An adaptive isogeometric finite element analysis

Abstract

In this thesis we will explore the possibilities of making a finite element solver for partial differential equations using the isogeometric framework established by Hughes et al. Whereas general B-splines and NURBS only allow for tensor product refinement, a new technology called T-splines will open for true local refinement. We will give an introduction into T-splines along with B-splines and NURBS on which they are built, presenting as well a refinement algorithm which will preserve the exact geometry of the T-spline and allow for more control points in the mesh. For the solver we will apply a residual-based a posteriori error estimator to identify elements which contribute the most to the error, which in turn allows for a fully automatic adaptive refinement scheme. The performance of the T-splines is shown to be superior on problems which contains singularities when compared with more traditional splines. Moreover the T-splines along with a posteriori error estimators are shown to have a very positive effect on badly parametrized models, as it seem to make the solution grid independent of the original parametrization.