Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

International Journal for Numerical Methods in Engineering - Tập 114 Số 10 - Trang 1131-1159 - 2018
Elena Atroshchenko1, Satyendra Tomar2, Gang Xu3, Stéphane Bordas2,4
1Department of Mechanical Engineering, University of Chile. Santiago, Chile
2Institute of Computational Engineering, Faculty of Sciences Communication and Technology, University of Luxembourg, Luxembourg City, Luxembourg
3Hangzhou Dianzi University, Hangzhou, China
4Institute of Mechanics and Advanced Materials, School of Engineering, Cardiff University, Cardiff, UK

Tóm tắt

SummaryThis paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer‐aided design geometry (for example, given by nonuniform rational B‐splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T‐splines, LR‐splines, (truncated) hierarchical B‐splines, and PHT‐splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer‐aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

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Thông tin xuất bản

International Journal for Numerical Methods in Engineering

Tập 114 Số 10

1131-1159

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