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Application of higher order basis
functions (HOBFs) on a quad mesh is the foundation of WIPL-D Pro EM
solver efficiency. As a result, very large structures are simulated on
inexpensive computers.
WIPL-D Pro models a large structure with about ten times less unknowns
than MoM codes using triangular mesh and Rao-Wilton-Glisson (RWG) basis
functions [1]. However, demands for simulation of ever larger structures
(e.g. in car, aircraft or ship industries), are going beyond the
capabilities of higher order MoM.
Hence, Multilevel Fast Multipole Method (MLFMM) has been applied to the
higher order MoM setup to extend these limits. MLFMM is applied to the
same models previously treated by MoM, with no changes to the mesh.
Maximally orthogonalized HOBFs [2] and system preconditioning enhance
the convergence of the iterative solution algorithm, making it
applicable to scatterers, antennas, metallic-dielectric structures, etc.
In MoM, interactions between all basis functions in the model are
calculated independently. The MLFMM groups basis functions. In case when
groups are far apart in the model, it calculates interactions between
groups, rather than between individual basis functions. This way, the
MLFMM algorithm provides dramatic memory savings compared to the MoM.
Fighter Airplane
The fighter airplane (Fig 1) is excited with a plane wave, coming in
from 30° under the horizon. Fuselage is 12 m long, wing span is about 7
m. The airplane is simulated at 3 GHz (it is 120 λ long) and 4 GHz (it
is 160 λ long). The simulation report is given in Table 1. Higher order
MoM models requiring 153646 and 307170 unknowns are equivalent to around
1.5 million and 3 million RWG unknowns, respectively. By applying the
MLFMM, memory requirements are reduced to just 3.2 GB and 7.2 GB
respectively. The calculated RCS in the incident plane, at 4 GHz, is
shown in Fig 2.
At 3 GHz the simulation was done on a Intel Core2
Quad CPU at 2.66 GHz clock
and 4 GB of RAM. At 4 GHz the simulation was done on a Dell PowerEdge
2900 workstation comprising 2.33 GHz Quad Xeon and 24 GB RAM.
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Figure 1. 160 λ long fighter airplane
model
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Table 1. Simulation reports
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Table 1.
Simulation reports |
|
Higher
Order MoM |
MLFMM |
|
No. of
unknowns |
RAM
[GB] |
Iterations |
RAM
[GB] |
Simulation time |
|
153646 |
189 |
65 |
3.2 |
0.8
hours |
|
307170 |
754 |
83 |
7.2 |
3.5
hours |
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Figure 2. Radiation pattern, incident
plane, at 4 GHz
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Conclusion
WIPL-D Pro offers several sophisticated techniques for solving
challenging radar cross-section computation problems, such as MLFMM. In
addition, the out-of-core solver can be used in case when there is not
enough RAM to perform simulation, at a cost of slight decrease in
simulation speed. It is often not necessary to turn to asymptotic
methods to solve RCS of electrically large aircraft. Using the advanced
algorithms of WIPL-D Pro instead, both accurate and reliable results are
acquired in reasonable time.
References
[1] B. M. Kolundzija and A. M. Djordjevic, Electromagnetic modeling of
composite metallic and dielectric structures, Artech House, Norwood, MA,
USA, 2002.
[2] D. S. Sumic and B. M. Kolundzija: “Efficient Iterative Solution of
Surface Integral Equations Based on Maximally Orthogonalized Higher
Order Basis Functions”, Proceedings of the 2005 international IEEE AP-S
Symposium, session #116, paper #5, July 2005.
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