Algebraic multigrid for complex symmetric systems

The two dimensional quasistatic time-harmonic Maxwell formulations yield complex Helmholtz equations. Multigrid techniques are known to be efficient for solving the discretization of real valued diffusion equations. In this paper these multigrid techniques are extended to handle the complex equation. The implementation of geometric multigrid techniques can be cumbersome for practical engineering problems. Algebraic multigrid (AMG) techniques on the other hand automatically construct a hierarchy of coarser discretizations without user intervention given the matrix on the finest level. In the linear calculation of an induction motor the use of AMG as preconditioner for a Krylov subspace solver resulted in a six-fold reduction of the CPU time compared to an optimized incomplete LU factorization and in a twenty-fold reduction compared to symmetric successive overrelaxation.