This paper deals with an adaptive finite element method originally developed by Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, we investigate the extension of the adaptive algorithm for isogeometric analysis performed with B-spline basis functions. We restrict ourselves to h-adaptivity, since the polynomial order of approximation must be fixed in the isogeometric case. ...

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local h-refinement and quadrilateral meshes. In THU-spline construction, an mesh is taken as the input control mesh, where degenerated-patch [20] adopted in irregular regions to define $$C^1$$ -continuous bicubic splines, whereas regular only involve $$C^2$$ B-splines. Irregular are then...

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials local support, B-splines shows its advantages when intensive numerical computations involved the subsequent applications. To obtain an optimal B-splines, we need to select bandwidth (i.e., distance of two adjacent knots) for uniform B-spline...

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

In this paper, we suppose that a density of probability f is expressed as a finite linear combination of second order B-spline functions. Then, we obtain a finite mixture of B-spline. We extend the Expectation Maximization (EM) algorithm in order to estimate the new mixture density. The experiments show that the proposed estimator using B-spline functions can produce a satisfactory estimation o...