A multigrid solver for 3D electromagnetic diffusion

The performance of a multigrid solver for the time-harmonic electromagnetic problem in geophysical settings is investigated. The frequencies are sufficiently small for waves travelling at the speed of light to be negligible, so that a diffusive problem remains. The discretization of the governing equations is obtained by the finite-integration technique, which can be viewed as a finite-volume generalization of Yee's staggered grid scheme. The resulting set of discrete equations is solved by a multigrid method. The convergence rate of the multigrid method decreased when the grid was stretched. The slower convergence rate of the multigrid method can be compensated by using bicgstab2, a conjugate-gradient-type method for non-symmetric problems. In that case, the multigrid solver acts as a preconditioner. However, whereas the multigrid method provides excellent convergence with constant grid spacings, it performs less than satisfactorily when substantial grid stretching is used.