This is a good question and you are correct with a keen eye. However to understand it clearly we need come to the FDTD algorithm its self.
In the continuous world the inner line is the math boundary.
In FDTD, which is a discrete mesh world, there is NO such clear line boundary! This is because in the Yee cell, Ex,Ey,Ez and Hx,Hy, Hz are not located in the same point. Please refers to this image:
I can assure you that FDTD will keep the discrete mesh periodic for all the 6 field components.
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