电-热多物理场耦合的对偶有限元分析

Dual finite element methods for stationary electro-thermal coupling analysis

随着集成电路、微机电系统的快速发展,各种物理场的交互作用成为影响电路可靠性或者增加设计难度的重要问题。其中,大量工程应用中都会发生稳恒电流场和热场的相互作用。电流场产生的焦耳热与电阻率的温变特性是这两个物理场之间双向相互耦合的联系因素。当几何结构复杂时,分析该多物理场问题会有计算方面的挑战。通常利用有限元法来求解多物理问题,其中采取节点单元法来处理电流场。本论文首先在多物理耦合分析中实现了棱边单元法来分析电流场,并通过一个典型的微阻梁算例问题,与常规方法进行充分对比,考察了随着网格加密、与热场耦合迭代深度的对偶特点及收敛特性。

With the rapid development of integrated circuits and MEMS,the interaction among multiple physical fields has become one of importance issues. The interaction between steady direct current field and thermal field occurs in various engineering applications. The fields are mutually two-way coupled due to the heat generated by electric current and temperature-dependent resistivity. It is a computational challenge to analyze such multiphysics problems when the geometric structures are complicated. The finite element method is usually adopted to solve multiphysics problems while the nodal element method is used for current field. The vector element method is firstly used and implemented in multiphysics coupling analysis to analyze the current field in the paper. It is fully compared to the traditional nodal method through a micro-resistor beam benchmark problem. The complementarity of dual finite element formulations of steady current field,the performance and convergence are investigated and demonstrated along with the enrichment of mesh and the iteration depth of electro-thermal coupling.