On the equivalence of demagnetization tensors as discrete cell size approaches zero in three-dimensional space

The calculation of the demagnetization field is crucial in various disciplines, including magnetic resonance imaging and micromagnetics. A standard method involves discretizing the spatial domain into finite difference cells and using demagnetization tensors to compute the field. Different demagnetization tensors can result in contributions from adjacent cells that do not approach zero, nor do their differences, even as the cell size decreases. This work demonstrates that in three-dimensional space, a specific set of magnetization tensors produces the same total demagnetization field as the Cauchy principal value when the cell size approaches zero. Additionally, we provide a lower bound for the convergence speed, validated through numerical experiments.