Strategic Dual Image method (SDI) for three-dimensional magnetic field problems is proposed. The basic idea of the SDI method is that the open boundary solution is in-between the Dirichlet and Neumann solutions. The relationship between the specific topology (e.g. sphere, and ellipsoid) of the boundary and the averaging weight has been discussed in the previous literature, however no discussions on the arbitrary topology. In this paper, combined with “the perturbation approach using equivalence theorem”, the methodology to derive the averaging weight of Dirichlet and Neumann solutions on the arbitrary topology has been proposed. Some numerical examples are also demonstrated.