Object oriented implementation of the T-spline based isogeometric analysis

Isogeometric analysis has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. Initially, the isogeometric approach has been developed using the NURBS and although it has been shown that it can outperform the classical finite element method in many aspects, there are several drawbacks, namely related to the handling trimmed geometries and to the refinement of the adopted discretization. These may be overcome by extending the concept of isogeometric analysis to so-called T-splines which are a generalization of NURBS. This paper presents how the isogeometric analysis based on T-spline can be integrated within an object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality of the finite element code is reused. The missing data and algorithms are developed and implemented in such a way that the object oriented features are fully retained. The performance of the implemented T-spline based isogeometric analysis methodology is presented on a simple example.