We generate a basis of the space of bicubic and biquartic C-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω ⊂ R. The basis functions are obtained by suitably combining C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [16]). They are described by simple explicit formulas for their spline coefficie...

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical ...

In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the original implementation based on the nowadays standard and wellestablished numerical solution technique, the finite element method. The isogeometric removes the nee...

Isogeometric analysis, as a special field of the finite element method (FEM) which integrates geometric and finite element mesh modelling, is one of the promising directions of FEM development. The paper presents a concept of isogeometric FEM analysis of thin-walled structures based on the Kirchhoff-Love shell formulation and NURBS as basis functions. The basic properties of isogeometric shell ...

One primary problem in shape optimization of structures is making a robust link between design model (geometric description) and analysis model. This paper investigates the potential of Isogeometric Analysis (IGA) for solving this problem. The generic framework of shape optimization of structures is presented based on Isogeometric analysis. By discretization of domain via NURBS functions, the a...

We study the linear space of C-smooth isogeometric functions defined on a multi-patch domain Ω ⊂ R. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the C-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (G-smoot...

Article history: Received 20 February 2015 Accepted 11 March 2015 Available online 24 March 2015

We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of Bsplines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear ...

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In this paper the isogeometric Nyström method is presented. It’s outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only pointwise function evaluations just like isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral...