Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions

The Kronecker tensor-product approximation combined with the -matrix techniques provides an efficient tool to represent integral operators as well as certain functions F(A) of a discrete elliptic operator A in ℝ ^d with a high spatial dimension d. In particular, we approximate the functions A ⁻¹ and sign(A) of a finite difference discretisation A∈ℝ ^{N × N} with a rather general location of the spectrum. The asymptotic complexity of our data-sparse representations can be estimated by (n ^p log ^q n), p = 1, 2, with q independent of d, where n=N ^{1/ d} is the dimension of the discrete problem in one space direction. In this paper (Part I), we discuss several methods of a separable approximation of multi-variate functions. Such approximations provide the base for a tensor-product representation of operators. We discuss the asymptotically optimal sinc quadratures and sinc interpolation methods as well as the best approximations by exponential sums. These tools will be applied in Part II continuing this paper to the problems mentioned above.     

Convergence Results of One-Leg and Linear Multistep Methods for Multiply Stiff Singular Perturbation Problems

One-leg methods and linear multistep methods are two class of important numerical methods applied to stiff initial value problems of ordinary differential equations. The purpose of this paper is to present some convergence results of A-stable one-leg and linear multistep methods for one-parameter multiply stiff singular perturbation problems and their corresponding reduced problems which are a class of stiff differential-algebraic equations. Received April 14, 2000; revised June 30, 2000     

L ∞-error estimates of higher order mixed finite element approximations for elliptic optimal control problems

In this paper, we investigate the L ^∞-error estimates of the numerical solutions of linear-quadratic elliptic control problems by using higher order mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k≥1). Optimal L ^∞-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for optimal control problems.     

65米射电望远镜副面调整系统姿态精度监测与回零策略

上海天文台65米射电望远镜的副面调整机构为Stewart型并联机器人,为了及时发现该并联机器人因机械磨损或误差累积造成的精度下降问题,使用倾角传感器对并联机器人动平台姿态进行检测,求得动平台姿念均方根误差并将其与设计指标进行比较,从而用户可以判断是否需要进行维修或回零操作.为了提高并联机器人的易维护性,设计了光电传感器回零和磁尺(磁致伸缩位移传感器)回零两种回零方式,分析了两种回零方式以及通过回零操作对光电传感器和磁尺精度进行检测的原理.总结了该并联机器人需要进行回零操作的不同状况,并给出了相应的回零控制策略.实验证明本文提出的回零控制策略是解决并联机器人回零问题的一种有效方法.     

Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations

h –p–adaptive projection with respect to any prescribed threshold value for the visual error. This projection can then be processed by various local rendering methods, e.g. color coding of data or isosurface extraction. Especially for color coding purposes modern texture capabilities are used to directly render higher polynomial data by superposition of polynomial basis function textures and final color look-up tables. Numerical experiments from CFD clearly demonstrate the applicability and efficiency of our approach. Received September 25, 2001; revised March 31, 2003 Published online: May 26, 2003 The authors acknowledge the valuable hints of the anonymous referees.     

Numerical integration of singular integrands using low-discrepancy sequences

We investigate quasi-Monte Carlo integration for functions on thes-dimensional unit cube having point singularities. Error bounds are proved and the theoretical results are verified by computations using Halton, Sobol’ and Niederreiter sequences. Supported by the Austrian Science Foundation (Project 10223-PHY).     

Discrete least-squares technique for eigenvalues. Part I: The one-dimensional case

A discrete least-squares technique for computing the eigenvalues of differential equations is presented. The eigenvalue approximations are obtained in two steps. Firstly, initial approximations of the desired eigenvalues are computed by solving a quadratic matrix eigenvalue problem resulting from the least-squares method applied to the equation under consideration. Secondly, these initial approximations, being of sufficient accuracy in some cases, are improved by using the Gauss-Newton method. Results from numerical experiments are reported that show great efficiency of the proposed technique in solving both regular and singular one-dimensional problems. The high flexibility of the technique enables one to use also the multidomain approach and the trial functions not satisfying any of the prescribed boundary conditions.     

Q345E低合金高强度钢Φ600 mm连铸圆坯的生产实践

Q345E钢(/%:0.14~0.17C、0.20~0.30Si、1.28~1.38Mn、≤0.011P、≤0.005S、0.015~0.030Al、0.032~0.045V)大圆坯的生产流程为65 t LD-LF-VD-Φ600 mm圆坯CC工艺。通过出钢时滑板挡渣,加入预熔合成渣(/%:40~50CaO、≤9SiO₂、30~40Al₂O₃~7MgO、8~10Al)、钢芯铝、脱氧剂和合金,控制拉速0.22 m/min,32 t中间包钢水过热度(25±5)℃,恒液面900 mm,全程保护浇铸和电磁搅拌等措施,试生产法兰用Q345E钢Φ600mm连铸圆坯。生产结果表明,铸坯表面无可见冷疤、鼓肚等缺陷,中心缩孔0.5级,中心疏松1.0级,碳偏析≤1.09,-50℃低温冲击功超过100 J,完全满足标准要求。     

热轧材冷拉过程65钢硬线断裂分析

65钢(/%:0.62～0.。70C、0.18～0.28Si、0.55～O.75Mn)硬线盘条的生产流程为120 t转炉-LF-170mm×170 mm连铸-高速线材轧制。采用光学和扫描电子显微镜分析了65钢φ6.5 mm热轧盘条在冷拉至φ1.85mm过程中断裂的原因。实验结果表明,断口宏观特征为笔尖状,盘条横截面组织均匀性较差;裂纹起源于心部粗大的先共析铁素体和粗片状渗碳体,断裂的主要原因是索氏体化率低,存在大块先共析铁素体和中心碳偏析。     

不同厂家直缝埋弧焊钢管的主要性能差异

通过对比测试采用不同厂家生产的钢板制成同规格、同钢级JCOE钢管成分、拉伸和冲击等性能,同时分析了不同厂家钢管的主要性能差异。结果表明,国内钢厂钢管比国外钢厂钢管具有较好的强度和低温夏比冲击韧性,其中钢管的屈服强度比国外钢厂钢管的屈服强度高33MPa,其母材冲击功比国外钢厂的要高107J;同时从基体成分分析了直缝埋弧焊管强度和韧性高于国外钢厂焊管的原因。