Numerical Time Integration in Quasistatic Computational Electromagnetics

Under certain conditions, electromagnetic time-domain modeling can be performed using the regimes of quasistatic approximations. The corresponding mathematical models represent then systems of first order ordinary differential equations or index I differential-algebraic equations. To resolve the time dependencies of the transient processes described by these equations, numerous time integration schemes can be employed. In this work, we give an overview of the mostly used time integration algorithms and discuss the main features, peculiarities and typical numerical difficulties associated with them. The materials presented in the paper are illustrated with corresponding numerical examples.