发表机构
School of Mathematics and Statistics, Xidian University（西安电子科技大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种切割有限元方法，用于多材料电子封装结构的瞬态热传导模拟，通过背景网格嵌入几何特征，避免贴体网格生成，并采用Nitsche公式和幽灵惩罚稳定化，数值实验验证了其准确性、效率和可扩展性。
AI 中文摘要
先进的电子封装结构是延续摩尔定律的关键技术途径。电子封装结构由多种具有不同性质的材料组成，构成具有复杂空间架构的复合结构。本文针对具有复杂材料界面的多材料电子封装结构中的瞬态热传导模拟，提出了一种非贴体的切割有限元方法（CutFEM）。在所提出的计算框架中，电子封装结构的异质空间几何特征被嵌入并表征在规则背景网格中，从而避免了在复杂界面上生成贴体网格。界面温度和热通量传输条件通过系数加权的对称Nitsche公式施加。此外，幽灵惩罚稳定化控制了物理材料与背景网格之间任意小的相交。进一步地，提出了半离散和全离散数值格式，并详细推导了显式能量估计。最后，设计了包含基板、模塑化合物、芯片和焊球的三维电子封装结构，以验证其在模拟具有挑战性的瞬态热问题中的准确性、效率和可扩展性。
英文摘要
Advanced electronic packaging structures represent a key technological approach for extending Moore's Law. An electronic packaging structure consists of multiple materials with distinct properties, constituting a composite structure with complex spatial architecture. This paper develops an unfitted cut finite element method (CutFEM) for transient heat conduction simulation in multi-material electronic packaging structures with complex material interfaces. In the proposed computational framework, the heterogeneous spatial geometric features of electronic packaging structures is embedded and characterized in a regular background mesh, thereby avoiding the generation of body-fitted meshes on complicated interfaces. Interface temperature and heat-flux transmission conditions are imposed by a coefficient-weighted symmetric Nitsche formulation. In addition, a ghost-penalty stabilization controls arbitrarily small intersections between the physical materials and background meshes. Furthermore, the semi-discrete and fully-discrete numerical schemes are proposed, and an explicit energy estimate is derived in detail. Finally, two-dimensional and three-dimensional electronic packaging structures containing substrate, molding compound, die, and solder balls are designed to validate its accuracy, efficiency, and scalability in simulating challenging transient thermal problems.
