on sufficiently coarse grids, or in conjunction with standard iterative methods, such as Conjugate Gradient, to substantially reduce the number of iterations needed to solve the problem to a specified accuracy. The solution is formulated analytically for a generic anisotropic problem using arbitrary coordinates, hopefully bringing this method into the scope of a wide variety of applications.     

An efficient numerical method for time-dependent NLTE radiation transfer

We present a numerical method for performing coupled time-dependent radiation transfer and atomic rate equation calculations. The method incorporates the desirable features of time-dependent, non-local thermodynamic equilibrium (NLTE) radiation transfer calculations. It has the advantage that it allows existing time-dependent calculations to be adapted to model time dependent effects. The approximations which are used are discussed.Calculations have been performed for a highly ionised silicon plasma with a single optically thick line. The line is taken to have a top-hat profile which is independent of position. Although the model is simple, it serves to illustrate some important features of time-dependent calculations.     

An efficient Jacobian scaling method for time-domain optical mammography

<正>Time-domain diffuse optical tomography can efficiently reconstruct optical parameters which can be further applied in diagnosing early breast cancer.Nevertheless,the performances of reconstructed imaging are badly influenced by different Jacobian magnitudes of absorption coefficient and reduced scattering coefficient.With the introudction of a relative data type based on generalized pulse spectrum technique, an efficient Jacobian scaling method is proposed.The interrelated simulated validation is also revealed for the enhancing performances.     

Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.