Transformation Optics for Multiscale Electromagnetic–Thermal Multiphysics Simulation

In a multiphysics simulation model based on the finite-element method (FEM), the large spatial scale difference will produce a large number of grids, which makes the simulation impossible. A rapid computing method for multiscale simulation based on transformation optics is proposed to solve this problem. The fine element in the object was expanded to reduce the spatial scale difference in the object by the transformation optics, and the number of grids and the computation time can be reduced. First, we deduce the expansion method for electromagnetic–thermal coupling in stacked objects in free space and the compensation method in the enclosed space. Second, a multilayer microstrip antenna comprising different thickness substrates is used to verify the method. The number of grids and computing time can be reduced to about 60% and 30%, respectively. The simulation results agree well with the experimental results. Finally, we simulate the waveguide filter with fine dielectric rods using the proposed method. The computing time can be reduced to about 40%. The proposed rapid computing method can be used to solve computational problems caused by large spatial scale differences inside the simulation objects.