分子积分中辅助函数的任意精度计算(Ⅲ)——不完全Gamma函数Fm(x)向后递推算法的优化

对不完全Gamma函数F_m(x)两种向后递推算法(级数展开和连分式逼近)进行了严格的误差分析.论证了这两种算法的稳定条件,给出了总体优化方案,并对数值实验结果进行了讨论.     

任意精度的三点紧致显格式及其在CFD中的应用

通过在泰勒级数展开中运用逐阶迭代的方法,推导出了空间任意精度的三点紧致显格式的表达式,又由Fourier分析法得到了格式的数值弥散和耗散特性．与以往的高精度紧致差分格式不同,提出的格式不用隐式求解代数方程组并且可以达到任意精度．通过方波问题和顶盖方腔流的算例表明,格式在稀疏网格下可以得到很高的精度,不仅能节省计算量,而且易于编程,有很高的计算效率．     

粗糙集理论中近似空间的精细及近似精度

讨论了近似空间的精细与粗糙的概念及其两个等价描述,研究了给定集合的上下近似集在精细与粗糙近似空间中的性质,即随着近似空间的加细,给定集合X的最佳下近似单调上升、最佳上近似单调下降．还讨论了近似精度问题,指出Pawlak近似精度的一个不舍理现象,并且新定义了一种近似精度．     

Two nonlinear models of a transversely vibrating string

Modeling transverse vibration of nonlinear strings is investigated via numerical solutions of partial-differential equations and an integro-partial-differential equation. By averaging the tension along the deflected string, the classic nonlinear model of a transversely vibrating string, Kirchhoff’s equation, is derived from another nonlinear model, a partial-differential equation. The partial-differential equation is obtained via neglecting longitudinal terms in a governing equation for coupled planar vibration. The finite difference schemes are developed to solve numerically those equations. An index is proposed to compare the transverse responses calculated from the two models with the transverse component calculated from the coupled equation. A steel string and a rubber string are treated as examples to demonstrate the differences between the two models of transverse vibration and their deviation from the full model of coupled vibration. The numerical results indicate that the differences increase with the amplitude of vibration. Both models yield satisfactory results of almost the same precision for vibration of small amplitudes. For large amplitudes, the Kirchhoff equation gives better results.     

计算机软硬件配置对有限元计算速度和精度的影响

针对有限元模拟,如发展板材轧制快速有限元计算对计算精度和计算速度的不断提高,研究了快速发展的计算机软硬件条件对计算速度和计算精度的影响.自行开发了板材轧制刚塑性有限元程序,选用了1台工作站和4台不同硬件配置PC机,装有三种常用操作系统windows,Linux,IRIX,分析了计算机软硬件对板材轧制有限元计算精度如轧制力和前滑,和对计算时间和迭代次数的影响.提出了有限元计算的合理计算机配置,为有限元模拟计算机配置的选择提供参考,并为板材轧制高精度的快速在线计算提供计算机软硬件平台.     

A novel four-node quadrilateral element with continuous nodal stress

Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress（Q4-CNS）are presented.Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element（FE-LSPIM QUAD4）, which is a hybrid FE-meshless method.Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation.It is found that,compared with the standard four-node quadrilateral element（QUAD4）,Q4- CNS can achieve significantly better accuracy and higher convergence rate.It is also found that Q4-CNS exhibits high tolerance to mesh distortion.Moreover,since derivatives of Q4-CNS shape functions are continuous at nodes,Q4-CNS is potentially useful for the problem of bending plate and shell models.     

TWO-GRID DISCRETIZATION SCHEMES OF THE NONCONFORMING FEM FOR EIGENVALUE PROBLEMS

This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou （Math. Comput., 70 （2001）, pp.17-25） to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly.     

一种高精度偏振遥感探测方式的精度分析

检偏器的角度误差是影响偏振遥感探测精度的重要因素之一,是许多高精度定量化偏振遥感需要考虑的一个问题。在检偏器(0°,60°,120°)放置的测量系统中,当入射光偏振角接近于0°或180°时偏振测量易产生最大误差值,而偏振角接近30°,90°和150°时,偏振度的测量具有很高的精度;在检偏器(0°,45°,90°)放置方式中,偏振角接近45°的光束测量易具有最大误差值,而偏振角接近于0°,90°和135°时,角度误差对偏振度测量精度的影响很小。除了个别偏振角外,对高偏振度入射光束的偏振测量通常具有较大的偏振测量误差。因此,引进线偏振光的平均偏振度测量精度描述偏振测量装置的优劣,结果表明检偏器(0°,60°,120°)放置方式优于检偏器(0°,45°,90°)放置方式。     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.