Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes

Abstract

A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential equations (ODE). The ODE system is integrated in time using the explicit Euler scheme, which is conditionally stable by a maximum time step size. To overcome this limit, an explicit multistage Runge-Kutta-Chebyshev time integration method of higher order is employed to enlarge the maximum stable time step size. Both time integration methods are compared regarding the overall computational effort.