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.