A class of methods based on a septic non-polynomial spline function for the solution of sixth-order two-point boundary value problems

Two new second- and fourth-order methods based on a septic non-polynomial spline function for the numerical solution of sixth-order two-point boundary value problems are presented. The spline function is used to derive some consistency relations for computing approximations to the solution of this problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods up to order four and has a lower computational cost. Convergence analysis of these two methods is discussed. Three numerical examples are included to illustrate the practical use of our methods as well as their accuracy compared with existing spline function methods.     

基于曲线和曲面控制的多边形物体变形反走样

基于参数曲线和曲面控制的空间变形是重要的几何外形编辑和柔性物体动画实现手段．当这两类变形方法的对象是多边形物体时,如何对变形物体进行重采样以得到高质量结果,是计算机动画和几何造型领域中的一个重要问题．该文针对B-样条曲线和曲面控制的空间变形方法,提出了面向多边形物体的空间变形反走样方法．在该方法中,利用等距技术将B-样条曲线或曲面所张成的变形空间近似表示为张量积B-样条参数体,结合作者提出的多边形物体精确B-样条自由变形方法,实现了参数曲线和曲面控制的多边形物体变形反走样．     

Discrete cubic spline method for second-order boundary value problems

In this paper, we use discrete cubic spline based on central differences to obtain approximate solution of a second-order boundary value problem. It is shown that the method is of order 4 if a parameter takes a specific value, else it is of order 2. Two numerical examples are included to illustrate our method as well as to compare the performance with other numerical methods proposed in the literature.     

异构CAD 数据交换中样条草图的处理方法

针对现有异构CAD 系统间的产品数据交换方法对样条草图处理不足问题,提出了 支持样条草图参数化交换的草图数据交换构架。将草图数据交换分为简单参数草图数据交换和 复杂参数草图数据交换。重点分析了复杂参数草图数据交换问题,通过引入Hausdorff 距离作 为适应度评价方法,构建了基于粒子群优化求解的样条草图参数化交换算法,利用曲率自适应 学习因子来避免局部最优解,使得不同曲率区域的参数点位置合理分布。所提方法在异构CAD 系统间进行了实验测试,结果证明了本方法的有效性。     

On the use of cubic splines to solve certain circular plate problems

It is well known that the evaluation of the deformation due to a uniform load on a circular annulus that is of varying thickness and clamped at both inner and outer radii reduces to the solution of a two-point boundary value problem. A cubic spline solution to the governing equations is obtained and an accurate comparison is made with a shooting method of solution. Computing times for both methods are also compared. The evidence is that cubic spline methods are viable for the solution of problems of the type considered here.     

求解应力强度因子的样条虚边界元交替法

为求解平面裂纹问题的应力强度因子,提出基于Muskhelishvili基本解和样条虚边界元法的样条虚边界元交替法.该方法将平面内带裂纹有限域问题分解成带裂纹无限域问题与不带裂纹有限域问题的叠加.带裂纹无限域问题利用Muskhelishvili基本解法直接得出,不带裂纹有限域问题采用样条虚边界元法求解.利用该方法对复合型中心裂纹方板和I型偏心裂纹矩形板进行分析.数值结果表明该方法精度高且适用性强.     

A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh

In this paper, we propose a new two-level implicit method of order two in time and four in space directions, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear parabolic partial differential equation on a uniform mesh. We have discussed the derivation of the proposed method in detail and have also discussed the stability analysis for a model problem. We have extended the method to non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed methods.     

Weibull renewal equation solution

The existing solution methods for the Weibull Renewal Equation suffer from a lack of sufficient accuracy due to the singularity at the origin for some parameter values of the weibull density. The proposed method of solution provides accuracy to any desired degree of precision for all parameter values particularly in the singular range. The method utilizes a cubic spline approximation of the unknown renewal function and applies the Galerkin technique of integral equation solution. Gaussian quadratures are used to evaluate integrals. The singular nature of the integrand is handled by the Gauss-Jacobi quadrature. Results are compared with those obtained by simulation.     

Spline approximate solution of eighth-order boundary-value problems

We use non-polynomial spline functions to develop numerical methods for the solution of the eighth-order linear boundary-value problems. End conditions of the spline are derived. We compare our results with the results produced by decomposition method and polynomial spline method. However, it is observed that our approach produce better numerical solutions in the sense that max |e _i | is minimum.     

Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications

Nonpolynomial quintic spline functions are used to develop a numerical algorithm for computing an approximation to the solution of a system of second order boundary value problems associated with heat transfer. We show that the approximate solutions obtained by our algorithm are better than those produced by other spline and domain decomposition methods. A comparison of our algorithm with nonpolynomial quadratic spline method is discussed with the help of two numerical examples.     

Finite-difference technique based on exponential splines for the solution of obstacle problems

In this paper, we introduce a new technique based on cubic exponential spline functions for computing approximations to the solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and four and gives approximations which are better than those produced by other collocation, finite difference and spline methods. Numerical evidence is presented to illustrate the applicability of the new methods.     

基于多结点样条磨光函数的几何迭代法

几何迭代法在计算机辅助几何设计(CAGD)中有广泛地应用,为了提高传统的 B-样 条曲线插值在几何迭代中的收敛速度和迭代精度,提出了基于多结点样条磨光函数的几何迭代 法,引入多结点样条磨光函数,在曲线拟合时把多结点样条磨光方法和几何迭代方法结合,经过 磨光和迭代,在 L-BFGS 迭代算法的最优解下构造具有高逼近性的曲线拟合方法。实验结果表明, 在相同精度下,该方法不仅减少了迭代次数,且提高了迭代速度,可以用于飞机、汽车等外形设 计上,亦可用于文物、房屋等外形重构和重建,以及卫星图形图像的处理中。     

Existence,Uniqueness and Applications of the Spline Method for Functional-Differential Equation of Neutral Type

This paper presents a class of numerical method for the approximate solution for the functional-differential equation of neutral type. These methods are essentially based on the spline functions. The study of existence and uniqueness are considered of 3h-step spline function of degree m =4. Numerical examples and comparisons with other methods are given.     

A new high-resolution two-level implicit method based on non-polynomial spline in tension approximations for time-dependent quasi-linear biharmonic equations with engineering applications

Engineering with Computers - In this present work, a new two-level implicit non-polynomial spline in tension method is proposed for the numerical solution of the 1D unsteady quasi-linear biharmonic...     

三次样条构造的伪逆解法

为了提高三次样条构造的可行性, 基于矩阵的伪逆方法, 提出一种不依赖额外约束条件的三次样条构造的伪逆解法。该解法通过求解出三次样条二阶导数的最小范数解, 从而较好地构造出三次样条函数。理论分析及数值实验结果表明该三次样条构造的伪逆解法具有简单、有效等特点。综合分析各种构造解法的性质, 对各种三次样条构造解法进行归类比较, 为在实际工程计算应用中选择合适的三次样条构造解法提供了指导方向。     

分数阶B样条小波域的图像变分去噪

分数阶B样条具有分数阶逼近,可以更好地刻画图像纹理部分。将分数阶B样条小波推广到二维领域,利用分数阶B样条小波进行图像阈值去噪,提出了分数阶B样条小波域图像去噪的变分模型。同传统小波函数与全变差结合模型比较,分数阶B样条小波在保持纹理和去噪方面得到了明显改进。     

具有局部性质的球面插值样条曲线的构造

高维球面样条曲线拟合技术在计算机动画和惯性导航等领域都受到广泛地关注.实际中常需球面曲线插值给定的数据点,并要求曲线具有一定的连续性和良好的局部性质.此前的方法存在一定的局限性.为此,基于球面Bézier曲线,提出了一种仅利用插值点位置信息便可在任意维空间中构造C 2球面插值样条曲线的新方法.首先,通过映射拟合出了插值...     

The use of polynomial spline functions for the solution of system of second order delay differential equations

This paper presents the use of spline functions of polynomial form to approximate the solution of system of second order delay differential equations. The error analysis and stability of the method are theoretically investigated. A numerical example is given to illustrate the applicability, accuracy and stability of the proposed method.     

混合B样条实体模型的等几何拓扑优化

等几何拓扑优化方法将经典拓扑优化理论中的有限元分析过程更改为等几何分析计算,从而提高了拓扑优化的效率与稳定性.针对现有的等几何拓扑优化方法在处理复杂实体结构优化问题时具有一定的局限性,提出一种非结构化样条实体等几何拓扑优化方法.基于混合B样条构造技术,在非结构化六面体网格上构造具有复杂结构的样条实体,并将其作为拓扑优化...     

Collocation method for solving systems of Fredholm and Volterra integral equations

In this paper, a numerical method based on based quintic B-spline has been developed to solve systems of the linear and nonlinear Fredholm and Volterra integral equations. The solutions are collocated by quintic B-splines and then the integral equations are approximated by the four-points Gauss-Turán quadrature formula with respect to the weight function Legendre. The quintic spline leads to optimal approximation and O(h⁶) global error estimates obtained for numerical solution. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods which show that our method is accurate.