Hierarchical Matrix Preconditioning for Low-Frequency–Full-Maxwell Simulations

In this paper, we propose to use hierarchical matrices as fast and robust preconditioners for a recent formulation of Maxwell's equations. This formulation was introduced by Hiptmair (IEEE Trans. Magn., vol. 44, no. 6, pp. 682-685, Jun. 2008) and remains stable in the stationary limit for nonconductive domains. The preconditioner is constructed based on a decoupling of the magnetic and electric potential. Numerical results are presented for real-life geometries and both sequential and parallel implementations.