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A new scalar potential formulation for three-dimensional problems is described. This formulation avoids cancellation errors within ferromagnetic objects and discontinuities and nonuniqueness of a scalar potential outside these objects. These deficiencies are peculiar to reduced and total scalar potential formulations, respectively. The finite-element discretization is applied to the new scalar potential formulation, and a novel approach to smoothing and extension of finite-element solutions is presented. Some numerical results obtained using the new scalar potential formulation are reported.