Geophysical modelling of 3D electromagnetic diffusion with multigrid

The performance of a multigrid solver for time-harmonic electromagnetic problems in geophysical settings was investigated. With the low frequencies used in geophysical surveys for deeper targets, the lightspeed waves in the earth can be neglected. Diffusion of induced currents is the dominant physical effect. The governing equations were discretised by the Finite-Integration Technique. The resulting set of discrete equation was solved by a multigrid method. The multigrid method provided excellent convergence with constant grid spacings, but not on stretched grids. The slower convergence rate of the multigrid method could be compensated by using bicgstab2, in which case multigrid acted as a preconditioner. Still, the overall performance was less than satisfactory with substantial grid stretching.