The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities ...

We study minimal energy interpolation, discrete and penalized least squares approximation problems on the unit sphere using nonhomogeneous spherical splines. Several numerical experiments are conducted to compare approximating properties of homogeneous and nonhomogeneous splines. Our numerical experiments show that nonhomogeneous splines have certain advantages over homogeneous splines.

PHT-splines (polynomials splines over hierarchical T-meshes) are a generalization of B-splines over hierarchical T-mesheswhich possess a very efficient local refinement property. This property makes PHT-splines preferable in geometric processing, adaptive finite elements and isogeometric analysis. In this paper, we first make analysis of the previously constructed basis functions of PHT-splines...

For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

When he was growing up in the 1940s and 1950s, teachers and parents told Helaman Ferguson he would have to choose between art and science. The two fields inhabited different realms, and doing one left no room for the other. “If you can do science and have a lick of sense, you’d better,” he recalled being told, in a 2010 essay in the Notices of the American Mathematical Society (1). “Artists sta...

This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following; the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed ...

Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed. Introduction. In [9], H.B. Curry and I.J. Schoenberg have pointed out that univa...

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...