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...

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...

We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. The proposed technique only demands the surface of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and a simple parametric domain. To do that, an adaptive tetrahedral mesh of the parametric dom...

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...

Fracture analysis of orthotropic cracked media is investigated by applying the recently developed extended isogeometric analysis (XIGA) (Ghorashi et al., 2012) using the T-spline basis functions. The signed distance function and orthotropic crack tip enrichment functions are adopted for extrinsically enriching the conventional isogeometric analysis approximation for representation of strong dis...

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equatio...