Quadratic B-spline Functions Research Articles

The quadratic finite element/strip with generalized degrees of freedom and their application

This paper presents a quadratic finite element with generalized degrees of freedom (GDOF) and a quadratic finite strip with GDOF based on the principle that the local displacement fields of elements should be compatible with the global displacement field of the corresponding systems. Firstly, a global displacement field is developed using quadratic B-spline functions. Secondly, local displacement fields of elements and strips are constructed, employing multi-term interpolation polynomials of second degree. Making the local displacement fields of elements and strips be compatible with their corresponding global displacement fields, respectively, models of the finite element with GDOF and the finite strip with GDOF are accordingly generated. On the other hand, the quadratic B-spline function is convenient to derive the explicit form of characteristic equations for computing model because of its lower order, and accordingly simplifies the computation, compared with cubic and quintic spline functions. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present element and strip in the analysis of thin-walled structures.

Least-squares quadratic B-spline finite element method for the regularised long wave equation

An approximate solution consisting of a combination of the quadratic B-spline functions is incorporated into the least-squares method. An application of this method is presented for computing the solution of the Regularised Long Wave (RLW) equation. Quadratic B-spline solution of the RLW equation leads to tridiagonal matrix system which is solved easily by using the Thomas algorithm. Performance of this scheme is tested by obtaining a solitary wave solution of the equation and by studying the development of the undular bore. Numerical results of the proposed algorithm is shown to have higher accuracy in terms of L 2-error norm compared studying the migration of the solitary wave. A Fourier stability analysis of the method is investigated.

Complexity reduction in radial basis function (RBF) networks by using radial B-spline functions

In this paper, new basis consisting of radial cubic and quadratic B-spline functions are introduced together with the CORDIC algorithm, within the context of RBF networks as a means of reducing computational complexity in real-time signal-processing applications. The new basis are compared with two other existing and popularly used basis families, namely the Gaussian functions and the inverse multiquadratic functions (IVMQ) in terms of approximation performance and computational requirements. The new basis are shown to achieve approximation performance very similar to the Gaussian basis functions and are better than the IVMQ functions with less computational load and without any need for approximation methods such as table-lookup.

A new numerical technique for calculating current distributions on curved wire antennas - parametric B-spline finite element method

A new numerical technique is presented for calculating the current distributions on wire antennas with a high degree of curvature. The geometry of the wire antenna is expressed by a parametric equation and the current is directly expanded into a series of quadratic B-spline basis functions of the parameter, so that the truncation error in modeling the curved wire structure is avoided. This algorithm is used to analyze a circular loop antenna, a conical equiangular-spiral antenna, and a four-arm Archimedian spiral antenna to demonstrate its validity and practical value.

Extension of spline wavelets element method to membrane vibration analysis

The B-spline wavelets element technique developed by Chen and Wu (1995a) is extended to the membrane vibration analysis. The tensor product of the finite splines and spline wavelets expansions in different resolutions is applied in the development of a curved quadrilateral element. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions is transformed into edges and internal modes via elemental geometric conditions and “two-scale relations”. The “multiple stages two-scale sequence” of quadratic B-spline function is provided to accelerate the sequential transformations between different resolution levels of wavelets. The hierarchical property of wavelets basis approximation is also reserved in this extension. For membrane vibration problems where variations lack regularity at certain lower vibration modes, the present element can still effectively provide accurate results through a multi-level solving procedure. Some numerical examples are studied to demonstrate the proposed element.

A smooth signal generator based on quadratic B-spline functions

A hardware system of quadratic spline interpolation is proposed. Its properties are that switching noise with digital-to-analog (D-A) converter chips does not appear and that the output is smooth without any analog lowpass filters that disorganize the phase characteristics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Automatic curve fitting with quadratic B-spline functions and its applications to computer-assisted animation

Automatic fitting to digitized curves by quadratic B-spline functions is discussed. Due to its simplicity, it is possible to find a quick fit within a given error tolerance bound which is defined as the maximum distance between the fitted curve and the original curve. Again due to the simple form of a quadratic polynomial, some complicated computations in computer-assisted animation such as hidden line removal can also be easily handled.

Automatic curve fitting with Quadratic B-spline Functions and its applications to computer-assisted animation

Automatic curve fitting with Quadratic B-spline Functions and its applications to computer-assisted animation