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Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes
发布时间：2025-04-30
点击次数：
- 发布时间：
- 2025-04-30
- 论文名称：
- Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes
- 发表刊物：
- Computer Methods in Appl Mech and Engng
- 摘要：
- In the partition of unity (PU)-based methods, the global approximation is built by multiplying a partition of unity by local approximations. Within this framework, high-order approximations are achieved by
directly adopting high-order polynomials as local approximations, and therefore nodes along sides or inside elements, which are usually adopted in the conventional finite element methods, are no more required. However, the PU-based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom. In this paper, the origin of the rank deficiency in the PU-based approximation space is first dissected at an element level, and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency. Finally, examples are investigated to validate the present approach. The current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix. It can be resolved in its own manner.
- 合写作者：
- X.M. An, L.X. Li, G.W. Ma, H.H. Zhang
- 卷号：
- 200
- 页面范围：
- 665-674
- 是否译文：
- 否
- 发表时间：
- 2011-10-18
