A Difference Subgridding Method for Solving Multiscale Electro-Thermal Problems

Abstract

Because of less memory costs and time consumption, a finite difference subgrid technique can effectively deal with multiscale problems in electromagnetic fields. When used in Maxwell equation, symmetric elements of the matrix are required; otherwise, the algorithm will be unstable. Usually, the electro-thermal problem also contains multiscale structures. However, the coefficient matrix of the heat transfer equation is asymmetric because the parameters of the equation vary with temperature and the Robbin boundary condition is used as well. In this paper, a three-dimensional (3D) finite difference subgridding method is proposed to simulate the electro-thermal coupling process of the multiscale circuits. The stability condition of the algorithm is deduced with a matrix method. And the efficiency and the effectiveness of the proposed subgridding approach are verified through square- and n-shaped resistances. Compared with the results of the COMSOL software and the traditional finite difference method (FDM), the proposed subgridding method has less unknowns and faster speed.