This paper proposes a framework of waveform relaxation methods to simulate
electromagnetic fields coupled to electric networks. Within this framework, a guarantee for
convergence and stability of Gauß–Seidel-type methods is found by partial differential
algebraic equation (PDAE) analysis. It is shown that different time step sizes in different parts
of the model can be automatically chosen according to the problem's dynamics. A finite-
element model of a transformer coupled to a circuit illustrates the efficiency of multirate …

This paper proposes a framework of waveform relaxation methods to simulate
electromagnetic fields coupled to electric networks. Within this framework, a guarantee for
convergence and stability of Gauß-Seidel-type methods is found by partial differential
algebraic equation (PDAE) analysis. It is shown that different time step sizes in different parts
of the model can be automatically chosen according to the problem's dynamics. A finite-
element model of a transformer coupled to a circuit illustrates the efficiency of multirate …