The fast solution of linear systems arising from an isogeometric discretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid solver is naively applied to a linear sys...

We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a threedimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configurati...

‎in this paper we introduce a numerical approach that solves optimal control problems (ocps)‎‎using collocation methods‎. ‎this approach is based upon b-spline functions‎.‎the derivative matrices between any two families of b-spline functions are utilized to‎‎reduce the solution of ocps to the solution of nonlinear optimization problems‎.‎numerical experiments confirm our theoretical findings‎.

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental re...

Stitching or merging B-spline curves is a frequently used technique in geometric modeling, and is usually implemented in CAD-systems. These algorithms are basically numerical interpolations using the least squares method. The problem, how to replace two or more curves which are generated separately and defined as B-spline curves, has well functioning numerical solutions, therefore, relatively f...