Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy-Current Problems

The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential-algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by applying a generalized Schur complement for nonconducting parts. The ODE can be integrated in time using explicit time-integration schemes, such as the explicit Euler method. This requires the repeated evaluation of a pseudo-inverse of the discrete curl-curl matrix in nonconducting material by the preconditioned conjugate gradient (PCG) method, which forms a multiple right-hand side problem. The subspace projection extrapolation method and proper orthogonal decomposition are compared for the computation of suitable start vectors in each time step for the PCG method, which reduce the number of iterations and the overall computational costs.