Adaptive isogeometric analysis using rational PHT-splines

Polynomial splines over hierarchical T-meshes (PHT-splines) have an efficient and simple local refinement algorithm, but fail to represent exactly certain complex engineering geometries. In this paper, based on the current isogeometric framework, we overcome the drawbacks of PHT-splines by extending these to Rational PHT-splines (RPHT-splines), and explore RPHT-splines as the basis for analysis. A residual-based posteriori error estimator using RPHT-splines basis functions is derived to guide the local refinement process adaptively. Numerical examples show the potential of RPHT-splines as the basis for the adaptive isogeometric analysis. (C) 2011 Elsevier Ltd. All rights reserved.