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102 I. Sazonov et al.
H z
1
exact
FETD
Yee
Co-volume
H z
1
0
139 140 x 141
(a)
exact
Yee
FEDT
Co-volume
0
139 140 x 141
(b)
Fig. 3. Propagation of a plane harmonic TE wave in a waveguide: magnetic field
after 170 cycles at a distance x ≈ 140λ, using (a) δ ≈ λ/15, (b) δ ≈ λ/30.
mesh. Table 1 compares the computational performance of the algorithms, in
terms of the required number of steps per cycle (spc), the CPU time needed
(time), the computed phase velocity (C) and the maximum amplitude (A) of
the magnetic field in the range 0 ≤ x ≤ 160λ. This table also enables computation
of the speed-up factor, between the co-volume method and FETD,
which is achieved on both meshes. The effect of dispersion error on the phase
velocity, as a function of time step, is shown in Figure 4. A theoretical phase
velocity of one was specified for the present computation. This figure shows
the computed phase velocity, for various values of the time step, on the unstructured
meshes using the co-volume scheme and the FETD scheme and, on
the structured meshes, using the Yee scheme, compared to the theoretically
expected Yee values [TH00]. The phase velocity achieved using the co-volume
method is much superior to the phase velocity expected from the structured
grid implementation.