Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems

This paper concerns a numerical study of convergence properties of the boundary knot method (BKM) applied to the solution of 2D and 3D homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems. The BKM is a new boundary-type, meshfree radial function basis collocation technique. The method differentiates from the method of fundamental solutions (MFS) in that it does not need the controversial artificial boundary outside physical domain due to the use of non-singular general solutions instead of the singular fundamental solutions. The BKM is also generally applicable to a variety of inhomogeneous problems in conjunction with the dual reciprocity method (DRM). Therefore, when applied to inhomogeneous problems, the error of the DRM confounds the BKM accuracy in approximation of homogeneous solution, while the latter essentially distinguishes the BKM, MFS, and boundary element method. In order to avoid the interference of the DRM, this study focuses on the investigation of the convergence property of the BKM for homogeneous problems. The given numerical experiments reveal rapid convergence, high accuracy and efficiency, mathematical simplicity of the BKM.     

A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions

The Wave Based Method (WBM) is an alternative numerical prediction method for both interior and exterior steady-state dynamic problems, which is based on an indirect Trefftz approach. It applies wave functions, which are exact solutions of the governing differential equation, to describe the dynamic field variables. The smaller system of equations and the absence of pollution errors make the WBM very suitable for the treatment of Helmholtz problems in the mid-frequency range, where element-based methods are no longer feasible due to the associated computational costs. A sufficient condition for convergence of the method is the convexity of the considered problem domain. As a result, only problems of moderate geometrical complexity can be considered and some geometrical features cannot be handled at all. In this paper, these limitations are alleviated through the development of a general modelling framework based on existing WBM methodologies which allows for the efficient introduction of inclusion configurations in bounded WBM models for problems governed by one or more Helmholtz equations. The feasibility and efficiency of the method is illustrated by means of numerical verification studies in which the methodology is applied to two types of dynamic problems. On the one hand, a single Helmholtz equation associated with the steady-state dynamic behaviour of acoustic cavities is studied. On the other hand, the framework is applied to the solution of the Navier system of partial differential equations that describe the elastodynamic response of two-dimensional perforated solids.     

On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin–Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.     

Combined Vector Field Approach for 2D and 3D Arbitrary Twice Differentiable Curved Path Following with Constrained UAVs

Path following is an essential requirement for unmanned aerial vehicles (UAVs). Path following problems of 2-dimensional (2D) straight lines and planar circles have been studied and many approaches have been proposed during the past few years. In this paper the problem of following arbitrary twice differentiable curved paths in both 2D and 3D spaces is investigated. Based on the Helmholtz theorem, respective combined guidance vector fields for any given 2D and 3D arbitrary twice differentiable curved paths are constructed by trading off the respective conservative and solenoidal vector fields making use of the defined distance between the UAV and the desired path. Conditions for the two combined vector fields to be globally feasible are given. UAV input constraints and constant wind disturbance are assumed to be present. By tracking the constructed combined vector fields, a saturated course rate controller for 2D curved path following and a jointly saturated course rate and climb rate controller for 3D curved path following are designed. The Lyapunov stability of the saturated course rate controller for 2D curved path following is proved. Numerical simulations are given to assess the proposed approach.     

Designing meta material slabs exhibiting negative refraction using topology optimization

This paper proposes a topology optimization based approach for designing meta materials exhibiting a desired negative refraction with high transmission at a given angle of incidence and frequency. The approach considers a finite slab of meta material consisting of axis-symmetric designable unit cells subjected to an exterior field. The unit cell is designed to achieve the desired properties based on tailoring the response of the meta material slab under the exterior field. The approach is directly applicable to physical problems modeled by the Helmholtz equation, such as acoustic, elastic and electromagnetic wave problems. Acoustic meta materials with unit cell size on the order of half the wave length are considered as examples. Optimized designs are presented and their performance under varying frequency and angle of incidence is investigated.     

A recent survey on computational techniques for solving singularly perturbed boundary value problems

This survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. In continuation of a survey performed earlier, this paper limits its coverage to some standard numerical methods developed by numerous researchers between 2000 and 2005. A summary of the results of some recent methods is presented and this leads to conclusions and recommendations regarding methods to use on singular perturbation problems. Because of space constraints, we considered one-dimensional singularly perturbed boundary value problems only.     

面向Agent开发策略探讨

面向Agent技术是新兴的软件开发技术,目前面向Agent开发缺乏系统化开发方法,面临不少问题和困难。文本分析了面向Agent开发的现状及存在的问题,并针对这些问题,提出了应对的解决办法和面向Agent开发的若干策略。     

分析化学中的多目标计算机寻优决策

本文综述了国内外各个科学领域中有关多目标决策分析的理论和方法研究的发展概况;探讨了分析化学中的多目标决策问题及发展前景。本文还简要地介绍了多目标规划数学模型的建立及几种常用的解法。     

服装CAD综述

文中对ＧＣＡＤ的历史和现状进行了全面综述,建立了ＧＣＡＤ系统的总体构架和工作流程,介绍了其主要内容和实现方法,并指出了现存的问题与可能的决策,最后,从创新的角度,对ＧＣＡＤ提出了研制量身定做子系统等几点构想及其发展的新方向。     

故障检测与诊断技术

本文介绍了故障检测与诊断技术的历史及发展状况,对其所用的各种方法分类进行了详细评述,指出了当前急待解决的若干前沿课题,并对这门技术的发展进行了展望。     

FTA的若干问题与进展

本文就故障树分析(Fault Tree Analysis)方法研究的历史与现状作一综述,重点介绍国内 外学者在FTA技术研究的各阶段所做的开创性工作.另外,对FTA理论中的若干关键问题 也扼要地进行了评论.     

面向对象技术述评

面向对象技术已成为信息系统应用和开发的主流技术。本文首先对应用情况做了概要的阐述，然后讨论面向对象的开发方法，并评论发展中存在的争论问题。     

An optimal compact sixth-order finite difference scheme for the Helmholtz equation

In this paper, we present an optimal compact finite difference scheme for solving the 2D Helmholtz equation. A convergence analysis is given to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, a refined optimization rule for choosing the scheme’s weight parameters is proposed. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters.     

Meshfree Particle Methods in the Framework of Boundary Element Methods for the Helmholtz Equation

In this paper, we study electromagnetic wave scattering from periodic structures and eigenvalue analysis of the Helmholtz equation. Boundary element method (BEM) is an effective tool to deal with Helmholtz problems on bounded as well as unbounded domains. Recently, Oh et al. (Comput. Mech. 48:27–45, 2011) developed reproducing polynomial boundary particle methods (RPBPM) that can handle effectively boundary integral equations in the framework of the collocation BEM. The reproducing polynomial particle (RPP) shape functions used in RPBPM have compact support and are not periodic. Thus it is not ideal to use these RPP shape functions as approximation functions along the boundary of a circular domain. In order to get periodic approximation functions, we consider the limit of the RPP shape function as its support is getting infinitely large. We show that the basic approximation function obtained by the limit of the RPP shape function yields accurate solutions of Helmholtz problems on circular, or annular domains as well as on the infinite domains.     

参数化设计研究

参数化设计是提高企业产品设计创新能力的关键。从参数化模型的不同表示方式，相应的求解方法，建立模型的交互手段等方面综述产品参数化设计的研究现状及未来发展中需要解决的问题。重点讨论传统CAD领域所涉及的二维图纸及三维零件造型等几何问题参数化设计，并在此基础上对传统的参数化的概念进行扩展，讨论产品全生命周期的参数化设计问题及产品参数化设计的相关国际标准。     

视景仿真的关键技术

针对视景仿真开发中的几个常见问题，提出了解决方案。包括：利用回调函数将OpencL代码嵌入到Vega应用程序中，实现Vega中未能提供的图形功能；分析了视景坐标系与模型坐标系之间的对应转换关系，给出两种常用的转换公式；概述了通用视点方式的设计方法，通过开发自定义运动模式实现了以输入设备控制视点的方法。     

微型计算机用于过程控制的几个问题

本文概述了近年来我国将微型计算机用于过程控制方面的进展及现存的一些问题.     

物体渐变技术现状与发展

物体渐变技术在虚拟现实、工业模拟、科学计算可视化、动画生成等领域有着广泛的应用，具有十分重要的意义，近年来，有许多研究者提出了一些效果不错的算法，对这些算法进行了分析，并对物体渐变的基本原理、物体的表示方法与渐变技术间的紧密联系、二维物体渐变技术和三维物体渐变技术做了较全面的综述，探讨了现有物体渐变技术中需要改进的关键问题，并给出了渐变技术在未来的发展方向。     

计算机动画中人体建模与皮肤变形技术的研究现状与展望

人体动画制作技术是计算机动画领域内的研究热点和难点。在制作真实感人体动画时,除了有真实的人体运动和灵活的运动控制方法外,还需要有逼真的人体造型和皮肤变形效果。为了使计算机动画研究领域的研究人员对当前各种人体建模与皮肤变形技术有较全面的了解,对计算机动画中的真实感人体建模与皮肤变形技术进行了较为全面的阐述,将现有的方法分为三大类:基于面模型的方法、基于体模型的方法和基于层次式模型的方法,并分析和比较了这些方法的优缺点。在回顾了现有的人体建模与变形技术的基础上指出,3维扫描技术的发展使人体建模和皮肤变形的研究面临新的契机。如何充分利用基于扫描技术建模的优点,并结合层次式建模与变形方法的灵活性的特点,创作出高度真实感的人体皮肤模型及其变形效果,是未来研究的重要方向。     

Molecular distance geometry methods: from continuous to discrete

Distance geometry problems (DGP) arise from the need to position entities in the Euclidean K‐space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph (graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties and nuclear magnetic resonance experiments; sensor networks can estimate their relative distance by recording the power loss during a two‐way exchange; finally, when drawing graphs in two or three dimensions, the graph to be drawn is given, and therefore distances between vertices can be computed. DGPs involve a search in a continuous Euclidean space, but sometimes the problem structure helps reduce the search to a discrete set of points. In this paper we survey some continuous and discrete methods for solving some problems of molecular distance geometry.