The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement

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Abstract

We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element-wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T-splines are used for the description of the geometry as well as for the approximation of the solution space in the analysis. The refinement is conducted with the aid of a subdivision operator, which is computed by again exploiting the Bézier extraction operator. The concept and algorithm of an element-based adaptive isogeometric analysis are illustrated. Numerical examples are given to examine the accuracy, the convergence, and the condition number.

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de Borst, R., & Chen, L. (2018). The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement. International Journal for Numerical Methods in Engineering, 113(6), 999–1019. https://doi.org/10.1002/nme.5696

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