Multi-patch parameterization method for isogeometric analysis using singular structure of cross-field

Journal Article (2024)
Author(s)

Yi Zhang (Dalian University of Technology)

Ye Ji (Dalian University of Technology)

Chun Gang Zhu (Dalian University of Technology)

Affiliation
External organisation
DOI related publication
https://doi.org/10.1016/j.camwa.2024.03.001
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Publication Year
2024
Language
English
Affiliation
External organisation
Volume number
162
Pages (from-to)
61-78

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.

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