SINGINT: Automatic numerical integration of singular integrands

We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion and are runtime and memory optimized, respectively. SINGINT, a C implementation of the algorithms, is introduced and its utilization in the calculation of particle scattering amplitudes is exemplified.     

An adaptive Monte Carlo integration algorithm with general division approach

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The algorithm uses iteratively the idea of separating the domain of integration into 2^s$2^s$subregions. The proposed algorithm can be applied directly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional integral using a two-division approach. The numerical results show that the proposed algorithm gives better results than using one-division approach.     

An adaptive single-point algorithm for global numerical optimization

This paper describes a novel algorithm for numerical optimization, called Simple Adaptive Climbing (SAC). SAC is a simple efficient single-point approach that does not require a careful fine-tunning of its two parameters. SAC algorithm shares many similarities with local optimization heuristics, such as random walk, gradient descent, and hill-climbing. SAC has a restarting mechanism, and a powerful adaptive mutation process that resembles the one used in Differential Evolution. The algorithms SAC is capable of performing global unconstrained optimization efficiently in high dimensional test functions. This paper shows results on 15 well-known unconstrained problems. Test results confirm that SAC is competitive against state-of-the-art approaches such as micro-Particle Swarm Optimization, CMA-ES or Simple Adaptive Differential Evolution.     

应用Laguerre小波算子矩阵求二重数值积分

基于Laguerre小波函数及其对应的积分算子矩阵给出了一个求二重积分的数值方法。该方法通过对被积函数进行恰当的离散化,将二重数值积分问题转化为矩阵运算,从而易于求解、方便计算。该方法不仅适用于积分区域是矩形区域,也适用于二重变限积分的情况。数值算例验证了该方法的可行性及有效性。     

NICE—An explicit numerical scheme for efficient integration of nonlinear constitutive equations

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for the integration of a system of algebraic and differential equations in general, the scheme is primarily developed for use with the direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed explicit scheme, where no iteration is required, the implementation simplicity of the forward-Euler scheme and the accuracy of the backward-Euler scheme are successfully combined. The properties of the proposed NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, are compared with the properties of the classical forward-Euler scheme and backward-Euler scheme. For this purpose two highly nonlinear examples, with the von Mises and GTN material model considered, have been studied. The accuracy of the new scheme is demonstrated to be at least of the same level as experienced by the backward-Euler scheme, if we compare them on the condition of the same CPU time consumption. Besides, the simplicity of the NICE scheme, which is due to implementation similarity with the classical forward-Euler scheme, is its great Advantage.     

用人工鱼群算法求解二重数值积分

提出了利用人工鱼群算法求解二重数值积分的方法,将不等距离分割方法与人工鱼群算法相结合来求解数值积分同时在积分求和式子中引入一个参数。最后给出几个数值积分算例,并与其它数值积分方法作了比较,仿真结果分析表明,该方法具有更高阶的精度和更快的收敛速度。     

An agent-based approach for e-manufacturing and supply chain integration

A major problem facing manufacturing organisations is how to provide efficient and cost-effective responses to the unpredictable changes taking place in a global market. This problem is made difficult by the complexity of supply chain networks coupled with the complexity of individual manufacturing systems within supply chains. Current systems such as manufacturing execution systems (MES), supply chain management (SCM) systems and enterprise resource planning (ERP) systems do not provide adequate facilities for addressing this problem. This paper presents an approach that would enable manufacturing organisations to dynamically and cost-effectively integrate, optimise, configure, simulate, restructure and control not only their own manufacturing systems but also their supply networks, in a co-ordinated manner to cope with the dynamic changes occurring in a global market. This is realised by a synergy of two emerging manufacturing concepts: Agent-based agile manufacturing systems and e-manufacturing. The concept is to represent a complex manufacturing system and its supply network with an agent-based modelling and simulation architecture and to dynamically generate alternative scenarios with respect to planning, scheduling, configuration and restructure of both the manufacturing system and its supply network based on the coordinated interactions amongst agents.     

Some numerical integration methods based on Bernstein polynomials

In this work we find numerical integration of a function by some approximations of the function using Bernstein polynomials, and we introduce a new fast method to approximate the value of a definite integral and we compare them.     

Cuba—a library for multidimensional numerical integration

The Cuba library provides new implementations of four general-purpose multidimensional integration algorithms: Vegas, Suave, Divonne, and Cuhre. Suave is a new algorithm, Divonne is a known algorithm to which important details have been added, and Vegas and Cuhre are new implementations of existing algorithms with only few improvements over the original versions. All four algorithms can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces.

Program summary

Title of program:CubaCatalogue identifier: ADVHProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVHProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which is has been tested:Designed for: all platforms with an ISO C99 C compilerTested on: x86 (Linux/gcc), Alpha (Tru64 Unix/gcc)Operating systems or monitors under which the program has been tested: Linux, Tru64 UnixProgramming language used: CMemory required to execute with typical data: 1M wordsNo. of bits in a word: 8No. of processors used: 1Has the code been vectorized or parallelized?: Not yetNo. of lines in distributed program, including test data, etc.: 9380No. of bytes in distributed program, including test data, etc.: 131 293Distribution format: tar.gzNature of the physical problem: Multidimensional numerical integrations, e.g., of phase spaces.Method of solution: The Cuba library contains the four algorithms Vegas, Suave, Divonne, and Cuhre with the following characteristics:

Routine	Basic integration method	Algorithm type	Variance reduction
Vegas	Sobol quasi-random sample	Monte Carlo	importance sampling
Suave	Sobol quasi-random sample	Monte Carlo	globally adaptive subdivision
Divonne	Korobov quasi-random sample	Monte Carlo	stratified sampling,
	or Sobol quasi-random sample	Monte Carlo	aided by methods from
	or cubature rules	deterministic	numerical optimization
Cuhre	cubature rules	deterministic	globally adaptive subdivision

Full-size table

     

基于局部自适应混合积分的动态布料模拟快速方法

针对布料动态模拟中快速稳定求解的瓶颈问题,提出了一种局部自适应的混合积分方法。在每一时间步长,网格中质点利用自身模拟参数求解一稳定的判断准则,据此自适应判定该质点相连弹簧不同弹性力部分引起的运动方程采用何种数值积分求解,从而有效提高了模拟效率且可以并行计算。另外,针对线性方程组的特点,用快速超松弛迭代法代替传统的共轭梯度法来求解,进一步提高了系统的性能表现。实验表明,该方法具有近似线性的复杂度,便于并行计算,并有良好的稳定视觉效果。     

基于遗传算法求任意函数的数值积分

针对复杂函数的数值积分问题,给出了若干个任意分割积分区间的数值积分的误差结果,并提出一种基于遗传算法的不等距节点分割的数值积分方法。该方法初始时在积分区间内任意选取一定的节点,通过遗传算法优化这些节点,在相邻节点间利用Simpson公式近似计算积分,最后得到较准确的积分结果。数值计算结果表明,该方法计算精度高,而且可以计算奇异函数及震荡函数的积分。     

Important aspects of geometric numerical integration

At the example of Hamiltonian differential equations, geometric properties of the flow are discussed that are only preserved by special numerical integrators (such as symplectic and/or symmetric methods). In the ‘non-stiff’ situation the long-time behaviour of these methods is well-understood and can be explained with the help of a backward error analysis. In the highly oscillatory (‘stiff’) case this theory breaks down. Using a modulated Fourier expansion, much insight can be gained for methods applied to problems where the high oscillations stem from a linear part of the vector field and where only one (or a few) high frequencies are present. This paper terminates with numerical experiments at space discretizations of the sine-Gordon equation, where a whole spectrum of frequencies is present.     

An adaptive coherence filter

This paper derives an adaptive coherence filter for canceling interference from a signal of interest whose power spectral density is symmetric. A basic property of the Fourier transform of real signals is that their spectra are Hermitian symmetric. This property is exploited to determine which part of a spectrum is interference and which part is the signal of interest. An unconstrained Wiener filter is derived that exploits the frequency domain symmetry of the signal of interest. While the adaptive coherence filter is based on the Fourier transform property of real signals, an extension of the algorithm is provided so the filter can be used on any signal that displays spectral symmetry. A practical method for implementing the filter is provided. The filter has application in the area of telecommunications, but is applicable in wireless communication applications where a signal, that displays spectral symmetry, is corrupted by interfering signals within the signal of interest's bandwidth.     

An iterative integration scheme for solving second-order ordinary differential equations

This paper presents an iterative solution method for the numerical integration of second-order ordinary differential equations using a simple program for microcomputers (PC). The method of integration proposed is based on the geometrical considerations in the phase plane. The numerical results are compared to those obtained by the fourth-order Runge-Kutta method and to the closed form solutions when possible. Tests show good accuracy and, in some cases, computer time saving with respect to the Runge-Kutta's method for th same accuracy. The method of integration in the phase plane seems very good for treating every kind of nonlinear second-order differential equation whatever the degree of nonlinearity.     

An adaptive control algorithm for robotic deburring

This paper presents the topic of adaptive control for robotic deburring by presenting some nonreal-time and some real-time schemes found in literature. Thereafter, a real-time adaptive control algorithm for robotic deburring is presented. Experiments are presented in which an IBM RS/1 robot is used to simulate the operation of the algorithm.     

一种面向数值模拟软件的持续集成平台

随着软件复杂度的增加和交付需求的变化,快速集成和自动部署成为高性能数值模拟软件推广应用的瓶颈。为满足软件构建和发布的差异化需求,简化从用户需求到软件发布的工作流程,基于Jenkins设计持续集成平台,实现软件静态审查、编译、测试和发布流程的自动化,全面记录软件构建日志和测试结果。利用Docker技术将构建环境容器化,实现环境的快速搭建和配置管理,满足多样化目标环境需求。该平台的实际应用效果显示,基于该平台的产品发布周期相比之前缩短约75%,可极大简化软件安装和部署难度。     

An adaptive variable structure control for a class of nonlinear systems

Motivated by the recent advance in adaptive output-feedback control for a class of nonlinear systems which can be transformed into the so-called output-feedback form [7,10,11], an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem. It is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time-varying.     

An adaptive controller for nonlinear teleoperators

In Chopra et al (2008) [Chopra, N., Spong, M. W., & Lozano, R. (2008). Synchronization of bilateral teleoperators with time-delay. Automatica, 44(8), 2142-2148], an adaptive controller for teleoperators with time-delays, which ensures synchronization of positions and velocities of the master and slave manipulators, and does not rely on the use of the ubiquitous scattering transformation, is proposed. In this paper it is shown that this controller will tend to drive to zero the positions of the joints where gravity forces are non-zero. Hence, the scheme is, in general, applicable only to systems without gravity. We also prove in this paper that this limitation can be obviated, replacing the positions and velocities-that are used in the coordinating torques and the adaptation laws-by their errors. Simulation results illustrate the performance of both schemes.     

An adaptive high-gain observer for nonlinear systems

In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously (1) extended Kalman filter’s good noise filtering properties, and (2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations.The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example.