In this article, a new numerical algorithm, a finite-difference method in a nonorthogonal curvilinear coordinate system, is presented. This algorithm can be used for efficient simulation of a disk-edge held emitter. With the boundary-conforming coordinate lines, this method can deal with arbitrary microemitter shapes. Simulation results are presented for a unit cell, consisting of a disk-edge field emitter with "cocktail glass" structure. Dependence of the field enhancement factor, electron trajectories, and emission current upon geometrical factors are presented.