A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains

The way boundary conditions are imposed when applying Chebyshev collocation methods to Poisson and biharmonic-type problems in rectangular domains is investigated. It is shown that careful selection of the number of collocation points leads to a linear system ofn linearly independent equations inn unknowns.     

清涧河流域不同水土保持措施配置下蓄水拦沙效益分析

从分析清涧河流域不同年代水土保持措施配置人手，以蓄水拦沙效益为研究目标，探讨了水土保持措施优化配置问题。分析认为：水土保持措施配置与蓄水拦沙效益是密切相关的，淤地坝在水土保持措施配置中应占有合理比重，坡面治理措施配置中需进一步加大封禁治理比例。     

POLARIZATION BEHAVIOR OF PACKED-BED ELECTRODES: A COMPARATIVE STUDY OF EXPERIMENTAL AND MODELING RESULTS

The current distribution and overall polarization behavior of electrodeposition at a flow-through (packed bed or fluidized bed) electrode are modeled by means of a one-dimensional model involving a primary reacting species and a simultaneous side reaction. The model equations are solved by orthogonal collocation; the time and storage requirements compare favorably to those of finite-difference methods. Experimental data obtained using a packed-bed electrode are compared with the model predictions and various methods of fitting the data are compared.     

Conforming spectral methods for Poisson problems in cuboidal domains

A Chebyshev collocation strategy is introduced for the subdivision of cuboids into cuboidal subdomains (elements). These elements are conforming, which means that the approximation to the solution isC ⁰ continuous at all points across their interfaces.     

SMB色谱分离过程计算机仿真

针对模拟移动床(SMB)综合速率模型，采用有限元法和正交配点法分别对柱向和颗粒径向模型进行离散化，利用MatLab ODE求解器对SMB过程进行数值求解。通过仿真，验证了该方法的可行性。     

Application of orthogonal collocations to some transport phenomena problems in co-axial cylinders and spheres

Collocation methods are developed for the solution of some differential equation models for transport phenomena problems in one-and two-dimensions in co-axial annuli of spherical and cylindrical shapes. General formulae are developed to obtain orthogonal polynomials over an arbitrary interval using two types of weighting functions. The convergence and accuracy of the methods are demonstrated using two test problems, i.e., calculation of effectiveness factors in (a) a spherical pellet with peripherally deposited catalyst and (b) a Raschig ring type cylindrical catalyst pellet. Comparisons of results obtained from the present methods with analytic solutions for the first-order reactions indicate good agreement. Numerical solutions are also obtained for the second-and the third-order reactions for which analytic solutions are not available. Results obtained in terms of a new Thiele modulus involving the ratio of volume of peripherally deposited part of catalyst to exterior surface area indicate that this normalization brings effectiveness factor versus Thiele modulus curves close together for co-axial spherical and long cylindrical pellets, as it does for these geometries without the inner co-axial portion.     

基于配点型无网格法的金属挤压过程数值模拟

阐述了配点型无网格法的基本原理,及其用于求解偏微分方程的步骤和方法,对Al在挤压成形过程中的塑性变形情况进行了三维无网格法模拟。该方法避免了有限元法因网格畸变需要重新划分网格的问题,同时解决了伽辽金型无网格法计算效率低的问题。计算实例表明,配点型无网格法可以利用初始节点完成全部计算,得到与有限元法相吻合的结果,是模拟金属塑性变形过程的一种有效的新方法。     

基于遗传算法的航空弹药保障人员优化配置

航空弹药保障任务中人员合理高效的配置是一个多约束条件下的组合优化问题。在建立保障人员配置模型的基础上,通过操作因子对模型的合理描述,应用遗传算法对模型进行优化求解,得到合理的保障人员数量和最优的保障人员配置方案。实例仿真验证了模型的正确性及算法的有效性。     

精馏过程动态机理模型建立

为了实现精馏过程的动态优化和先进控制,必须解决精确的动态数学模型的建立问题.本文介绍了精馏过程动态机理建模的方法,该模型的特点是考虑每块塔板温度、压力、汽相流量、液相流量、汽相浓度、液相浓度和持液量的动态特性,并且,利用正交配置方法离散模型方程,利用牛顿一拉夫逊方法解模型方程,研究结果表明该模型精度高,误差小于3%,适合于精馏过程的动态优化和先进控制策略研究.     

Multilevel augmentation algorithms based on fast collocation methods for solving ill-posed integral equations

This paper continues the theme of the recent work Chen et al. (2008) [18], in which fast collocation methods are introduced for solving ill-posed Fredholm integral equations of the first kind. We develop in this paper multilevel augmentation algorithms, which lead to fast solutions of the discrete equations resulting from fast collocation methods. Regularization parameter choice strategies are given for proposed methods. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.