An algebraic multilevel preconditioner for field-circuit coupled problems

Quasi-stationary magnetic field formulations are often coupled with lumped parameter models for the driving electrical system. The finite element discretization of such formulations yields linear systems with a large sparse coefficient matrix bordered by dense coupling blocks. The presence of these blocks prevents the straightforward application of black box algebraic multigrid solvers. We present a modified multigrid cycle that takes the coupling blocks into account. The resulting algebraic multigrid solver is used as a preconditioner for the conjugate gradient method for complex symmetric systems. We give evidence of the efficiency of the new method for the calculation of an induction motor.