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arXiv · 1404.4346

Hierarchical analysis-suitable T-splines: Formulation, B\'{e}zier extraction, and application as an adaptive basis for isogeometric analysis

Emily J. Evans·Michael A. Scott·Xin Li·Derek C. Thomas
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Abstract

In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of T-spline spaces results in simple, highly localized refinement algorithms which can be utilized in a design or analysis context. A detailed theoretical formulation is presented including a proof of local linear independence for analysis-suitable T-splines, a requisite theoretical ingredient for HASTS. B\'{e}zier extraction is extended to HASTS simplifying the implementation of HASTS in existing finite element codes. The behavior of a simple HASTS refinement algorithm is compared to the local refinement algorithm for analysis-suitable T-splines demonstrating the superior efficiency and locality of the HASTS algorithm. Finally, HASTS are utilized as a basis for adaptive isogeometric analysis.

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Emily J. Evans, Michael A. Scott, Xin Li, Derek C. Thomas. 2014-04-16. Hierarchical analysis-suitable T-splines: Formulation, B\'{e}zier extraction, and application as an adaptive basis for isogeometric analysis. https://doi.org/10.1016/j.cma.2014.05.019

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