• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.355-360
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• 2000

This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"＋ λ²u＝0, u(0.0)＝u(0.0)＝0, 0≤x≤1.0.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.1-8
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• 1998

We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.5 no.1
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• pp.40-45
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• 2002

The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.21-27
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• 1991

This paper outlines the method of formulating the bi-cubic B-spline surface of ship hull, employing the open uniform knot vector as well as the periodic uniform knot vector. An appropriate set of B-spline control vertices to generate the B-spline surface is determined by obtaining the pseudoinverse matrix of basis functions. The comparison between the given offsets and the resulting coordinates from the generated ship hull surface shows a good agreement. To check the fairness of the surface Gaussian curvature is calculated on many small subpatches and displayed on the black-and-white plot of the isoparametric net of the surface.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.492-495
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• 2001

In order to utilize a parallel machine tool for CAM system, the development of adequate interpolator is necessary. This paper presents a quintic B-spline interpolator with algorithm of limiting maximum interpolation error. The favored property of near arc-length parametrization in the curve representation is used in the implementation of the reference command generation. Then, this interpolator is applied to cubic parallel manipulator to show its validity.

• East Asian mathematical journal
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• v.33 no.1
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.31-37
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• 1994

When a lot of input data are not distributed uniformly n a chord-span direction or when the given shape is complicated, it is very difficult to obtain an inverse matrix which represents the smooth Bi-cubic B-spline surface of the initial shape. To overcome this problem, we suggest image Surface Expansion Method(ISE Method) which is suggested for vertex creation of B-spline curves and surfaces. Its basic concept, convergency and verification are shown. Also B-spline curves and Surfaces represented by ISE Method were compared with those represented by the existing method which is based on the inverse matrix method, the pseudoinverse matrix method and the chord length approximation method for vertex yielding. Ship Hull Forms which have Knuckle, Bulbous Bow, Transom and Stern frame were represented by the ISE Method.

• Journal of Advanced Navigation Technology
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• v.9 no.1
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• pp.41-47
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• 2005

In this paper, the performances of various channel estimation schemes for DVB-H system are investigated. The linear interpolation, the second order interpolation, the cubic spline interpolation, and the time-domain interpolation, which are used in frequency domain, are chosen as the channel estimation schemes. We derived the performances of Mean Square Error (MSE), Bit Error Rate (BER), and the complexity of calculation in Rayleigh and Rician fading channel through computer simulations. From the simulation results, the cubic spline interpolation shows the best performance under high $E_b/N_0$ environments.