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101.
Marie-Laurence Mazure 《Numerical Algorithms》2005,39(1-3):257-288
We review the main properties of blossoms along with their important repercussions in all aspects of geometric design. Not only are they an elegant and efficient tool to express all classical algorithms, but they are also a fundamental concept, as proven by the fact that their existence is equivalent to the existence of B-spline bases.
AMS subject classification 65D17 相似文献
102.
参数定义在矩形域与三角域上的De Boor递推算法在曲面造型中得到了广泛的应用,该文介绍了矩形域与三角域上的De Boor递推算法,并研究了在控制点存在扰动与计算过程存在舍入误差的情况下对曲面计算的影响. 相似文献
103.
Alan M. Davies 《国际流体数值方法杂志》1993,16(2):105-131
The paper deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no-slip condition is used at the seabed with a flow-dependent eddy viscosity related to the depth-mean current or the bed frictional velocity. Calculations show that it is essential to accurately resolve the high-shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high-shear layers which occur in these regions. With a flow-independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow-dependent viscosity, in particular a viscosity computed from the frictional velocity, a non-linear numerical instability can occur. A method of maintaining numerical stability in this case is also described. The importance of near-bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations. The influence of stratification on the computed tidal profiles is shown in the latter part of the paper. 相似文献
104.
由原子的模型势出发,利用B样条函数方法研究了钾和铯原子的里德堡态在静电场中Stark态能级反交叉位置以及微波场中钾原子的多光子共振吸收谱.研究表明我们的结果与实验和其他理论结果符合得很好. 相似文献
105.
Mehrdad Lakestani Mehdi Dehghan Safar Irandoust-pakchin 《Communications in Nonlinear Science & Numerical Simulation》2012,17(3):1149-1162
Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper. 相似文献
106.
针对光纤振动信号受噪声干扰严重、特征提取单一和识别时间长的问题,提出了改进的局部特征尺度分解和蚁群算法优化深度置信网络的识别方法。首先,采用三次B样条函数插值拟合均值曲线改进局部特征尺度分解算法,并对原始信号进行分解得到一系列内禀尺度分量之和。其次,利用峭度因子和能谱系数构成融合指标筛选有效分量。然后,分别提取有效分量在时域、频域和时-频域的熵值特征进行融合并降维。最后,将综合特征向量馈入蚁群优化后的深度置信网络进行训练和识别,提高算法效率和识别率。采用实测数据进行实验验证,结果表明,信噪比平均提升8 dB,信号平均识别率可达95.83%,平均识别时间为0.715 s。 相似文献
107.
采用非均匀有理B样条曲面延展光学元件面形误差 总被引:1,自引:0,他引:1
在离子束抛光工艺中,为了提高驻留时间求解算法在工件边缘处的求解精度,通常需要对原始面形误差数据进行边缘虚拟延展。要求原始面形误差数据与虚拟延展面光滑拼接,并在延展区域具有可控的不确定性。非均匀有理B样条(NURBS)曲面常用在机械制造领域对复杂形状物体进行三维建模。引入非均匀有理B样条曲面并结合泽尼克(Zernike)多项式拟合对一典型的圆形光学元件面形误差自由曲面数据进行延展。通过对典型面形误差曲面延展前后的等效功率谱密度曲线分析可以看出,延展后在面形误差频率大于0.05mm-1时其面形误差改善量均大于70%;将该典型延展面应用于特定驻留时间求解算法中,使得预测加工精度的均方根值由1.18nm改善至0.19nm。这表明,采用非均匀有理B样条曲面延展光学元件面形误差能够获得光滑拼接的虚拟延展曲面,并能大大改善离子束抛光工艺中驻留时间算法的求解精度。 相似文献
108.
109.
The B-spline expansion technique and the time-dependent multilevel approach (TDMA) are used to study the interaction between a microwave field and sodium atoms. The Rydberg sodium atom energy levels of p states in zero field are calculated, and the results are in good agreement with the other theoretical ones. The time evolutions during the population transfers of the five states from n = 75 to n = 79 in different microwave fields are obtained. The results show that the coherent control of the population transfer from the lower states to the higher ones can be accomplished by optimizing the microwave pulse parameters. 相似文献
110.