The paper presents a Bézier triangle based isogeometric shape optimization method. Bézier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, a coarse Bézier triangular parameterization is automatically generated. This coarse mesh is used to maintain parameterization quality and move mesh by solving a pseudo linear ela...

We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider two types of singular parameterizations, domains where a part of the boundary is mapped onto one point and do...

We present a novel technique for segmenting a three-dimensional solid with a 3-vertex-connected edge graph consisting of only convex edges into a collection of topological hexahedra. Our method is based on the edge graph, which is defined by the sharp edges between the boundary surfaces of the solid. We repeatedly decompose the solid into smaller solids until all of them belong to a certain cla...

Acknowledgements I would like to express my gratitude to Professor Alfio Quarteroni, who gave me the possibility to work within the Chair of Modeling and Scientific Computing (CMCS) to my Master Project, and to Luca Dedè, who was very supportive during these months and always available to provide valuable advice and ideas. My thanks go to everyone in the CMCS group, in particular to Andrea and ...

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary twodimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize current l...

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions appear, for instance, in domains with re-entrant corners on the boundary of the computational domain, in problems with changing boundary conditions, in interfa...

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping sub...

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...

This paper presents an approach for isogeometric analysis of 3D objects using rational Bézier tetrahedral elements. In this approach, both the geometry and the physical field are represented by trivariate splines in Bernstein Bézier form over the tetrahedrangulation of a 3D geometry. Given a NURBS represented geometry, either untrimmed or trimmed, we first convert it to a watertight geometry re...

A comprehensive scheme is described to construct rational trivariate solid T-splines from boundary triangulations with arbitrary topology. To extract the topology of the input geometry, we first compute a smooth harmonic scalar field defined over the mesh, and saddle points are extracted to determine the topology. By dealing with the saddle points, a polycube whose topology is equivalent to the...