We carry out phase field simulations to study properties of the comblike step patterns induced by an adatom source. When an adatom source advances right in front of a step, step wandering is caused by the asymmetry of the surface diffusion field and small protrusions are formed. If the velocity of the source V_{p} is smaller than a critical value V_{p}^{c}, the protrusions follow the adatom source with coarsening of the step pattern, and a regular comblike pattern with finger-like protrusions is formed. With a sufficiently small V_{p}, the gap of the supersaturation is large at the adatom source. Since the period of protrusions, Λ, decreases with increasing V_{p}, the coarsening of step pattern is irrelevant for the protrusions to catch up with the adatom source. Near V_{p}^{c}, the gap of the supersaturation at the adatom source is small. Taking account of the increase in Λ with increasing V_{p}, the coarsening of the step pattern is essential for the protrusions to follow the adatom source.