Adaptive isogeometric analysis by local h-refinement with T-splines |
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| Authors: | Michael R. Dörfel Bert Jüttler Bernd Simeon |
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| Affiliation: | 1. Lehrstuhl für Numerische Mathematik, Technische Universität München, Zentrum Mathematik, Boltzmannstr. 3, 85748 Garching b. München, Germany;2. Institute of Applied Geometry, Johannes Kepler University, Faculty of Natural Sciences and Engineering, Altenberger Straße 69, 4040 Linz, Austria;1. Department of Civil and Environmental Engineering, Brigham Young University, Provo, UT 84602, USA;2. Department of Physics & Astronomy, Brigham Young University, Provo, UT 84602, USA;3. Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;1. Technische Universität Dresden, Institute for Solid Mechanics, George-Bähr-Straße 3c, 01062 Dresden, Germany;2. Rheinische Friedrich-Wilhelms-Universität Bonn, Institute for Numerical Simulation, Wegelerstr. 6, 53115 Bonn, Germany;1. School of Naval Architecture & Marine Engineering, National Technical University of Athens, Greece;2. School of Engineering, Nazarbayev University, Kazakhstan;3. Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, UK;4. EPICE AROMATH, Inria, Sophia Antipolis Méditerranée, France;1. Departamento de Métodos Matemáticos, Universidade da Coruña, Campus de A Coruña, 15071, A Coruña, Spain;2. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA;3. Department of Civil Engineering and Architecture, University of Pavia, via Ferrata 3, 27100, Pavia, Italy;4. Technische Universität München–Institute for Advanced Study, Lichtenbergstraße 2a, 85748, Garching, Germany;5. Institute of Applied Mechanics–TU Braunschweig, Bienroder Weg 87, 38106 Braunschweig, Germany;1. University of Science and Technology of China, Hefei, Anhui, PR China;2. Hefei Technological University, Hefei, Anhui, PR China |
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| Abstract: | 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. |
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