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The magnetic induction tomography (MIT) image reconstruction is a distributed parameter estimation problem normally solved iteratively, where each iteration engages several 3-D harmonic eddy-current problems. These calculations are the main time-consuming process in the MIT reconstruction. In this paper, an approach to accelerate the resolution of a set of similar eddy-current problems to be used in the reconstruction process is presented. Each eddy-current problem is described by a reduced magnetic vector potential eddy-current formulation using the finite integration technique (FIT) framework defined over an octree based subgridding scheme with several performance precautions. The solver accuracy is compared with analytical solutions of appropriate geometrical scenarios. A performance assessment is presented for a full set of eddy-current problems that constitutes a forward problem. The new method reduced the computing time approximately to 11% of a similar problem without performance concerns maintaining a relative mean error inferior to 1.5% relatively to analytical simulations.