Question about the feed gap of FDTD

recently i am confused with a problem in FDTD about excitation.Take dipole antenna as an example.Generally the feed gap only one cell.When I decrease the grid length to half of origin, then feed gap have more than one cell(note:feed gap has a fixed area).Unfortunally the impedance results vary a lot.
the question is :if feed gap have several cells in 3 axis directions,is there anything should be care in using FDTD?
Besides,I have checked the program for several times and have't found where hide the problem.
thank you for your answers.