关于人工势场法局部极小问题的一种解决方法

利用人工势场法进行移动机器人路径规划是十分有效的,在使用人工势场法进行避障的时候,由于移动机器人对周围环境信息的感知具有局限性,容易导致局部极小问题的出现。针对此问题提出一种基于“沿边行为”的方法,当移动机器人进入局部极小状态时激活该行为,使机器人沿着障碍物的边缘运动,使移动机器人在只感知局部信息的条件下,能迅速地摆脱局部极小的状态。仿真实验表明这种方法是可行的,可以有效地解决移动机器人因获取的环境信息不足而陷入局部极小点。     

基于人工势场与IB-LBM的机器蛇水中2D避障控制算法

为了提高多冗余度、多自由度机器蛇水下环境运动适应能力,提出了基于人工势场与IB-LBM （immersed boundary method-lattice Boltzmann method）相结合的机器蛇水中2D智能避障算法.首先,采用格子Boltzmann方法描述2D水中障碍模型、构造统一形式.然后,运用浸入边界法,结合现有的蛇形曲线运动方程,在计入人工势场法引力和斥力作用的情况下,推导得到机器蛇2D水中避障模型.之后,通过改变障碍影响距离、机器蛇摆动振幅、摆动频率、障碍点斥力增益系数、雷诺数以及目标点引力增益系数等重要参数,研究机器蛇在不同情况下的避障效率和避障安全性.最后,通过多次仿真求取各项参数的最优值.仿真结果表明,在各项参数都最优时,该算法能使机器蛇快速、安全、有效地避开水下复杂环境中的静态障碍而到达目标点.该方法不仅能够充分研究机器蛇在水中的流固耦合特性,获得实时避障效果,而且能够利用已知的环境信息生成最优路径.     

圆筒电容器静电场的数值分析

在 110kV电容分压式电压互感器设计的过程中 ,电容器本身的绝缘是很关键的。应用有限元法对圆筒电容器的电势分布进行了计算 ,为绝缘结构的设计奠定了理论基础     

Computational Finite-Element Schemes for Optimal Control of an Elliptic System with Conjugation Conditions

New optimal control problems are considered for distributed systems described by elliptic equations with conjugate conditions and a quadratic minimized function. Highly accurate computational discretization schemes are constructed for the case where a feasible control set coincides with the full Hilbert space of controls.     

一种新型多维加速度传感器弹性体设计与仿真分析

基于E型膜片设计了一种新型多维加速度传感器弹性体结构，并介绍了这种低成本传感器的工作原理。有限元仿真分析得到了弹性体结构的静态和动态特性，结果表明该结构对各轴向加速度都具有较高的灵敏度，并能够消除各轴向加速度间的耦合。     

Absorbing Boundary Conditions of the Second Order for the Pseudospectral Chebyshev Methods for Wave Propagation

In this paper we describe the implementation of one-way wave equations of the second order in conjuction with pseudospectral methods for wave propagation in two space dimensions. These equations are first reformulated as hyperbolic systems of the first order and the absorbing boundaries are implemented by an appropriate modification of the matrix of this system. The resulting matrix corresponding to one-way wave equation based on Padé approximation has all eigenvalues in the complex negative half plane which allows stable integration of the underlying system by any ODE solver in the sense of eigenvalue stability. The obtained numerical scheme is much more accurate than the schemes obtained before which utilized absorbing boundary conditions of the first order, and is also capable of integrating the wave propagation problems on much larger time intervals than was previously possible.     

The exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions

In this article, a new integral equation is derived to solve the exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions, and existence and uniqueness is proven for all wave numbers. We apply the boundary element collocation method to solve the system of Fredholm integral equations of the second kind, where we use constant interpolation. We observe superconvergence at the collocation nodes and illustrate it with numerical results for several smooth surfaces.     

Numerical Solution of a Flow Equation of the Ideal Liquid whose Vorticity Is Proportional to the Flow Function

The paper deals with the solution of an equation that describes a particular case of the flow of the ideal liquid in which the vorticity is proportional to the flow function. To solve the equation, two methods are used, namely, the finite-difference method and a method based on the Hermite formula. The results of solution of model problems by both methods are presented and compared.     

The Variable Order Fast Multipole Method for Boundary Integral Equations of the Second Kind

We discuss the variable order Fast Multipole Method (FMM) applied to piecewise constant Galerkin discretizations of boundary integral equations. In this version of the FMM low-order expansions are employed in the finest level and orders are increased in the coarser levels. Two versions will be discussed, the first version computes exact moments, the second is based on approximated moments. When applied to integral equations of the second kind, both versions retain the asymptotic error of the direct method. The complexity estimate of the first version contains a logarithmic term while the second version is O(N) where N is the number of panels.This work was supported by the NSF under contract DMS-0074553     

新型矿用局部通风机风量风压测量装置的研究

介绍了一种以MSP430149单片机为核心的新型矿用局部通风机风量风压测量装置的工作原理及其软、硬件设计。该装置具有风量风压数值实时显示、停风报警等功能,并可以将风量风压信号转换成频率信号传送给上位机,适用于各种井下局部轴流通风机,填补了目前国内市场上的空白。测试结果表明,该装置操作简便,测量精度及可靠性高。     

切比契夫谱元素局部混合基函数构造

针对切比契夫谱方法,该文首次构造了两类局部混合基函数,据此发展了一种新的谱元素方法:在元素端点采用局部拉格朗日插值基,元素内部采用经调整后的切比契夫多项式。这里的两类混合基函数在计算精度上可与传统的拉格朗日基相媲美,而且元素矩阵具有稀疏特征和数据重用性。该文给出的局部混合基函数对传统的谱元素方法进行了扩充。     

On a method for solving a local boundary problem for a nonlinear stationary system with perturbations in the class of piecewise constant controls

The wide class of nonlinear stationary systems of ordinary differential equations taking into account restrictions on control and external perturbation is considered. An algorithm for constructing a discrete control function that guarantees the transfer of the systems from the initial state to the origin and an arbitrary neighborhood of the origin is proposed. A constructive sufficient condition of the Kalman type, in which the specified translation is possible, is obtained. The problem of robot‐manipulator control is considered and its numerical simulation is carried out.     

第一类边界对流扩散方程LDG方法的稳定性

针对一维常系数对流扩散模型方程,讨论了当含有第一类边界条件时,局部间断有限元方法（LDG方法）的稳定性。利用有限元理论基本分析技巧,证明了当边界条件为第一类的边界条件时,LDG方法为稳定的,并利用数值算例证明理论分析的正确性。     

Numerical simulation of steady planar die swell for a Newtonian fluid using the spectral element method

This paper is concerned with two dimensional numerical simulations of plane extrusion of a Newtonian fluid. The problem is discretized using the spectral element method and the free surface is evolved according to an ALE treatment. Numerical simulations are performed over a wide range of Reynolds and Weber numbers to highlight the effects of inertia and surface tension, respectively. Convergence of the numerical approximations with respect to polynomial order is demonstrated for the sensitive measures of free surface location and downstream relaxation distance. The higher the inertia the further downstream the relaxation occurs. Numerical results show good qualitative and quantitative agreement with predictions of other numerical schemes and experiments.     

A front-fixing finite element method for the valuation of American options with regime switching

American option problems under regime-switching model are considered in this paper. The conjectures in [H. Yang, A numerical analysis of American options with regime switching, J. Sci. Comput. 44 (2010), pp. 69–91] about the position of early exercise prices are proved, which generalize the results in [F. Yi, American put option with regime-switching volatility (finite time horizon) – Variational inequality approach, Math. Methods. Appl. Sci. 31 (2008), pp. 1461–1477] by allowing the interest rates to be different in two states. A front-fixing finite element method for the free boundary problems is proposed and implemented. Its stability is established under reasonable assumptions. Numerical results are given to examine the rate of convergence of our method and compare it with the usual finite element method.     

Shared-Memory Parallel Vector Implementation of the Immersed Boundary Method for the Computation of Blood Flow in the Beating Mammalian Heart

This paper describes the parallel implementation of the immersed boundary method on a shared-memory machine such as the Cray C-90 computer. In this implementation, outer loops are parallelized and inner loops are vectorized. The sustained computation rates achieved are 0.258 Gflops with a single processor, 1.89 Gflops with 8 processors, and 2.50 Gflops with 16 processors. An application to the computer simulation of blood flow in the heart is presented.     

横向磁通感应加热温度场的数值模拟

介绍了横向磁通感应加热原理,在电磁学和传热学基本理论基础上,建立感应加热电磁场和温度场分布的有限元计算模型,运用ANSYS软件对一实际加热过程进行模拟,得到被加热工件温度在空间、时间上的分布,通过与实验测量值的比较,证明数值模拟结果是可靠的。     

Numerical results for linear Fredholm integral equations of the first kind over surfaces in three dimensions

Linear Fredholm integral equations of the first kind over surfaces are less familiar than those of the second kind, although they arise in many applications like computer tomography, heat conduction and inverse scattering. This article emphasizes their numerical treatment, since discretization usually leads to ill-conditioned linear systems. Strictly speaking, the matrix is nearly singular and ordinary numerical methods fail. However, there exists a numerical regularization method – the Tikhonov method – to deal with this ill-conditioning and to obtain accurate numerical results.     

The generalized finite element method for Helmholtz equation. Part II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment

In Part I [T. Strouboulis, I. Babuška, R. Hidajat, The generalized finite element method for Helmholtz equation: theory, computation, and open problems, Comput. Methods Appl. Mech. Engrg. 195 (2006) 4711-4731] we introduced the q-version of the generalized finite element method (GFEM) for the Helmholtz equation and we addressed its: (a) pollution error due to the wave number; (b) exponential q-convergence; (c) robustness to perturbations of the mesh, the roundoff and numerical quadrature errors; and (d) a-posteriori error estimation. Here we continue the development of the GFEM for Helmholtz and we address the effects of: (a) alternative handbook functions and mesh types; (b) the error due to the artificial truncation boundary conditions and its assessment. The conclusions are: (1) the employment of plane-wave, wave-band, and Vekua handbook functions lead to equivalent results; and (2) for high q, the most significant component of error may be the one due to the artificial truncation boundary conditions. A rather straightforward approach for assessing this error is proposed.