This paper presents an adaptive multi-patch isogeometric framework for modeling heat conduction in isotropic/orthotropic media. The proposed adaptive scheme is a novel combination of local mesh refinement and adaptive time-stepping to improve the calculation efficiency and reduce meshing burden. The local adaptive refinement is driven by a recovery-based error estimator. Truncated hierarchical NURBS (TH-NURBS) are utilized for local adaptive mesh refinement due to their excellent properties, such as linear independence, partition-of-unity, and exact description of complex geometry. Multi-patch technique is applied to model complex structures, with Nitsche’s method as the coupling strategy. The computational accuracy of the proposed model is verified through several 3D numerical examples. The high efficiency of the adaptive scheme is demonstrated by comparing with uniform refinement method and fixed time-stepping method separately.

中文翻译：

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三维固体传热的自适应多面片等几何分析


本文提出了一个自适应多面片等几何框架，用于模拟各向同性/正交各向异性介质中的热传导。所提出的自适应方案是局部网格细化和自适应时间步进的新颖组合，旨在提高计算效率并减轻网格划分负担。局部自适应优化由基于恢复的误差估计器驱动。截断分层 NURB （TH-NURBS） 具有线性独立性、单位分割和复杂几何结构的精确描述等优异特性，因此用于局部自适应网格细化。多补丁技术应用于对复杂结构进行建模，以 Nitsche 的方法作为耦合策略。通过几个三维数值算例验证了所提模型的计算精度。通过与均匀细化法和固定时间步进法的分别比较，证明了自适应方案的高效率。