Page 354 - Integrated Wireless Propagation Models

332 C h a p t e r F i v e

For H-field:

(5.6.2.2.8)

(5.6.2.2.9)

(5.6.2.2.10)

Maxwell's equations from Eq. (5.6.2.2.5) to Eq. (5.6.2.2.10), these six equations are
used for FDTD algorithm. In the next, section, we review the Discretize Space and
Discretize Time named by Yee.64
Figure 5.6.2.2.1 gives us a clean picture of the "Yee" cell, named after Kane Yee, who
developed this method in 1966. In the figure, the E, H components are located at differ­
ent locations and are a half cell apart, as shown in Fig. 5.6.2.2.2.
In Fig. 5.6.2.2.2, the E and H components will be at different times (E , E , and E
y
are separated at times n ± t, and H , H , Hz are separated at times (n + 1 / 2) ± t. This
Z
X
x
Y
is "leapfrogging in time" and is useful for defining the central differences in time
(d/ dt).
Then the derivative terms can be replaced by difference terms according to the cen­
tral difference formulas in space and time:

H z

Hy
/
E z

FIGURE 5.6.2.2.1 "Yee" cell diagra m .