Partial Differential Equations - Modelling and ... - ResearchGate

Electromagnetic Scattering 105
100
E SW,dB
10 -1
10 -2
10-3
8 16 32 64 128
Fig. 7. Scattering of a plane TE wave by a circular PEC cylinder of diameter λ
showing the variation of the computed error, with the number of elements, λ/δ, per
wavelength, for the co-volume scheme and the FETD scheme on the unstructured
meshes.
Table 2. Scattering of a plane TE wave by a circular PEC cylinder of diameter λ.
Co-volume FETD Speed up ratio
λ/δ spc time E SW spc time E SW FETD/Co-volume
8 21 0.15 0.744 31 1.2 0.750 8
16 42 0.5 0.275 61 15. 0.102 30
32 83 4.0 0.060 122 117 0.026 30
64 165 37 0.019 242 922 0.007 25
128 239 250 0.006 485 7295 0.002 30
one location. The values of spc, time and E SW are shown in Table 2 for the
co-volume scheme and the FETD scheme on these unstructured meshes. It
can be observed that, for these simulations, the co-volume scheme is nearly
30 times faster than the FETD scheme.
As a more challenging variation of this example, we also consider scattering
of a plane single frequency wave by a perfectly conducting circular cylinder
of diameter 15λ. The mesh employed is generated to meet a mesh spacing
requirement of δ = λ/15. Again, the minimum distance from the PML region
to the cylinder is λ. The solution is advanced for 50 cycles of the incident
wave and the computed and exact scattering width distributions are compared
in Figure 8(a). Excellent agreement with the exact solution is observed
using both schemes. The distribution of the computed total magnetic field
in the complete domain, including the PML, is shown in Figure 8(b). For
this example, the co-volume scheme is nearly 34 times faster than the FETD
scheme.