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Adaptive isogeometric analysis by local \(h\)-refinement with T-splines. (English) Zbl 1227.74125

Summary: Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead. T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM. Obeying a few straightforward rules, rectangular patches in the parameter space of the T-splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry. Furthermore, it is shown how state-of-the-art a posteriori error estimation techniques can be combined with refinement by T-splines. Numerical examples underline the potential of isogeometric analysis with T-splines and give hints for further developments.

MSC:

74S99 Numerical and other methods in solid mechanics
76M99 Basic methods in fluid mechanics
65D07 Numerical computation using splines

Software:

ISOGAT; ALBERTA
Full Text: DOI

References:

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