基于GPU集群的Level Set并行高精度演化

设计实现基于张量积B样条的并行Level Set演化算法,张量积B样条提高了演化精度和并行度;每步演化都需要反算B样条系数.针对对角占优三对角方程组,设计实现基于精确LU分解的高精度并行追赶法,并用它反算B样条系数;采用两步通信方法,消除通信的依赖关系,实现有效的并行通信.实验表明,本文的并行算法可以有效加速演化过程.     

A multi-phase level set framework for source reconstruction in bioluminescence tomography

We propose a novel multi-phase level set algorithm for solving the inverse problem of bioluminescence tomography. The distribution of unknown interior source is considered as piecewise constant and represented by using multiple level set functions. The localization of interior bioluminescence source is implemented by tracing the evolution of level set function. An alternate search scheme is incorporated to ensure the global optimal of reconstruction. Both numerical and physical experiments are performed to evaluate the developed level set reconstruction method. Reconstruction results show that the proposed method can stably resolve the interior source of bioluminescence tomography.     

Parallel keyed hash function construction based on chaotic maps

Recently, a variety of chaos-based hash functions have been proposed. Nevertheless, none of them works efficiently in parallel computing environment. In this Letter, an algorithm for parallel keyed hash function construction is proposed, whose structure can ensure the uniform sensitivity of hash value to the message. By means of the mechanism of both changeable-parameter and self-synchronization, the keystream establishes a close relation with the algorithm key, the content and the order of each message block. The entire message is modulated into the chaotic iteration orbit, and the coarse-graining trajectory is extracted as the hash value. Theoretical analysis and computer simulation indicate that the proposed algorithm can satisfy the performance requirements of hash function. It is simple, efficient, practicable, and reliable. These properties make it a good choice for hash on parallel computing platform.     

Application of radial basis functions to evolution equations arising in image segmentation

In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.     

The numerical approximation of a delta function with application to level set methods

It is shown that a discrete delta function can be constructed using a technique developed by Anita Mayo [The fast solution of Poisson’s and the biharmonic equations on irregular regions, SIAM J. Sci. Comput. 21 (1984) 285–299] for the numerical solution of elliptic equations with discontinuous source terms. This delta function is concentrated on the zero level set of a continuous function. In two space dimensions, this corresponds to a line and a surface in three space dimensions. Delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function. The numerical implementation of these delta functions achieves the expected order of accuracy.     

An MPI parallel level-set algorithm for propagating front curvature dependent detonation shock fronts in complex geometries

We present a parallel, two-dimensional, grid-based algorithm for solving a level-set function PDE that arises in Detonation Shock Dynamics (DSD). In the DSD limit, the detonation shock propagates at a speed that is a function of the curvature of the shock surface, subject to a set of boundary conditions applied along the boundaries of the detonating explosive. Our method solves for the full level-set function field, φ(x, y, t), that locates the detonation shock with a modified level-set function PDE that continuously renormalises the level-set function to a distance function based off of the locus of the shock surface, φ(x, y, t)=0. The boundary conditions are applied with ghost nodes that are sorted according to their connectivity to the interior explosive nodes. This allows the boundary conditions to be applied via a local, direct evaluation procedure. We give an extension of this boundary condition application method to three dimensions. Our parallel algorithm is based on a domain-decomposition model which uses the Message-Passing Interface (MPI) paradigm. The computational order of the full level-set algorithm, which is O(N ⁴), where N is the number of grid points along a coordinate line, makes an MPI-based algorithm an attractive alternative. This parallel model partitions the overall explosive domain into smaller sub-domains which in turn get mapped onto processors that are topologically arranged into a two-dimensional rectangular grid. A comparison of our numerical solution with an exact solution to the problem of a detonation rate stick shows that our numerical solution converges at better than first-order accuracy as measured by an L1-norm. This represents an improvement over the convergence properties of narrow-band level-set function solvers, whose convergence is limited to a floor set by the width of the narrow band. The efficiency of the narrow-band method is recovered by using our parallel model.     

Redistancing by flow of time dependent eikonal equation

Construction of signed distance to a given interface is a topic of special interest to level set methods. There are currently, however, few algorithms that can efficiently produce highly accurate solutions. We introduce an algorithm for constructing an approximate signed distance function through manipulation of values calculated from flow of time dependent eikonal equations. We provide operation counts and experimental results to show that this algorithm can efficiently generate solutions with a high order of accuracy. Comparison with the standard level set reinitialization algorithm shows ours is superior in terms of predictability and local construction, which, for example, are critical in local level set methods. We further apply the same ideas to extension of values off interfaces. Together, our proposed approaches can be used to advance the level set method for fast and accurate computations of the latest scientific problems.     

A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids

A balanced force refined level set grid method for two-phase flows on structured and unstructured flow solver grids is presented. To accurately track the phase interface location, an auxiliary, high-resolution equidistant Cartesian grid is introduced. In conjunction with a dual-layer narrow band approach, this refined level set grid method allows for parallel, efficient grid convergence and error estimation studies of the interface tracking method. The Navier–Stokes equations are solved on an unstructured flow solver grid with a novel balanced force algorithm for level set methods based on the recently proposed method by Francois et al. [M.M. Francois, S.J. Cummins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, M.W. Williams, A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, J. Comput. Phys. 213 (2006) 141–173] for volume of fluid methods on structured grids. To minimize spurious currents, a second order converging curvature evaluation technique for level set methods is presented. The results of several different test cases demonstrate the effectiveness of the proposed method, showing good mass conservation properties and second order converging spurious current magnitudes.     

Design of piezoelectric actuators using a multiphase level set method of piecewise constants

This paper presents a multiphase level set method of piecewise constants for shape and topology optimization of multi-material piezoelectric actuators with in-plane motion. First, an indicator function which takes level sets of piecewise constants is used to implicitly represent structural boundaries of the multiple phases in the design domain. Compared with standard level set methods using n scalar functions to represent 2ⁿ phases, each constant value in the present method denotes one material phase and 2ⁿ phases can be represented by 2ⁿ pre-defined constants. Thus, only one indicator function including different constant values is required to identify all structural boundaries between different material phases by making use of its discontinuities. In the context of designing smart actuators with in-plane motions, the optimization problem is defined mathematically as the minimization of a smooth energy functional under some specified constraints. Thus, the design optimization of the smart actuator is transferred into a numerical process by which the constant values of the indicator function are updated via a semi-implicit scheme with additive operator splitting (AOS) algorithm. In such a way, the different material phases are distributed simultaneously in the design domain until both the passive compliant host structure and embedded piezoelectric actuators are optimized. The compliant structure serves as a mechanical amplifier to enlarge the small strain stroke generated by piezoelectric actuators. The major advantage of the present method is to remove numerical difficulties associated with the solution of the Hamilton–Jacobi equations in most conventional level set methods, such as the CFL condition, the regularization procedure to retain a signed distance level set function and the non-differentiability related to the Heaviside and the Delta functions. Two widely studied examples are chosen to demonstrate the effectiveness of the present method.     

基于C-V模型的改进快速水平集图像分割法

针对水平集方法计算复杂度高,无法满足实时系统要求的缺陷,提出一种改进的快速水平集算法。该算法对快速水平集算法进行简化,采用单链表表示轮廓曲线。利用C-V模型的二值拟合项来设计曲线演化的速度函数,保留了C-V模型的全局优化特性。还给出了一个基于单链表中轮廓点个数变化的水平集演化终止准则。该算法不仅明显提高了分割速度,且对噪声图像也能实现高效的分割。     

Study on the unified algorithm for three-dimensional complex problems covering various flow regimes using Boltzmann model equation

The Boltzmann simplified velocity distribution function equation describing the gas transfer phenomena from various flow regimes will be explored and solved numerically in this study. The discrete velocity ordinate method of the gas kinetic theory is studied and applied to simulate the complex multi-scale flows. Based on the uncoupling technique on molecular movement and colliding in the DSMC method, the gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by extending and applying the unsteady time-splitting method from computational fluid dynamics. The Gauss-type discrete velocity numerical quadrature technique for different Mach number flows is developed to evaluate the macroscopic flow parameters in the physical space. As a result, the gas-kinetic numerical algorithm is established to study the three-dimensional complex flows from rarefied transition to continuum regimes. The parallel strategy adapted to the gas-kinetic numerical algorithm is investigated by analyzing the inner parallel degree of the algorithm, and then the HPF parallel processing program is developed. To test the reliability of the present gas-kinetic numerical method, the three-dimensional complex flows around sphere and spacecraft shape with various Knudsen numbers are simulated by HPF parallel computing. The computational results are found in high resolution of the flow fields and good agreement with the theoretical and experimental data. The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes from the gas-kinetic point of view of solving the Boltzmann model equation. Supported by the National Natural Science Foundation of China (Grant Nos. 90205009 and 10321002) and the National Parallel Computing Center     

基于迭代拟合的集装箱角件边缘检测算法

噪声通常是影响集装箱角件图像中低层次语义信息提取精度的重要因素,传统的边缘检测算法通常通过改进滤波器和阈值来消除图像中的物理噪声和环境噪声,但是却无法去除边缘检测后的噪声,为解决这一问题,提出了一种基于迭代拟合的边缘检测算法。首先,对角件图像进行一系列预处理操作获取边缘点集,其次,使用拟合算法处理点集并且得到函数表达式,然后定义偏差值度量并计算,用于衡量目标点集到拟合或者检测结果的偏差,最后,去除定义下距离拟合结果最远的指定数量的点,如此迭代拟合直至评价函数收敛。实验结果与分析表明,该算法可以有效地去除边缘点集中的非真实边缘点,相比于传统的边缘检测算法更能去除特殊噪声,算法具有收敛速度快、准确率较高、灵活性好等特点。     

Modified level set method with Canny operator for image noise removal

The level set method is commonly used to address image noise removal. Existing studies concentrate mainly on determining the speed function of the evolution equation. Based on the idea of a Canny operator, this letter introduces a new method of controlling the level set evolution, in which the edge strength is taken into account in choosing curvature flows for the speed function and the normal to edge direction is used to orient the diffusion of the moving interface. The addition of an energy term to penalize the irregularity allows for better preservation of local edge information. In contrast with previous Canny-based level set methods that usually adopt a two-stage framework, the proposed algorithm can execute all the above operations in one process during noise removal.     

History matching of facies distribution with the EnKF and level set parameterization

In this work, we develop a methodology to combine the Ensemble Kalman filter (EnKF) and the level set parameterization for history matching of facies distribution. With given prior knowledge about the facies of the reservoir geology, initial realizations are generated by commonly used software as the prior guesses of the unknown field. Furthermore, level set functions are used to reparameterize these initial realizations. In the reparameterization process, a representing node system is set up, on which the values of level set functions are assigned using Gaussian random numbers. The mean and the standard deviation of the Gaussian random numbers are designed according to the facies proportion, and the sign of the random numbers depends on the facies type at the representing nodes. The values of the level set functions at the other grid nodes are obtained by linear interpolation. The level set functions on the representing nodes are the model parameters of the EnKF state vector and are updated in the data assimilation process. On the basis of our numerical examples for two-dimensional reservoirs with two or three facies, the proposed method is demonstrated to be able to capture the main features of the reference facies distributions.     

单通道光学相关实现击中与否运算

给出了一种单通道光学相关实现击中与否运算的算法和光学装置，此法基于形态学中的腐蚀运算和光学相关的关系及阈值操作，在非相干光学相关器中，将前景结构核元素编码为１，背景结构核元素编码为ａ（ａ满足一定条件），只需用原图像与前景和背景结构进行相关，然后对相关结果取阈值的Ｋ（前景结构核元素的像素数）即可得到击中与否运算，击中与否运算可以光学并行一步实现。     

Shape and topology optimization for electrothermomechanical microactuators using level set methods

In this short note, a shape and topology optimization method is presented for multiphysics actuators including geometrically nonlinear modeling based on an implicit free boundary parameterization method. A level set model is established to describe structural design boundary by embedding it into the zero level set of a higher-dimensional level set function. The compactly supported radial basis functions (CSRBF) are introduced to parameterize the implicit level set surface with a high level of accuracy and smoothness. The original more difficult shape and topology optimization driven by the Hamilton–Jacobi partial differential equation (PDE) is transferred into a relatively easier parametric (size) optimization, to which many well-founded optimization algorithms can be applied. Thus the structural optimization is transformed to a numerical process that describes the design as a sequence of motions of the design boundaries by updating the expansion coefficients of the size optimization. Two widely studied examples are chosen to demonstrate the effectiveness of the proposed method.     

应用改进的特征基函数法和自适应交叉近似算法快速分析导体目标电磁散射特性

特征基函数的构造是特征基函数法的关键步骤之一, 传统方法在构造特征基函数时, 需要在每个子域设置足够多的入射波激励, 生成的特征基函数个数较多, 奇异值分解时间较长. 为了加快特征基函数的构造, 本文提出了一种改进的特征基函数法. 该方法充分考虑每个子域之间的耦合作用, 求出每个子域的次要特征基函数, 从而降低入射波激励的个数, 大大减少了特征基函数的个数; 并且结合自适应交叉近似算法加速阻抗矩阵元素的计算, 提高了次要特征基函数求解和缩减矩阵构建过程中的矩阵矢量相乘的速度. 数值结果证明了本文方法的精确性和高效性. 关键词： 电磁散射 矩量法 特征基函数法 自适应交叉近似     

显微视觉自动聚焦研究

提出一种评估空域聚焦函数的方法。从计算时间与聚焦曲线变化率两个方面,提出四个参量作为评估依据．可从多个函数中筛选出最佳聚焦测度。针对研制的微对准装配自动聚焦系统的评估结果表明：灰度熵函数是适合于该系统的最佳聚焦测度。为克服聚焦搜索运动中的机械传动回差,提出不同于传统聚焦策略的“定位法”。该方法的核心是建立聚焦函数值与离焦量之间的函数关系,提出采用多项式拟合、高斯函数拟合以及样条插值拟合的方法可以构建这种函数关系;并给出了计算结果。最后综合灰度熵函数与定位法策略进行自动聚焦实验．得到自动聚焦精度为3．4μm;完成一次自动聚焦平均时间为3．3s。实验结果证明所述方法可以实现准确、实时地自动聚焦。