Adaptive refinement of hierarchical T-splines

Abstract

We present an adaptive local refinement technique for isogeometric analysis based on hierarchical T-splines. An element-wise point of view is adopted, which exploits Bézier extraction, and allows adaptive refinement of standard hierarchical T-splines and truncated hierarchical T-splines in a straightforward and unified manner. No explicit basis function operations are required to build the hierarchical basis function space, as only matrix manipulations are involved. This makes the efficiency superior to that of existing implementations. In particular, the implementation of truncated hierarchical T-splines requires no explicit truncation of the basis functions. In the analysis, a multi-level T-mesh is constructed by successive cell subdivisions of an initial, coarse T-mesh. An important feature is that Bézier extraction is employed to compute the refinement operator between two successive hierarchical levels, and that, at each level, Bézier extraction is applied to obtain the stiffness matrix without, initially, considering multi-level interaction. This interaction is recovered through a subdivision operator. Numerical examples are presented for validation purposes, and to assess the convergence properties.