A good knowledge of the electromagnetic fields of metal detectors which are used for mine detection is mandatory for reducing the false alarm rate, originating in the disqualification of the metal detector to decide whether there is a mine or just another metal object. Therefore the comparison of the measured signal from the detector with the pre-calculated signatures of standard mines was proposed. In order to set up a database of mine signatures it is mandatory to use different resolutions in discretising the typically very small metal parts in land mines, the soil and the detector coil. The latter is about two orders magnitudes larger and apart from the mine. Here, a domain decomposition method with Lagrange multipliers is used