Explicit time integration of transient eddy current problems

For time integration of transient eddy current problems, commonly implicit time integration methods are used, where in every time, step 1 or several nonlinear systems of equations have to be linearized with the Newton-Raphson method because of ferromagnetic materials involved. In this paper, a generalized Schur complement is applied to the magnetic vector potential formulation, which converts a differential-algebraic equation system of index 1 into a system of ordinary differential equations with reduced stiffness. For the time integration of this ordinary differential equations system of equations, the explicit Euler method is applied. The Courant-Friedrich-Levy stability criterion of explicit time integration methods may result in small time steps. Applying a pseudoinverse of the discrete curl-curl operator in nonconducting regions of the problem is required in every time step. For the computation of the pseudoinverse, the preconditioned conjugate gradient method is used. The cascaded subspace extrapolation method is presented to produce suitable start vectors for these preconditioned conjugate gradient iterations. The resulting scheme is validated using the nonlinear TEAM 10 benchmark problem.