Title :
Hierarchical Matrix Preconditioning for Low-Frequency–Full-Maxwell Simulations
Author :
Bebendorf, Mario ; Kramer, Frederik
Author_Institution :
Inst. for Numerical Simulation, Univ. of Bonn, Bonn, Germany
Abstract :
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.
Keywords :
Maxwell equations; electric potential; electromagnetic coupling; Maxwell equation; electric potential decoupling; hierarchical matrix preconditioning; low-frequency-full-Maxwell simulation; magnetic potential decoupling; nonconductive domain; real-life geometries; Eddy currents; Electric potential; Magnetic domains; Mathematical model; Maxwell equations; Robustness; Eddy current; Maxwell; electromagnetic; finite element method; hierarchical matrix; low frequency; preconditioner; quasi-static; robust Maxwell formulation;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/JPROC.2012.2204849
