Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. De Prenter et al. [Computer Methods in Applied Mechanics and Engineering, 316 (2017) pp. 297–327] present an analysis for symmetric positive definite (SPD) immersed problems, and for this class of problems an algebraic precondition...

Isogeometric analysis is a novel approach to numerical simulation that has the potential to bridge the gap between geometric design and numerical analysis. It uses the same exact geometry representation in all stages of the product development. In this paper we present recent results which demonstrate the competitiveness of the new concept in an industrial environment, more precisely, in the ch...

Isogeometric analysis is a quickly emerging alternative to the standard, polynomialbased finite element analysis. It is only the question of time, when it will be implemented into major software packages and will be intensively used by engineering community to the analysis of complex realistic problems. Computational demands of such analyses, that may likely exceed the capacity of a single comp...

Isogeometric analysis (IGA) aims to bridge the geometric divide between CAD systems and FEA software tools. It is founded on the idea of using the same basis functions to represent the CAD geometry and to approximate the physical quantities appearing in analysis. It promises to revolutionize the design and analysis processes for automobile, aerospace and marine industry by eliminating the need ...

In the present paper, an approach is proposed for structural topology optimization based on combination of Radial Basis Function (RBF) Level Set Method (LSM) with Isogeometric Analysis (IGA). The corresponding combined algorithm is detailed. First, in this approach, the discrete problem is formulated in Isogeometric Analysis framework. The objective function based on compliance of particular lo...

In the Isogeometric Analysis framework for treating realistic problems, it is usually necessary to decompose the domain into volumetric subdomains (patches). At the end of the procedure for constructing suitable parametrization mappings for the subdomains, the control points related to interfaces may not appropriately match resulting in non-matching parametrized interfaces. In this case, gap re...

This paper presents a method for isogeometric analysis using rational Triangular Bézier Splines (rTBS) where optimal convergence rates are achieved. In this method, both the geometry and the physical field are represented by bivariate splines in Bernstein Bézier form over the triangulation of a domain. From a given physical domain bounded by NURBS curves, a parametric domain and its triangulati...

We present an introduction to Isogeometric Analysis, a new methodology for solving partial differential equations (PDEs) based on a synthesis of Computer Aided Design (CAD) and Finite Element Analysis (FEA) technologies. A prime motivation for the development of Isogeometric Analysis is to simplify the process of building detailed analysis models for complex engineering systems from CAD represe...

We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element-wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T-splines are used for the description of the geometry as well...