1. Multi-patch parameterization method for isogeometric analysis using singular structure of cross-field.
- Author
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Zhang, Yi, Ji, Ye, and Zhu, Chun-Gang
- Subjects
- *
ISOGEOMETRIC analysis , *PARAMETERIZATION , *BOUNDARY element methods , *COMPUTER-aided engineering , *VECTOR fields , *COMPUTER-aided design - Abstract
Isogeometric analysis is an innovative numerical paradigm with the potential to bridge the gap between Computer-Aided Design and Computer-Aided Engineering. However, constructing analysis-suitable parameterizations from a given boundary representation remains a critical challenge in the isogeometric design-through-analysis pipeline, particularly for computational domains with complex geometries, such as high-genus cases. To tackle this issue, we propose a multi-patch parameterization method for computational domains grounded in the singular structure of cross-fields. Initially, the vector field functions over the computational domain are solved using the boundary element method. The cross-field is then obtained through the one-to-one mapping between the vector field and the cross-field. Subsequently, we acquire the position information and topological connection relations of singularities and streamlines by analyzing the singular structure of the cross-field. Moreover, we introduce a simple and effective method for computing streamlines. We propose a novel segmentation strategy to divide the computational domain into several quadrilateral NURBS sub-patches. Once the multi-patch structure is established, we develop two methods to construct analysis-suitable multi-patch parameterizations. The first method is a direct generalization of the barrier function-based approach, while the second method yields smoother parameterizations by incorporating the interface control points of sub-patches into the optimization model. Numerical experiments demonstrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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