Hi Jing, it is good to see you again.
The reason why a higher mesh density is needed for the highest field intensities is because generally, the strongest fields are predominantly responsible for the operation of a device. Therefore, having a looser mesh (and as a result, slightly less accurate field solutions) in areas of less field intensity won't contribute much to the inaccuracy of the simulation. The compliment is also true -- for high field intensities, you want to have a large mesh density to best approximate the actual field structure, because any small differences with real life may contribute largely to the inaccuracy of the simulation.
Based on the look of your antenna, I would surmise that these regions are the gaps in the tops of your "mushroom"-like structures.
Good Luck!