Adaptive isogeometric analysis using rational PHT-splines

Authors:
Ping Wang;Jinlan Xu;Jiansong Deng;Falai Chen
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China and Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Venue:
Computer-Aided Design
Year:
2011

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Abstract

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.