An adaptive isogeometric method based on d-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In this paper we provide a complexity estimate, i.e., an estimate on how the number of mesh elements grows with respect to the number of elements that are marked ...

We propose a discontinuous Galerkin Isogeometric Analysis method for the numerical solution of elliptic diffusion problems on decompositions into volumetric patches with non-matching interfaces. Indeed, due to an incorrect segmentation procedure, it may happen that the interfaces of adjacent subdomains don’t coincide. In this way, gap regions, which are not present in the original physical doma...

Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameterizations of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings of airplanes. The second part of the p...

We derive Newton-type solution algorithms for a Bernoulli-type freeboundary problem at the continuous level. The Newton schemes are obtained by applying Hadamard shape derivatives to a suitable weak formulation of the freeboundary problem. At each Newton iteration, an updated free boundary position is obtained by solving a boundary-value problem at the current approximate domain. Since the boun...

This paper presents the use of Powell-Sabin splines in the context of isogeometric analysis for the numerical solution of advectiondiffusion-reaction equations. Powell-Sabin splines are piecewise quadratic C functions defined on a given triangulation with a particular macro-structure. We discuss the Galerkin discretization based on a normalized Powell-Sabin B-spline basis. We focus on the accur...

Polynomial splines over hierarchical T-meshes (PHT-splines) have an efficient and simple local refinement algorithm, but fail to represent exactly certain complex engineering geometries. In this paper, based on the current isogeometric framework, we overcome the drawbacks of PHT-splines by extending these to Rational PHT-splines (RPHT-splines), and explore RPHT-splines as the basis for analysis...

A linear full elliptic second order Partial Differential Equation (PDE), defined on a d-dimensional domain Ω, is approximated by the isogeometric Galerkin method based on uniform tensor-product Bsplines of degrees (p1, . . . , pd). The considered approximation process leads to a d-level stiffness matrix, banded in a multilevel sense. This matrix is close to a d-level Toeplitz structure when the...

This paper describes multi-thread parallel open source JAVA implementation of alternating directions isogeometric L2 projections solver. The solver enables for fast numerical simulations of time-dependent problems. To apply our solver, the time-dependent problem must be discretized using isogeometric finite element method with B-spline basis functions in the spatial domain. The problem is solve...

The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows to overcome these difficulties by using a unique geometrical representation that yields a direct relationship...