On Improving Convergence Characterization to Solve the Electromagnetic–Thermal Model

Abstract

The electromagnetic (EM)–thermal partial differential equations illuminate the mechanism behind both thermal effect of microwaves on devices and microwave heating of materials. During the transient analysis, the differential equations must be discretized into time steps. Each time step corresponds to the solution of a nonlinear equation system. In order to accelerate convergence, the time steps should be as large as possible and the nonlinear equation system requires an efficient iterative method. In this article, the nodal heat imbalance ratio (NHIBR) is proposed as the basic for the adaptive time-stepping scheme. The normalized weighted mean (NWM) of the NHIBR is introduced to select different accuracy requirements for the temporal discretization and detect the convergence of solution for the steady state. Moreover, the Newton method is used to solve the nonlinear equations for its characterization of superlinear convergence. The finite-element method (FEM) is employed with edge elements for EM fields and node elements for temperature fields. Furthermore, the accuracy and advantages of the proposed analysis scheme are verified by numerical simulations.