Extrapolation strategies in numerical schemes for transient magnetic field simulations

For transient three-dimensional eddy current simulations, algorithmic improvements are presented based on the observation that, in the required implicit time stepping scheme, the iterative solvers applied to the large sparse (non-)linear systems of equations converge faster if more accurate start solutions are available. Different extrapolation techniques for new time-step solutions are compared in combination with the preconditioned conjugate gradient algorithm. Simple extrapolation schemes based on Taylor series expansion are used and compared to schemes derived especially for multistage implicit Runge-Kutta time stepping methods. Numerical tests show the resulting improvements in terms of computational efficiency for several test problems.